From 2c63610f12ec419490881be97f303d483a94faa8 Mon Sep 17 00:00:00 2001 From: HelixCopex Date: Sun, 13 Sep 2026 10:30:05 +0800 Subject: [PATCH] =?UTF-8?q?=E8=AE=BA=E6=96=87=E6=9B=B4=E6=94=B9=E4=B8=8E?= =?UTF-8?q?=E5=9B=BE=E6=9B=B4=E6=94=B9=20Co-authored-by:=20Pengheng=20?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .vscode/settings.json | 3 +- docs/B题建模分析与实施计划.md | 237 - docs/paper/README.md | 82 +- docs/paper/REWRITE_NOTES.md | 41 + docs/paper/data/audit.md | 18 + docs/paper/data/formal-cost-rows.tex | 4 + docs/paper/data/formal-file-list.tex | 13 + docs/paper/data/formal-macros.tex | 6 + docs/paper/data/formal-q3-rows.tex | 4 + docs/paper/data/formal-q4-rows.tex | 4 + docs/paper/data/formal-results.csv | 5 + docs/paper/data/formal-results.json | 150 + .../scripts/audit_paper_formal.py.tex | 197 + .../scripts/build_paper_support.py.tex | 231 + .../listing-source/src/mcm26b/__init__.py.tex | 21 + .../src/mcm26b/belief/__init__.py.tex | 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"/Users/peng/sample_project" } diff --git a/docs/B题建模分析与实施计划.md b/docs/B题建模分析与实施计划.md deleted file mode 100644 index 2e90430..0000000 --- a/docs/B题建模分析与实施计划.md +++ /dev/null @@ -1,237 +0,0 @@ -# B 题建模分析与实施计划 - -根据你们对工程实践和物理模型的熟悉程度，确定研究 B 题“无线电干扰源的快速自动定位与清除”。推荐采用**有界误差几何定位、主动选点、具有覆盖证明的搜索、按实际动作耗时调度**的统一框架。AI 辅助推导、实现与实验分析，策略只依赖题目允许的观测。 - -本文件已结合本次评审修订。问题一的几何内核、离线可视化和官方演练观测回放已经完成；问题二新增了安全候选圆盘证书，但主动选点优化器、问题三和四的全清闭环尚未完成。文中的覆盖结论是根据题设推导的，耗时估算不是演练成绩。当前工作仅离线复算既有演练记录，不使用正式测试。 - -依据：`issue/B题.pdf` 全文、`issue/附件/附件1.docx`《模拟器使用说明》、`issue/附件/附件2.docx`《模拟器通信接口说明及编程指南》。文档中的登录、测试和日志要求在这里作为交付约束分析，不作为自动执行正式测试的指令。 - -## 本次建议的取舍 - -| 建议 | 处理结论 | -| --- | --- | -| 四问复用几何内核、有界误差、覆盖证明、严格停止、幂等协议 | 保留，作为主线与验收条件 | -| 问题二的候选集合加入 $\Omega$ 和 1500 米上界 | 采纳，但仅加入在线候选集合 $K$，不改变问题一纯角域多边形 $P$ | -| 问题二首次测向后安全区域可能为空 | 对一般 $K$ 成立；本题首次窄角域可直接证明非空，见下文 | -| $Q$ 为空就去最小包围圆圆心并结合交会角 | 仅是一般情形的探索退化；$\rho>1000$ 时不保证接收，不能冒充保底方案 | -| 枚举所有直径对判断直径圆 | 简化为任意一组最远点对检查一次；失败时给出圆外顶点 | -| 定向无信号不直接删位置、失去信号后覆盖清除 | 采纳；执行前必须计算覆盖格数、路径和现实请求预算 | -| 现实20分钟优先控制请求数 | 采纳为硬约束；全部清除后仍按题目虚拟时间优化 | -| P0–P7分期与尽早正式测试 | 采纳分期；演练不限定3次，正式问题3/4各3次由团队另行安排 | -| `/detect` | 修正为附件规定的 `/measure` | - -## 1. 四问应当串成一条实现主线 - -| 问题 | 要回答的实质问题 | 推荐抽象 | 必须交付的结果 | -| --- | --- | --- | --- | -| 1 | 带误差的多个方位如何形成定位区域，其直径如何计算，直径圆是否覆盖区域 | 扇形角域的半平面交、凸多边形直径、最小包围圆 | 算法、边界情形、覆盖判断及反例 | -| 2 | 仅有一次测向时，下一步去哪里更有利 | 在未知目标位置条件下进行主动测量设计 | 明确的候选区域、选点目标和比较实验 | -| 3 | 数量未知的全向源如何全部找到并尽快清除 | 全域覆盖、逐频道候选区域、局部定位与路径调度 | 演练统计、3 次正式结果、原名正式日志 | -| 4 | 有未知朝向的定向源时，如何避免遗漏 | 加入朝向不确定性的观测模型、半平面覆盖、失去信号后的处理 | 演练统计、另外 3 次正式结果、正式日志 | - -第 1 问的定位区域和包围圆直接服务第 2 问选点与第 3、4 问清除；第 3 问的工程框架延伸到第 4 问。模型不必为每问重新搭建。 - -## 2. 用题面明确的观测能力约束物理抽象 - -目标区域为 $\Omega=\{(x,y):x^2+y^2\le 1800^2\}$。每个频道最多有一个源，源总数为 10–16，频道为 1–20。对一个存在的源 $c$，用未知位置 $g_c$、接收半径 $R_c\in[1000,1500]$、类型和定向朝向描述；全向源不需要朝向参数。 - -机器狗状态只需要位置 $p$、当前测向频道 $k$、虚拟时间、现实剩余时间、各频道的观测历史和处理状态。每个频道维护：未知／已发现待定位／可清除／已清除／已证明不存在，以及尚可能包含源的集合 $K_c$。 - -| 规则 | 数学或程序含义 | 容易出现的错误 | -| --- | --- | --- | -| 只返回 no_signal、near、direction；direction 附带示向度 | 这是带距离可见性门限的方位观测问题 | 构造接口并未提供的 RSSI、距离或场强数据 | -| 同地点误差固定，幅度不超过 $1^\circ$ | 用有界误差集合，保留空间相关性 | 原地重复测量取平均，假定可消除误差 | -| 示向度保留两位小数 | 题设模型取 $\pm 1^\circ$；实现可另设 $\pm 1.005^\circ$ 保守裕量 | 把额外舍入裕量写成题面规定 | -| 定向源覆盖朝向两侧各 $90^\circ$，包含边界 | 检测点须处于以源为界的发射半平面内 | 把无信号直接判定为没有源 | -| 可到目标圆域外检测与清除 | 目标位置受 $\Omega$ 限制，机器狗正常搜索不受 $\Omega$ 限制 | 所有搜索点强制留在圆域内，遗漏朝外发射的边界源 | -| 清除半径 20 米，不受定向朝向限制 | 清除可成为失去信号时的可靠后备手段 | 认为背面接收不到信号就无法清除 | -| /clear 不切换测向频道 | 保存独立的当前测向频道状态 | 清除后错误更新频道，算错下一次检测耗时 | - -不需要重新拟合电磁传播衰减公式：接口只暴露接收门限与方位，额外物理参数无法由题目观测充分辨识。工程经验主要用于设计可见性分析、测向几何和闭环决策。 - -精确的虚拟时间目标是： - -$$ -T=\frac{L}{5}+N_{\mathrm{switch}}+5N_{\mathrm{measure}} - +5N_{\mathrm{clear,success}}+3N_{\mathrm{clear,fail}}. -$$ - -$L$ 包括检测和清除引发的所有移动，切换次数只由被接受的检测动作决定。先满足全部清除，再减少 $T$；不能通过少清几个源来改善平均时间。程序运行时间是另一个硬约束，不能把虚拟检测的 5 秒实现为现实 `sleep(5)`。 - -## 3. 定位与选点的统一几何标准 - -在 $s_i$ 测到 $\theta_i$ 后，定义 $W_i$ 为从 $s_i$ 出发、方向范围 $[\theta_i-\delta,\theta_i+\delta]$ 的前向角域。它由两条线性半平面约束表示，必须正确处理 $0^\circ/360^\circ$ 跨界。 - -第 1 问的定位多边形 $P$ 为这些角域的交。求各边界直线交点并筛选可行点、排序成凸多边形后，小规模下直接枚举顶点对即可计算直径： - -$$ -D(P)=\max_{i,j}\lVert v_i-v_j\rVert. -$$ - -先用简单可靠的顶点对枚举作基准，规模确有需要时再换旋转卡壳。算法必须区分空集、单点、线段、有限多边形和无界区域；不能靠任意大方框截断后声称得到无界区域的真实直径。旋转卡壳的背景可参考 [McGill 计算几何研究页面](https://www-cgrl.cs.mcgill.ca/~godfried/research/calipers.html)。 - -**直径为 $D$ 的圆不一定覆盖直径为 $D$ 的区域。**例如边长为 $D$ 的等边三角形，最小包围圆半径为 $D/\sqrt{3}$，大于 $D/2$。后续保证清除应使用： - -$$ -\rho(K)=\min_z\max_{g\in K}\lVert g-z\rVert\le 20. -$$ - -到最小包围圆圆心清除是充分选择，并非唯一选择。所有可保证清除的位置组成 $C_{20}(K)=\bigcap_{g\in K}B(g,20)$；只要该集合非空，就可进一步选择距离机器狗最近的可行点来节省移动。$D\le 40$ 只是必要条件，不是充分条件。最小包围圆是已有标准计算几何问题，可参考 [CGAL Min_circle_2 文档](https://doc.cgal.org/latest/Bounding_volumes/classCGAL_1_1Min__circle__2.html)。实现时给 20 米阈值保留数值余量；数值阈值附近返回谨慎判断，不把浮点容差当作精确算术证明。 - -直径圆覆盖只需任意一组最远顶点 $A,B$：包含距离为 $D$ 的两点且半径为 $D/2$ 的圆，其圆心只能是 $(A+B)/2$。因此检查一次全部顶点即可；若失败，换另一组直径对也不可能产生覆盖圆。问题一实现现输出最坏超出距离、圆外顶点索引和一个具体反例顶点。 - -在线定位还可用 $\Omega$ 和“收到信号意味着距离 $\le 1500$”约束 $K$。圆盘交角域可能包含曲线边界；若用多边形近似，必须构造外包近似，才能维持“不丢失真源”的保证。用圆周采样点连成的内接多边形不能直接作为保守外包。 - -第 2 问建议先明确“较好的定位效果”：以新观测后的最坏包围圆半径为主要几何指标，再考虑移动和检测成本。交会角大、面积小可作为候选点筛选指标，但不是对所有未知位置都最优的证明。 - -第一次收到 `direction` 后，明确取 $K_1=\Omega\cap W(s_1,\theta_1\pm\delta)\cap B(s_1,1500)$。保留整个距离圆盘是保守处理，忽略 `direction` 还隐含的近距离排除不会丢失真源。对全向源，第二检测点的安全候选区域为： - -$$ -\mathcal{Q}=\left\{q:\max_{g\in K_1}\lVert q-g\rVert\le 1000\right\}. -$$ - -在这里测量，不论实际目标位于 $K_1$ 何处，接收距离都满足题目最小接收半径；可能返回 `direction`，也可能返回 `near`。若已知外包圆 $K_1\subseteq B(c,r)$，且 $r\le 1000$，则 $B(c,1000-r)$ 是充分候选区域，等号时是单点。不要误写成“距第一次检测点不超过 1000 米”。宽松外包圆的 $r>1000$ 不能证明真实 $\mathcal{Q}$ 为空。 - -本题还有比“检查 $\mathcal{Q}$ 是否为空”更强的解析结论。令 $R=1500$，$u$ 为第一次示向方向，$\delta\le 45^\circ$，定义 - -$$ -a=\frac{R}{2\cos\delta},\qquad c=s_1+au. -$$ - -整个截断角域 $W\cap B(s_1,R)$ 包含在 $B(c,a)$ 内。证明：任意候选 $g=s_1+tu_\varphi$ 满足 $0\le t\le R$、$|\varphi-\theta_1|\le\delta$，因此 - -$$ -\lVert g-c\rVert^2=t^2+a^2-2at\cos(\varphi-\theta_1). -$$ - -该式关于 $t$ 是凸函数，最大值在 $0$ 或 $R$ 取得；两端都不超过 $a^2$。于是 $K_1\subseteq B(c,a)$，从而 $B(c,1000-a)\subseteq\mathcal{Q}$。$\delta=1.005^\circ$ 时，$a\approx 750.115391$ 米，安全圆盘半径约 $249.884609$ 米，严格为正；题设 $\delta=1^\circ$ 同样成立。即使检测点或 $c$ 在 $\Omega$ 外也合法，因为机器狗不受源位置圆域限制。实现见 `geometry/planning.py::first_bearing_candidate_disk`。 - -因此，在本题一致的首次测向条件下无需依赖“$\mathcal{Q}$ 空集退化”。对后续更一般的非空紧集 $K$，$\mathcal{Q}$ 非空当且仅当 $\rho(K)\le 1000$；若确实 $\rho>1000$，去 MEC 圆心只是最小化最坏接收距离的探索动作，必须允许 `no_signal`。若 $K$ 为空，应先核查频道、数据、误差界与几何计算，不给空集编造中心。上述证书只保证距离；不能直接用于定向源的朝向可见性保证。 - -在上述安全圆盘内，围绕测向轴两侧取候选点，计算后验包围半径与动作代价。最坏情形目标可写为 $\sup_{\theta'}\rho\bigl(K_1\cap W(q,\theta')\bigr)$，其中 $\theta'$ 遍历与 $K_1$ 和误差界一致的读数；实现先用目标位置与误差区间端点采样，并加密检查。若返回 `near`，则候选源位于当前点 5 米以内，可直接在当前位置尝试清除该频道。交会角仅作筛选或同分择优，不为改善交会角越出已证明安全的候选区域。采样是启发式，不能称为严格最坏情形最优解；圆弧先验如需离散，使用外包切线多边形并记录逼近误差。 - -## 4. 搜索完整性和停止条件要有可验证的依据 - -第 3 问中，在 $s$ 对尚未清除频道测得 `no_signal`，可以排除以 $s$ 为中心、半径 1000 米的圆盘内存在该全向源。超过 1000 米仍可能存在接收半径较小的源，不能一律排除到 1500 米。 - -第 4 问中，同样的 `no_signal` 约束的是“位置、半径、朝向”的联合假设。若位置和朝向暂不联合维护，最简单的可靠基线就是不利用这一观测直接删除空间候选点，只记录覆盖检测已完成。后续加速版本再维护朝向可行集合。 - -可以先构造一个对全向、定向均适用的完整发现基线： - -$$ -S=\{(700i,700j):i,j=-3,-2,\ldots,3\},\quad |S|=49. -$$ - -这些点覆盖 $[-2100,2100]^2$，包含目标圆域，并允许到圆域外访问。对于位于一个网格单元内部的源 $g$，该单元 4 个顶点到 $g$ 的距离都不超过 $700\sqrt{2}\approx 989.95$ 米。$g$ 在这些顶点的凸包内部，所以经过 $g$ 的任意发射半平面总包含至少一个顶点。该顶点满足接收距离与发射角条件。源恰在网格边或顶点时，取相邻单元的顶点；由于目标圆域与外框有余量，两侧相邻点都存在，仍可选择距离合格、且不与源重合的可见点。 - -因此，对每个尚未解决的频道完成这些点的测量，能够保证发现该频道存在的源。实际实现可跳过已经清除或已经具有有效定位任务的频道，但必须保存逐频道的覆盖记录，不能把“路过某点”当作“测过所有频道”。 - -作为规模检查，49点全部扫描20频道最多需要980次检测。若从原点去网格一角，再按逐行折返路线扫完，纯扫描路程约36569.85米；每点检测成本上界120秒，纯扫描虚拟总耗时上界约13193.97秒，即3.665小时。**该估算不含定位、清除及其绕行，也不保证满足现实20分钟窗口。**它说明覆盖基线在100小时虚拟上限内有设计空间，现实可行性仍要测接口延迟、总请求数和日志大小。 - -发现源后，先通过主动测向缩小候选集合。若定向源再次失去信号，可对已知有界候选集合构造半径小于 20 米的有限圆盘覆盖，逐点调用 `/clear`，作为不依赖朝向的后备清除方法。边长 20 米方格中心距格内任何点不超过 $10\sqrt{2}$ 米；保留与候选集合相交的格子即可保守覆盖。格子按统一半开区间索引，源恰在网格线上时至少归入一个格子；若相交判定数值不确定则保留格子。 - -有限不等于现实预算可行。设候选外包框宽为 $w$、高为 $h$，使用全局 20 米网格枚举时，上界可取 $N\le(\lceil w/20\rceil+2)(\lceil h/20\rceil+2)$，再以实际相交格子列表得到精确请求上限。生成路径长度 $L$ 后，单源全失败清除耗时为 $L/5+3N$；若最后一次成功则为 $L/5+3(N-1)+5$。现实代价用 $N$ 乘实测单请求高分位耗时加本地计算时间估计。不满足剩余预算时应继续有希望的定位、选择其它任务或按预算退出，不能声称后备清除保证 20 分钟内成功。即使已知源落在半径 1500 米圆盘，按外包框枚举仍有约 $2.3$ 万个格子的量级，故宽候选集合不能直接盲扫。 - -停止成功的依据为以下任一项： - -- 已成功清除16个不同频道的源，达到题设数量上界。 -- 每个频道都已有清除成功记录，或通过完整覆盖证明不存在；所有已发现源均已处理完毕。 - -发现10个源、连续若干次无信号、候选采样点恰好为空，都不是充分停止条件。现实预算不足而退出应记为未证明完成，不能与成功退出混记。 - -## 5. 在可靠基线之上增加加速策略 - -先做“发现一个、定位清除一个”的简单闭环，保证功能可运行；再增加以下独立可开关的策略，以便消融比较： - -| 策略 | 所解决的问题 | 需要验证的收益 | -| --- | --- | --- | -| 共享检测位置 | 一次移动后顺便测多个未知频道 | 是否减少总移动时间，而非仅减少单目标测量数 | -| 目标队列和短路径排序 | 多个已发现源处理顺序不佳 | 路程减少是否抵消局部定位变差 | -| 第二点主动选取 | 共线或小交会角导致候选区域狭长 | 同等观测预算下包围圆半径、清除耗时改善 | -| 自适应覆盖 | 固定49点有冗余 | 跳点之后每个频道的覆盖证明是否仍成立 | -| 朝向可行集合 | 第4问盲区导致反复失去信号 | 是否减少无效检测，同时不误删真源 | -| 提前尝试清除 | 再测一次可能不如直接尝试便宜 | 失败的3秒和绕行是否值得；保留失败后的正确更新 | - -调度可以先采用“预期信息改善／增量虚拟耗时”之类的启发式，但要记录每项含义和参数，性能结论来自演练。不预设目标均匀分布，不假定测向误差独立或均匀分布。若研究统计模型，明确它是实验场景假设。 - -AI 的适合用法是把这些模块逐一变成可测试程序、生成边界案例、分析消融结果，以及在自建环境中搜索策略参数。先形成可解释基线，再判断学习方法是否有额外收益；避免把未建立的奖励与训练分布直接用于正式测试。 - -## 6. 抽象标准和验收标准 - -采用“来源—输入—状态—动作—观测—约束—代价—输出—验证”的统一模块记录格式。它是本项目建议的工程标准，不是竞赛另行规定的官方评分标准。每个假设注明是题面事实、保守近似还是实验启发式；每条结论注明是数学证明还是演练观察。 - -| 模块 | 最小接口职责 | 验收标准 | -| --- | --- | --- | -| 协议与状态 | 串行发送动作，更新位置、频道、两类时间 | 附件计时示例逐步得到105、111、194、199秒 | -| 观测与几何 | 根据 direction、near、clear结果更新候选集合 | 自建已知真值案例中真源始终保留；跨角度边界不出错 | -| 直径与包围圆 | 给出直径、圆心、包围半径 | 与顶点对枚举对照；等边三角形反例通过 | -| 主动选点 | 输出下一测量位置及选择依据 | 实际可见性、最坏误差与移动成本均有记录 | -| 覆盖与停止 | 管理每频道的覆盖记录和成功依据 | 边界朝外源不漏搜；10源和16源场景都能正确退出 | -| 后备清除 | 对有界候选集合建立20米以内圆盘覆盖 | 覆盖无空洞、每次失败后能继续、预算有上界估计 | -| 演练统计 | 从自身动作日志与演练结束真值统计结果 | 清除比例、平均时间、总时间与分项耗时可独立复算 | -| 正式交付 | 绑定案例编码、程序版本、统计与官方原始日志 | 问题3和4各3次；日志原名保留，核查上传与导出 | - -协议必须同时检查 HTTP 状态和 accepted。accepted=false 时不得更新状态，返回的 virtual_time_s=0 不能重置本地虚拟时钟。网络超时重试同一动作必须复用原 request_id 和完全相同的内容；处理重试响应也不能重复累加本地成功数与费用。新动作使用新ID，不并发调用不同动作。 - -用/enter返回的remaining_real_duration_s建立本地单调时钟截止时间；后续响应若提供剩余时间则校准，不能把首次剩余时间当成永远不变。记录每次请求的现实往返耗时，预留退出与故障恢复余量。例如先预留60秒，再由演练高分位延迟调节；60秒是初始工程参数，不是官方规定。估计剩余请求数时同时计入测量、失败重试、清除和退出，禁止并发动作。 - -980次检测在单次0.5–1秒的假设下占490–980秒（约8.17–16.33分钟），还没有定位清除余量。这个延迟范围不是实测结论；本地接口和模拟器计算的实际耗时应测量。当前14个动作的单次短演练不足以估计高分位延迟或全程稳定性。已清除频道跳过，已发现频道暂停覆盖并进入定位队列，移动到同一点后共享频道测量；自适应跳点必须保留逐频道覆盖证据。根据附件，正式上传日志不超过2MB，需监测官方日志体积；自建JSON大小不能冒充加密日志的大小。 - -基准实验至少覆盖：全向与混合源；数量 10 和 16；接收半径 1000 和 1500 米；目标贴近圆域边界且朝外；测向接近 $0^\circ/360^\circ$；误差取界值；检测点距离 5 米及清除距离 20 米的边界；重复请求、拒绝动作及短暂断连。样例数量按剩余时间和运行成本安排，不把有限样例通过等同于数学保证。 - -比较策略时先看是否全清，再比较同一批场景的总虚拟时间、平均每源时间、中位数与高分位耗时、程序时间、请求数。自建环境可用固定场景做配对比较；官方案例随机且不能重读真值，演练成绩单独记录，不声称是在完全相同的隐藏案例上比较。 - -## 7. 建议实施次序与阶段交付 - -下面按P0–P7列出可执行交付与当前状态。排期以验收门槛推进，避免把“几何代码完成”误认为“全清策略完成”。 - -| 阶段 | 交付与执行任务 | 验收门槛 | 当前状态 | -| --- | --- | --- | --- | -| P0 规则固定 | 规则表、状态机、四类API字段与成本 | 示例逐步105/111/194/199秒；clear不切换频道 | 已完成：`protocol/rules+timing+state` 工程化，`sim-check` 与 `tests/test_protocol_timing.py` 固化 | -| P1 协议基线 | enter/measure/clear/exit客户端；串行、幂等、截止时间 | accepted=false和超时重试不污染状态；主动退出；故障注入回放 | 已完成：`protocol/client`，`ScriptedFaultTransport`/`PlaybackTransport` 回放，`tests/test_protocol_client.py` 全过 | -| P2 几何内核 | 问题一解答、区域分类、直径圆证据、MEC、清除余量 | 跨界、退化、无界、解析反例、独立算法对照 | 已实现并优化，20项自动化测试通过 | -| P3 问题二选点 | $K_1$ 先验、安全候选盘、后验半径采样与 `near` 分支 | 距离证书有效；采样加密；不把探索当接收保证 | 已实现：`belief` 保守候选集 + `planner` 保证接收盘选点器（worst-posterior 采样、1/4 间距加密复核）；策略对比实验待做 | -| P4 全向闭环 | 49点覆盖记录、定位队列、清除、停止、日志统计 | 10/16源、边界源和错误响应案例；官方演练全清并正常退出 | 自建闭环已完成：`planner.OmnidirectionalLoop`（10/16/0 源、近边界源、预算耗尽、故障注入测试通过）；官方演练全清待团队执行 | -| P5 定向扩展 | no_signal联合约束、覆盖发现、有限清除后备与预算 | 朝外边界源不漏；真源不误删；格数与退出预算检查 | 已实现：`planner.DirectionalExtension`（49点覆盖对定向源成立、保证接收盘内 no_signal 记为观测到定向、对跖+环探梯子、`fallback_clear_cells` 有限圆盘覆盖后备清除带格数/预算双硬顶）；`tests/test_loop_q4.py` 全过；官方混合源演练待执行 | -| P6 加速消融 | 共享测点、自适应覆盖、目标排序、提前清除 | 配对案例全清不退化，时间/请求数改善可复算 | 可删减；闭环基线数据已可用于消融对照 | -| P7 正式与论文 | 固定版本、论文表1、日志原名、上传核查 | 问题3/4各3份正式记录与程序版本对应 | 团队后续安排；本任务不执行正式测试 | - -按2026年9月10日起的剩余时间，建议10日补齐P1并衔接P3，11日完成P4自建边界案例与全向演练，12日完成P5及混合源演练；未达验收就删减P6并优先修正闭环。演练不限3次，正式机会为问题3和4各3次。团队在版本稳定后自行安排正式记录，留出失败恢复和论文整理时间。附件建议9月13日15:30前完成正式测试，17:30后不能启动新的演练或正式测试；已进入上传队列的日志仍会继续上传。此处引用所给附件安排，运行前核对模拟器界面公告；这份排期不改变当前禁止使用正式测试的限制。 - -若时间不足，优先删减加速策略，保留可解释定位、覆盖证明、可靠协议和完整日志。开发组织可按几何算法、工程接口、实验论文分工，具体人员由团队安排。 - -建议后续代码划分为 protocol、geometry、belief、coverage、planner、local_simulator、evaluation 七个模块。官方客户端与自建环境使用同一动作接口；自建真值只对测试端开放，策略端只能看到观测，防止评估时意外使用隐藏答案。 - -## 8. 当前已落实的结论与下一步 - -已完成题面与附件核对、49点覆盖推导及扫描成本复算；此前497160个位置与朝向组合的辅助数值校核未发现覆盖遗漏，但采样不代替证明。问题一已通过官方演练三点观测离线验证；该次只有enter、measure、exit，没有清除动作，不能当作全清策略成绩。 - -本次将 MEC 从全支撑点枚举改为带固定随机种子的 Welzl 增量算法，保留原枚举法作独立对照；对外输出增加直径圆反例顶点、超出距离和 20 米清除余量。CLI 可显式追加 $0.005^\circ$ 舍入裕量。真实演练默认 $\delta=1^\circ$ 时 $D=23.996723$ 米、$\rho=12.068583$ 米；$\delta=1.005^\circ$ 时 $D=24.119088$ 米、$\rho=12.130377$ 米，两种口径下直径圆都不覆盖，但 MEC 半径都小于 20 米。原始演练记录未改写。 - -可复现报告见 `output/q1/optimization_report.json`，问题一证明、输入输出及数值限制见 `docs/问题一解答.md`。局部MEC基准只反映本地几何计算，不能据此宣称请求延迟、完整策略或官方成绩得到同样提升。 - -P0–P5（自建部分）与 P2 均已交付：协议层（串行幂等客户端、状态机、预算截止、 -故障回放）、几何内核、belief 保守候选集、保证接收盘选点器、`OmnidirectionalLoop` -全向闭环与 `DirectionalExtension` 混合源定向闭环（49 点覆盖对定向源同样成立、 -no_signal 联合约束基线不删候选、对跖+环探遮挡梯子、`fallback_clear_cells` -有限圆盘覆盖后备清除，格数与现实预算双硬顶下不盲扫）。自建验收： -`uv run pytest`（105 项）与 `uv run mcm26b sim-check`；随机场景自检： -`uv run mcm26b run --robot-id <队号> --self-test`（问题4加 `--problem 4`）。 - -评审修订（2026-09-11）：本地模拟器改为逐点固定误差场（同一"源×位置"读数 -恒定，与官方演练实测一致）；对跖复核探点公式修正（此前塌缩到 MEC 圆心 1m -内，浪费探点预算并推高后备清除）；环探"≥180° 可见弧"依据删除（最坏可见弧 -可退化为单点，梯子只是启发式，完备性由后备清除兜底）；断连/协议错误中断后 -仍尽力 /exit 并产出未完成 summary；库默认舍入裕量统一为 0.005°；后验评分 -补 near 分支；问题一近平行细长区域保留远端顶点。后备清除成本用 -`scripts/benchmark_q4.py` 批量种子扫描量化（结果落盘 `output/q4/`）。 - -下一步优先把两个闭环接入官方演练（问题3用全向、问题4用混合，先实测单请求 -延迟与总请求数，核对 1200s 现实预算与 2MB 日志体积），再做 P6 消融对照。 -顺序约束：上述模拟器与故障收尾修复先行合入，官方演练在修复后的版本上执行； -总请求口径必须计入后备清除（summary 的 `total_requests` 与 -`fallback_clear_attempts`），仅统计检测次数会低估现实耗时。 -基线量级供参照：10 源场景约 550–630 次检测、虚拟总时 1.4–1.7 万秒；16 源 -场景约 200–320 次检测即触发数量上界停止。该数字说明共享测点与跳点策略 -（P6）有明确改进空间。不要重复开发几何内核或提前堆叠学习算法；以官方演练 -的实际请求、日志和耗时决定 P6 加速投入。 diff --git a/docs/paper/README.md b/docs/paper/README.md index f48fb37..9f3c897 100644 --- a/docs/paper/README.md +++ b/docs/paper/README.md @@ -1,65 +1,49 @@ -# 论文（docs/paper） +# 论文与支撑材料 -2026 年高教社杯全国大学生数学建模竞赛 B 题论文 LaTeX 工程，格式依据 -`issue/论文格式/附件3. 全国大学生数学建模竞赛论文格式规范.pdf`（2026 年修订稿）。 +本目录为依据 issue 题目、2026 年论文格式规范和所给往届参考 PDF 重写的论文工程。四问对应 docs/algo-1.md 至 docs/algo-4.md，并对照当前源码说明实现及证明的适用范围。 -## 编译 +## 交付文件 -需要 TeX Live（含 XeLaTeX 与 ctex）。在本目录执行： +- main.pdf：定稿 PDF，摘要 1 页，正文及参考文献 22 页；之后为数据清单与完整源码附录。 +- main.tex、sections/：可编辑 LaTeX 源文件。 +- data/formal-results.json、formal-results.csv、audit.md：四份正式数据的匿名快照、复算结果及核对说明。 +- support-materials.zip：程序源码、正式原始日志、统计快照、论文源文件和逐文件哈希清单。 +- REWRITE_NOTES.md：重写范围、修正的论证和验证记录。 -```bash -latexmk -xelatex -outdir=build main.tex -# 或 -xelatex main.tex && xelatex main.tex -``` +## 数据口径 -输出 PDF：`build/main.pdf`（用第二种方式则为 `main.pdf`）。 +只使用 Jammers-simulator-full/test/q3 与 test/q4 下的四份正式导出。包与官方原始导出及结果侧文件进行 SHA-256 核对，再由公开头部的票据哈希关联官方正式统计队列。 -## 目录结构 +日志负载没有解密。论文可读快照不含账号、设备或票据内容。两问各只有两份所选正式记录，第三份以未提供记录表示；正式源总数未知，故不计算全清率。四次均为主动退出且清除失败计数为零，这不能替代全清证明。正式包没有与当前策略提交版本绑定，不能据此作配对消融或因果比较。 -| 路径 | 内容 | -| --- | --- | -| `main.tex` | 论文源文件（摘要、正文、附录及源码引用） | -| `mcm26b-paper.cls` | 论文版式模板（宏包、字体、标题、代码排版与通用命令） | -| `fonts/` | 从本机提取的中文字体（宋体 SC 常规/加粗、黑体 SC Light/Medium）与 Times New Roman 四体，约 150 MB，编译自包含 | -| `figures/` | 插图目录 | -| `build/` | 编译产物（已 gitignore） | +## 重算和编译 -VS Code 工作区已在 `.vscode/settings.json` 中将 LaTeX Workshop 的默认配方设为 -`xelatex`；也提供 `latexmk (xelatex)` 配方用于自动处理交叉引用。 +在项目根目录（Python 3.10 及以上）执行： -## 规范要点与工程实现 + python scripts/audit_paper_formal.py + python scripts/build_paper_support.py -- A4、四边距 2.5cm：`geometry` 宏包。 -- 页码从摘要专用页起、页脚中部、从 1 连续编号：摘要页 `\setcounter{page}{1}`。 -- 正文不要目录、不超过 30 页：未生成目录，正文当前远少于 30 页。 -- **电子版第一页必须是摘要专用页**（不含承诺书与编号专用页）：默认 - 不启用 `paper` class option。打印纸质版时将 `main.tex` 的 - `\documentclass[zihao=-4,a4paper]{mcm26b-paper}` 改为 - `\documentclass[zihao=-4,a4paper,paper]{mcm26b-paper}`，自动加入承诺书与编号专用页 - （占位文字，须替换为组委会当年发布的专用页原文）。 -- 摘要页含标题与关键词，不超过一页，无需英文。 -- 摘要页、正文、附录中不得出现姓名、学校、赛区等信息。 -- 附录含支撑材料文件列表与完整源码：源码以 `\lstinputlisting` 引用仓库内 - `src/mcm26b/geometry/` 等模块（相对路径 `../../`），提交前须确认与支撑材料 - 压缩包一致。 +第一条需要原电脑的官方正式统计队列；仅使用随包匿名快照重算时执行： -## 待办（正文中红色【待填/待补】标记） + python scripts/audit_paper_formal.py --snapshot docs/paper/data/formal-results.json -- 问题 3、4 演练统计值与正式测试结果（表 1 两张表）。 -- 问题 1 定位区域图、问题 2 候选区域示意图与选点对比实验。 -- 支撑材料文件列表更新；定稿前删除全部红色批注（`\todonote`）。 +快照模式可重算表格并核对现有原始包的哈希，不能在缺少官方队列时再次独立验证来源匹配。 -## 字体说明 +进入 docs/paper 后执行： -`fonts/` 下中文 字体自 macOS 系统字体（Songti.ttc、STHeiti）提取简体字面而来， -授权仅限本队参赛使用。若在 Windows/Overleaf 编译，可改用系统自带中易宋体/黑体， -将导言区字体设置替换为： + latexmk -xelatex -interaction=nonstopmode -halt-on-error main.tex -```latex -\setCJKmainfont{SimSun} -\setCJKsansfont{SimHei} -\setmainfont{Times New Roman} -``` +输出为本目录 main.pdf。VS Code 默认配方也已设为 latexmk (xelatex)，自动编译直至交叉引用稳定；仅运行一次 XeLaTeX 会在首次构建时产生问号。 + +在项目根目录生成支撑压缩包： + + python scripts/build_paper_support.py --package + +需要 TeX Live 的 XeLaTeX、ctex、TikZ。mcm26b-paper.cls 已恢复原模板，文档类选项和标题、摘要、关键词的版式也恢复原用法。精简支撑包不包含大体积字体，编译前需从原项目补齐 docs/paper/fonts/，不提供会改变原版式的字体回退。源码附录中的数学符号仍采用 LaTeX 转义命令。data/listing-source/ 只是生成的排版副本，可执行的 src/ 文件保持原样。 + +## 版式与验证 + +A4、四边距 2.5 cm，电子版由摘要页起连续编号，不含目录、承诺书和编号专用页。正文按问题重述、分析、假设、符号、四问模型与算法、正式结果、评价、参考文献组织。源码附录列出全部 31 个策略及配套 Python 模块和两个论文处理脚本。 + +统计表和耗时图从匿名快照生成；几何示意图使用正文明确给出的参数。几何推导和离散覆盖证书与正式测试结果分别说明。详见 REWRITE_NOTES.md。 -若仓库体积敏感，可将 `fonts/` 加入 `.gitignore`（此时每位队员需自备字体）。 diff --git a/docs/paper/REWRITE_NOTES.md b/docs/paper/REWRITE_NOTES.md new file mode 100644 index 0000000..7d42549 --- /dev/null +++ b/docs/paper/REWRITE_NOTES.md @@ -0,0 +1,41 @@ +# 论文重写与验证说明 + +## 依据与范围 + +阅读 issue 中的 B 题、两份接口与模拟器附件、2026 年论文格式规范、往届参考 PDF，并核对 docs/algo-1.md 至 algo-4.md 与 src/mcm26b 的当前实现。往届论文只用于组织结构与版式参考。重写摘要、问题重述、分析、假设、符号、四问模型和算法、正式实验、评价及附录；补入可复算表格和矢量图。 + +保留现有策略实现。正式导出不包含策略提交版本绑定，论文不把当前全部实现细节直接归因于这四次正式结果。源码中的旧实验注释保持原样，不作为论文的实验依据。 + +## 已明确的论证边界 + +- 第一问区分直径条件和最小包围圆条件，以边长 40 m 的等边三角形解释前者为何不足以保证 20 m 内清除。 +- 第二问证明首次测向的安全候选盘，说明在线有限候选和分支采样是启发式评价，不能自动升级为连续极小极大的严格上界。 +- 外切正多边形的径向外包误差为 r(sec(pi/M)-1)。代码中的额外非负余量可用于收紧清除条件，但其 r(1-cos(pi/M)) 表达式不应被称为精确外包误差上界。 +- 第三问给出七点连续覆盖证明，描述保守网格、贪心信息增益与滚动路径规划的实际默认实现，不宣称使用强化学习。 +- 第四问以 31 点计划为当前实现，验证范围仅为 15 m 网格和 72 个朝向。离散最坏距离与空间误差相加已超过 1000 m，且需另计朝向余量，不能据此声称连续覆盖保证。 +- 49 点方案作为已有严格备选方案，补足利用单元四顶点凸组合证明前向可见性的关键步骤；没有把它写成实际替换运行过的方案。 +- 说明联合位置与朝向信念的负观测更新保留“可能不可见”的朝向，以及 prob_detect 使用初始朝向档数归一化的真实口径。 +- 指出混合全向/定向类型下，仅以定向联合集为空判定缺席的局限。正文给出类型并集模型的改进方向，不宣称当前代码已经实现或正式测试验证了该修正。 + +## 正式数据核对 + +只选取官方模拟器 test/q3 与 test/q4 下的四份正式 jlog。与官方原导出逐字节哈希及同名 result.json 的 package_sha256 一致；以公开头部票据的 SHA-256 关联只读正式统计队列，提取所选案例的匿名字段。没有解密日志负载或读取隐藏源位置。 + +四份记录分别清除 13、15、13、10 个源，均主动退出、清除失败为零。问题三平均耗时为 238.075、232.889 s/个；问题四为 720.171、927.130 s/个。两问各缺第三份正式记录，源总数没有随统计公开，不能据此报告全清率。不同案例不是配对比较。 + +## 验证 + +- 四份正式包的身份匹配与哈希核对通过；匿名快照可以重新生成相同表格。 +- 四份记录的总时间与移动、检测、换频、清除分项满足精确十进制记账恒等式。 +- 第一问等边三角形例的直径和最小包围圆，以及七点覆盖的 984.539 m 上界均已复算。 +- 当前 q4_mincover_v2 计划的 3,256,200 个离散位置/朝向组合验证无遗漏；此结果不代表连续证明。 +- 源码显示副本仅转换数学符号为 LaTeX 转义命令；实际 Python 源文件不变。 +- PDF 经过 XeLaTeX 编译与逐页渲染检查；附录源码、数据和支撑包通过逐文件哈希清单保持对应。 + +本次重写未启动新的演练或正式模拟器测试，未用自建仿真替代正式数据。重写前论文源文件和 PDF 留存于 tmp/paper-rewrite/main-before.tex 与 main-before.pdf。 + +## 格式与交叉引用修正 + +根据反馈，将 mcm26b-paper.cls 恢复为原仓库模板，撤销 fontset=none 和一级标题编号样式覆盖，恢复原题名、摘要及关键词的排版用法。Windows 下标题重新使用原模板调用的 SimHei 黑体。 + +VS Code 默认配方原来只执行一次 XeLaTeX。首次构建主目录 PDF 时，引用尚未从辅助文件读回，因此文献、公式和图表引用出现问号。默认配方已改为 latexmk (xelatex)，构建会重复运行直至引用稳定，并直接更新 docs/paper/main.pdf。 diff --git a/docs/paper/data/audit.md b/docs/paper/data/audit.md new file mode 100644 index 0000000..9f5c6b4 --- /dev/null +++ b/docs/paper/data/audit.md @@ -0,0 +1,18 @@ +# 正式测试数据核对 + +只选择 `Jammers-simulator-full/test` 中的正式导出包。 +加密载荷不作解密。公开头部提供案例与票据；包哈希核对原件及 result 侧文件；票据哈希匹配官方正式统计数据库。 +导出快照不包含队号、设备信息、票据内容、密钥封装或账号信息。 + +| 案例 | 正式序号 | 原件一致 | 包 SHA-256 | +| --- | --- | --- | --- | +| 9HU7-UWJR-BPTR-VYAT | Q3-1 | 是 | `fbd7ab92f78a019887f603172ab6a39e274adb1f917fc2681f1e8073ff47d911` | +| 7TCG-C9EC-53VF-HZ5H | Q3-2 | 是 | `5d83ce87455ce22fadbcbddb60814d9b1f0be54de7bc9d0463777ba47b3922ef` | +| VQUM-ETQ5-74PP-ZQ3J | Q4-1 | 是 | `9a102295d324b5fb5aeed1c6036d13ae7e08a7d7fddb60ceb8dead24e62b15d3` | +| 5K5T-TRWZ-BPR2-ECAV | Q4-2 | 是 | `370aac9c2c5d324dd382e57e541ef0da7c5dd4759660d9ea0cba8373ce0ea9a1` | + +虚拟时间保留官方整数微秒，程序运行时间采用官方毫秒。平均定位清除时间 = 总虚拟秒数 / 清除数。 +移动时间由总时长减去检测、换频、成功及失败清除耗时反推；不是从解密轨迹逐动作复算所得。 +`confirmed` 仅指统计提交确认，`user_exit` 仅指主动退出。源总数未知，不能报告全清率。 +问题三、四均缺第三次正式导出；不以演练或自建模拟器结果替代。 +当前算法描述对应仓库代码；公开统计没有策略提交版本标识，不能用这四局作当前参数的配对消融。 diff --git a/docs/paper/data/formal-cost-rows.tex b/docs/paper/data/formal-cost-rows.tex new file mode 100644 index 0000000..6549a1b --- /dev/null +++ b/docs/paper/data/formal-cost-rows.tex @@ -0,0 +1,4 @@ +Q3-1 & 105 & 96 & 0 & 3094.978 & 2408.978 & 77.84\% \\ +Q3-2 & 117 & 108 & 0 & 3493.335 & 2725.335 & 78.02\% \\ +Q4-1 & 349 & 275 & 0 & 9362.226 & 7277.226 & 77.73\% \\ +Q4-2 & 361 & 315 & 0 & 9271.302 & 7101.302 & 76.59\% \\ diff --git a/docs/paper/data/formal-file-list.tex b/docs/paper/data/formal-file-list.tex new file mode 100644 index 0000000..367d3c9 --- /dev/null +++ b/docs/paper/data/formal-file-list.tex @@ -0,0 +1,13 @@ +\begin{longtable}{p{1.15cm}p{13.3cm}} +\caption{所选正式导出文件与完整包哈希}\label{tab:packages}\\ +\toprule 案例 & 原始文件名及 SHA-256\\\midrule\endfirsthead +\toprule 案例 & 原始文件名及 SHA-256\\\midrule\endhead +Q3-1 & \pathtext{formal-p3-1-9HU7-UWJR-BPTR-VYAT.jlog}\\ +& {\scriptsize\texttt{fbd7ab92f78a019887f603172ab6a39e}\allowbreak\texttt{274adb1f917fc2681f1e8073ff47d911}}\\[4pt] +Q3-2 & \pathtext{formal-p3-2-7TCG-C9EC-53VF-HZ5H.jlog}\\ +& {\scriptsize\texttt{5d83ce87455ce22fadbcbddb60814d9b}\allowbreak\texttt{1f0be54de7bc9d0463777ba47b3922ef}}\\[4pt] +Q4-1 & \pathtext{formal-p4-1-VQUM-ETQ5-74PP-ZQ3J.jlog}\\ +& {\scriptsize\texttt{9a102295d324b5fb5aeed1c6036d13ae}\allowbreak\texttt{7e08a7d7fddb60ceb8dead24e62b15d3}}\\[4pt] +Q4-2 & \pathtext{formal-p4-2-5K5T-TRWZ-BPR2-ECAV.jlog}\\ +& {\scriptsize\texttt{370aac9c2c5d324dd382e57e541ef0da}\allowbreak\texttt{7c5dd4759660d9ea0cba8373ce0ea9a1}}\\[4pt] +\bottomrule\end{longtable} diff --git a/docs/paper/data/formal-macros.tex b/docs/paper/data/formal-macros.tex new file mode 100644 index 0000000..e5a8509 --- /dev/null +++ b/docs/paper/data/formal-macros.tex @@ -0,0 +1,6 @@ +\newcommand{\QThreeCount}{28} +\newcommand{\QThreeWeighted}{235.297} +\newcommand{\QThreeMean}{235.482} +\newcommand{\QFourCount}{23} +\newcommand{\QFourWeighted}{810.153} +\newcommand{\QFourMean}{823.651} diff --git a/docs/paper/data/formal-q3-rows.tex b/docs/paper/data/formal-q3-rows.tex new file mode 100644 index 0000000..2e862d1 --- /dev/null +++ b/docs/paper/data/formal-q3-rows.tex @@ -0,0 +1,4 @@ +% Generated by scripts/audit_paper_formal.py; seconds; half-up rounding. +测试 1 & \texttt{9HU7-UWJR-BPTR-VYAT} & 13 & 238.075 & 5.596 \\ +测试 2 & \texttt{7TCG-C9EC-53VF-HZ5H} & 15 & 232.889 & 3.024 \\ +测试 3 & 未提供记录 & -- & -- & -- \\ diff --git a/docs/paper/data/formal-q4-rows.tex b/docs/paper/data/formal-q4-rows.tex new file mode 100644 index 0000000..5aa6c1d --- /dev/null +++ b/docs/paper/data/formal-q4-rows.tex @@ -0,0 +1,4 @@ +% Generated by scripts/audit_paper_formal.py; seconds; half-up rounding. +测试 1 & \texttt{VQUM-ETQ5-74PP-ZQ3J} & 13 & 720.171 & 7.668 \\ +测试 2 & \texttt{5K5T-TRWZ-BPR2-ECAV} & 10 & 927.130 & 5.724 \\ +测试 3 & 未提供记录 & -- & -- & -- \\ diff --git a/docs/paper/data/formal-results.csv b/docs/paper/data/formal-results.csv new file mode 100644 index 0000000..97cc0e8 --- /dev/null +++ b/docs/paper/data/formal-results.csv @@ -0,0 +1,5 @@ +problem_no,formal_index,case_code,entered,end_reason,cleared_jammer_count,measure_accepted_count,virtual_time_us,program_run_duration_ms,channel_switch_count,clear_failure_count,state,package_sha256,virtual_time_s,average_clear_time_s,program_run_duration_s,inferred_movement_time_s,inferred_distance_m,movement_share_percent,source_total,clear_fraction +3,1,9HU7-UWJR-BPTR-VYAT,1,user_exit,13,105,3094978068,5596,96,0,confirmed,fbd7ab92f78a019887f603172ab6a39e274adb1f917fc2681f1e8073ff47d911,3094.978068,238.075236,5.596,2408.978068,12044.890340,77.835061,, +3,2,7TCG-C9EC-53VF-HZ5H,1,user_exit,15,117,3493335140,3024,108,0,confirmed,5d83ce87455ce22fadbcbddb60814d9b1f0be54de7bc9d0463777ba47b3922ef,3493.33514,232.889009,3.024,2725.33514,13626.67570,78.015279,, +4,1,VQUM-ETQ5-74PP-ZQ3J,1,user_exit,13,349,9362225736,7668,275,0,confirmed,9a102295d324b5fb5aeed1c6036d13ae7e08a7d7fddb60ceb8dead24e62b15d3,9362.225736,720.171210,7.668,7277.225736,36386.128680,77.729655,, +4,2,5K5T-TRWZ-BPR2-ECAV,1,user_exit,10,361,9271302080,5724,315,0,confirmed,370aac9c2c5d324dd382e57e541ef0da7c5dd4759660d9ea0cba8373ce0ea9a1,9271.30208,927.130208,5.724,7101.30208,35506.51040,76.594442,, diff --git a/docs/paper/data/formal-results.json b/docs/paper/data/formal-results.json new file mode 100644 index 0000000..a7d824b --- /dev/null +++ b/docs/paper/data/formal-results.json @@ -0,0 +1,150 @@ +{ + "schema": "paper-formal-audit-v1", + "selection": "Only Jammers-simulator-full/test/**/*.jlog", + "statistics_source": "Official formal-statistics-queue.sqlite3; matched by SHA-256 of the public activation ticket", + "limitations": [ + "Encrypted action payloads are not decrypted; no trajectory or bearing observations are available.", + "Source totals and omnidirectional/directional counts are not disclosed.", + "Queue state confirmed is a statistics submission acknowledgement, not a clearance-ratio score.", + "No solver commit or configuration digest is bound to these public statistics.", + "The third formal attempt for each problem is not present in the selected data." + ], + "records": [ + { + "problem_no": 3, + "formal_index": 1, + "case_code": "9HU7-UWJR-BPTR-VYAT", + "client_version": "1.1.0", + "entered": 1, + "end_reason": "user_exit", + "cleared_jammer_count": 13, + "measure_accepted_count": 105, + "virtual_time_us": 3094978068, + "program_run_duration_ms": 5596, + "channel_switch_count": 96, + "clear_failure_count": 0, + "state": "confirmed", + "file": "test/q3/formal-p3-1-9HU7-UWJR-BPTR-VYAT.jlog", + "size_bytes": 106656, + "package_sha256": "fbd7ab92f78a019887f603172ab6a39e274adb1f917fc2681f1e8073ff47d911", + "activation_ticket_sha256": "41563c714553abf202fc0012fcde2503c64c6cec27a84c7229c487602b957516", + "created_at_utc": "2026-09-12T07:16:06.377Z", + "ended_at_utc": "2026-09-12T07:16:06.373Z", + "content_encryption": "aes-256-gcm-chunked", + "identity_and_ticket_content_omitted": true, + "same_as_official_original": true, + "derived": { + "virtual_time_s": "3094.978068", + "average_clear_time_s": "238.075236", + "program_run_duration_s": "5.596", + "inferred_movement_time_s": "2408.978068", + "inferred_distance_m": "12044.890340", + "movement_share_percent": "77.835061", + "source_total": null, + "clear_fraction": null + } + }, + { + "problem_no": 3, + "formal_index": 2, + "case_code": "7TCG-C9EC-53VF-HZ5H", + "client_version": "1.1.0", + "entered": 1, + "end_reason": "user_exit", + "cleared_jammer_count": 15, + "measure_accepted_count": 117, + "virtual_time_us": 3493335140, + "program_run_duration_ms": 3024, + "channel_switch_count": 108, + "clear_failure_count": 0, + "state": "confirmed", + "file": "test/q3/formal-p3-2-7TCG-C9EC-53VF-HZ5H.jlog", + "size_bytes": 106326, + "package_sha256": "5d83ce87455ce22fadbcbddb60814d9b1f0be54de7bc9d0463777ba47b3922ef", + "activation_ticket_sha256": "5f6d5ff4a369418f9f683ef0384398190bfb0b81bc71ce1c1bd6f728ff1fdf41", + "created_at_utc": "2026-09-12T07:47:20.065Z", + "ended_at_utc": "2026-09-12T07:47:20.061Z", + "content_encryption": "aes-256-gcm-chunked", + "identity_and_ticket_content_omitted": true, + "same_as_official_original": true, + "derived": { + "virtual_time_s": "3493.33514", + "average_clear_time_s": "232.889009", + "program_run_duration_s": "3.024", + "inferred_movement_time_s": "2725.33514", + "inferred_distance_m": "13626.67570", + "movement_share_percent": "78.015279", + "source_total": null, + "clear_fraction": null + } + }, + { + "problem_no": 4, + "formal_index": 1, + "case_code": "VQUM-ETQ5-74PP-ZQ3J", + "client_version": "1.1.0", + "entered": 1, + "end_reason": "user_exit", + "cleared_jammer_count": 13, + "measure_accepted_count": 349, + "virtual_time_us": 9362225736, + "program_run_duration_ms": 7668, + "channel_switch_count": 275, + "clear_failure_count": 0, + "state": "confirmed", + "file": "test/q4/formal-p4-1-VQUM-ETQ5-74PP-ZQ3J.jlog", + "size_bytes": 150315, + "package_sha256": "9a102295d324b5fb5aeed1c6036d13ae7e08a7d7fddb60ceb8dead24e62b15d3", + "activation_ticket_sha256": "d02cfdf2eed65dbe3bb4c7768a263f8bf57b56bc323b6453c1dfa2aec6e24810", + "created_at_utc": "2026-09-12T07:38:51.368Z", + "ended_at_utc": "2026-09-12T07:38:51.365Z", + "content_encryption": "aes-256-gcm-chunked", + "identity_and_ticket_content_omitted": true, + "same_as_official_original": true, + "derived": { + "virtual_time_s": "9362.225736", + "average_clear_time_s": "720.171210", + "program_run_duration_s": "7.668", + "inferred_movement_time_s": "7277.225736", + "inferred_distance_m": "36386.128680", + "movement_share_percent": "77.729655", + "source_total": null, + "clear_fraction": null + } + }, + { + "problem_no": 4, + "formal_index": 2, + "case_code": "5K5T-TRWZ-BPR2-ECAV", + "client_version": "1.1.0", + "entered": 1, + "end_reason": "user_exit", + "cleared_jammer_count": 10, + "measure_accepted_count": 361, + "virtual_time_us": 9271302080, + "program_run_duration_ms": 5724, + "channel_switch_count": 315, + "clear_failure_count": 0, + "state": "confirmed", + "file": "test/q4/formal-p4-2-5K5T-TRWZ-BPR2-ECAV.jlog", + "size_bytes": 151668, + "package_sha256": "370aac9c2c5d324dd382e57e541ef0da7c5dd4759660d9ea0cba8373ce0ea9a1", + "activation_ticket_sha256": "4918e4ca6a77367dd06cd40afb28d4415246ef0437c68c052bddf613f4f914b0", + "created_at_utc": "2026-09-12T07:42:29.854Z", + "ended_at_utc": "2026-09-12T07:42:29.851Z", + "content_encryption": "aes-256-gcm-chunked", + "identity_and_ticket_content_omitted": true, + "same_as_official_original": true, + "derived": { + "virtual_time_s": "9271.30208", + "average_clear_time_s": "927.130208", + "program_run_duration_s": "5.724", + "inferred_movement_time_s": "7101.30208", + "inferred_distance_m": "35506.51040", + "movement_share_percent": "76.594442", + "source_total": null, + "clear_fraction": null + } + } + ] +} diff --git a/docs/paper/data/listing-source/scripts/audit_paper_formal.py.tex b/docs/paper/data/listing-source/scripts/audit_paper_formal.py.tex new file mode 100644 index 0000000..33b7502 --- /dev/null +++ b/docs/paper/data/listing-source/scripts/audit_paper_formal.py.tex @@ -0,0 +1,197 @@ +"""Audit only the formal exports selected in the official simulator's test folder. + +No encrypted payload is opened. Match the public activation-ticket digest to the +official statistics queue, and the complete package digest to its result sidecar. +Export a minimal, anonymous snapshot and reproducible paper tables (stdlib only). +""" +from __future__ import annotations + +import argparse +import base64 +import csv +import hashlib +import json +import sqlite3 +import struct +from decimal import Decimal, ROUND_HALF_UP +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[1] +FIELDS = ( + "entered", "end_reason", "cleared_jammer_count", "measure_accepted_count", + "virtual_time_us", "program_run_duration_ms", "channel_switch_count", + "clear_failure_count", "state", +) + + +def sha(data: bytes) -> str: + return hashlib.sha256(data).hexdigest() + + +def public_header(path: Path) -> tuple[dict, str]: + data = path.read_bytes() + if data[:8] != b"JMBFLOG1" or len(data) < 14: + raise ValueError(f"Unsupported formal envelope: {path.name}") + version, size = struct.unpack(">HI", data[8:14]) + if version != 1 or not 0 < size <= len(data) - 14: + raise ValueError(f"Invalid envelope header: {path.name}") + header = json.loads(data[14:14 + size]) + if header["package_type"] != "formal_behavior_log": + raise ValueError("Practice logs are not admitted") + return header, sha(data) + + +def fixed(value: Decimal, digits: int = 3) -> str: + return str(value.quantize(Decimal(1).scaleb(-digits), rounding=ROUND_HALF_UP)) + + +def derive(row: dict) -> dict: + count = row["cleared_jammer_count"] + total = Decimal(row["virtual_time_us"]) / 1_000_000 + movement = total - (5 * row["measure_accepted_count"] + + row["channel_switch_count"] + 5 * count + + 3 * row["clear_failure_count"]) + if count <= 0 or movement < 0: + raise ValueError("Invalid counts or negative inferred movement time") + return { + "virtual_time_s": str(total), + "average_clear_time_s": fixed(total / count, 6), + "program_run_duration_s": fixed(Decimal(row["program_run_duration_ms"]) / 1000), + "inferred_movement_time_s": str(movement), + "inferred_distance_m": str(5 * movement), + "movement_share_percent": fixed(100 * movement / total, 6), + "source_total": None, + "clear_fraction": None, + } + + +def collect(sim: Path) -> list[dict]: + selected = sorted((sim / "test").rglob("*.jlog")) + if not selected: + raise ValueError("No formal exports in test/") + queue = sim / "JammersSimulatorData/formal-statistics-queue.sqlite3" + original = sim / "JammersSimulatorData/behavior-logs" + # Read the live queue including its WAL, without writing to the simulator. + with sqlite3.connect(queue.resolve().as_uri() + "?mode=ro", uri=True) as db: + db.row_factory = sqlite3.Row + query = "SELECT activation_ticket_sha256," + ",".join(FIELDS) + " FROM statistics_tasks" + statistics = {r["activation_ticket_sha256"]: dict(r) for r in db.execute(query)} + records = [] + for path in selected: + header, digest = public_header(path) + encoded = header["server_ticket_b64"] + ticket_hash = sha(base64.urlsafe_b64decode(encoded + "=" * (-len(encoded) % 4))) + sidecar = json.loads((original / (path.stem + ".result.json")).read_text("utf-8")) + for field in ("problem_no", "formal_index", "case_code"): + if header[field] != sidecar[field]: + raise ValueError(f"Mismatched case: {path.name}") + if digest != sidecar["package_sha256"] or digest != sha((original / path.name).read_bytes()): + raise ValueError(f"Mismatched formal package: {path.name}") + matched = statistics[ticket_hash] + row = {name: header[name] for name in ("problem_no", "formal_index", "case_code", "client_version")} + row.update({name: matched[name] for name in FIELDS}) + row.update({ + "file": path.relative_to(sim).as_posix(), "size_bytes": path.stat().st_size, + "package_sha256": digest, "activation_ticket_sha256": ticket_hash, + "created_at_utc": header["created_at_utc"], + "ended_at_utc": sidecar["ended_at_utc"], + "content_encryption": header["content_encryption"], + "identity_and_ticket_content_omitted": True, + "same_as_official_original": True, + }) + row["derived"] = derive(row) + records.append(row) + keys = [(r["problem_no"], r["formal_index"]) for r in records] + if len(set(keys)) != len(keys): + raise ValueError("Duplicate formal attempt") + return records + + +def write_outputs(rows: list[dict], out: Path) -> None: + out.mkdir(parents=True, exist_ok=True) + snapshot = { + "schema": "paper-formal-audit-v1", + "selection": "Only Jammers-simulator-full/test/**/*.jlog", + "statistics_source": "Official formal-statistics-queue.sqlite3; matched by SHA-256 of the public activation ticket", + "limitations": [ + "Encrypted action payloads are not decrypted; no trajectory or bearing observations are available.", + "Source totals and omnidirectional/directional counts are not disclosed.", + "Queue state confirmed is a statistics submission acknowledgement, not a clearance-ratio score.", + "No solver commit or configuration digest is bound to these public statistics.", + "The third formal attempt for each problem is not present in the selected data.", + ], + "records": rows, + } + (out / "formal-results.json").write_text(json.dumps(snapshot, ensure_ascii=False, indent=2) + "\n", "utf-8") + columns = ["problem_no", "formal_index", "case_code", *FIELDS, "package_sha256"] + with (out / "formal-results.csv").open("w", encoding="utf-8-sig", newline="") as handle: + writer = csv.DictWriter(handle, fieldnames=columns + list(rows[0]["derived"])) + writer.writeheader() + for row in rows: + writer.writerow({**{key: row[key] for key in columns}, **row["derived"]}) + for problem in (3, 4): + by_index = {r["formal_index"]: r for r in rows if r["problem_no"] == problem} + lines = ["% Generated by scripts/audit_paper_formal.py; seconds; half-up rounding."] + for index in (1, 2, 3): + row = by_index.get(index) + if row is None: + lines.append(f"测试 {index} & 未提供记录 & -- & -- & -- " + r"\\") + else: + avg = Decimal(row["virtual_time_us"]) / 1_000_000 / row["cleared_jammer_count"] + lines.append(f"测试 {index} & \\texttt{{{row['case_code']}}} & {row['cleared_jammer_count']} & {fixed(avg)} & {row['derived']['program_run_duration_s']} " + r"\\") + (out / f"formal-q{problem}-rows.tex").write_text("\n".join(lines) + "\n", "utf-8") + cost_lines, constants = [], [] + for row in rows: + label = f"Q{row['problem_no']}-{row['formal_index']}" + total = Decimal(row["virtual_time_us"]) / 1_000_000 + move = Decimal(row["derived"]["inferred_movement_time_s"]) + cost_lines.append(f"{label} & {row['measure_accepted_count']} & {row['channel_switch_count']} & {row['clear_failure_count']} & {fixed(total)} & {fixed(move)} & {fixed(100*move/total, 2)}\\% " + r"\\") + (out / "formal-cost-rows.tex").write_text("\n".join(cost_lines) + "\n", "utf-8") + for problem, word in ((3, "Three"), (4, "Four")): + group = [r for r in rows if r["problem_no"] == problem] + count = sum(r["cleared_jammer_count"] for r in group) + total = sum(Decimal(r["virtual_time_us"]) / 1_000_000 for r in group) + mean = sum(Decimal(r["virtual_time_us"]) / 1_000_000 / r["cleared_jammer_count"] for r in group) / len(group) + constants.extend([f"\\newcommand{{\\Q{word}Count}}{{{count}}}", + f"\\newcommand{{\\Q{word}Weighted}}{{{fixed(total/count)}}}", + f"\\newcommand{{\\Q{word}Mean}}{{{fixed(mean)}}}"]) + (out / "formal-macros.tex").write_text("\n".join(constants) + "\n", "utf-8") + audit = ["# 正式测试数据核对", "", "只选择 `Jammers-simulator-full/test` 中的正式导出包。", + "加密载荷不作解密。公开头部提供案例与票据；包哈希核对原件及 result 侧文件；票据哈希匹配官方正式统计数据库。", + "导出快照不包含队号、设备信息、票据内容、密钥封装或账号信息。", "", + "| 案例 | 正式序号 | 原件一致 | 包 SHA-256 |", "| --- | --- | --- | --- |"] + for row in rows: + audit.append(f"| {row['case_code']} | Q{row['problem_no']}-{row['formal_index']} | 是 | `{row['package_sha256']}` |") + audit += ["", "虚拟时间保留官方整数微秒，程序运行时间采用官方毫秒。平均定位清除时间 = 总虚拟秒数 / 清除数。", + "移动时间由总时长减去检测、换频、成功及失败清除耗时反推；不是从解密轨迹逐动作复算所得。", + "`confirmed` 仅指统计提交确认，`user_exit` 仅指主动退出。源总数未知，不能报告全清率。", + "问题三、四均缺第三次正式导出；不以演练或自建模拟器结果替代。", + "当前算法描述对应仓库代码；公开统计没有策略提交版本标识，不能用这四局作当前参数的配对消融。", ""] + (out / "audit.md").write_text("\n".join(audit), "utf-8") + + +def main() -> None: + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--sim-root", type=Path, default=ROOT / "Jammers-simulator-full") + parser.add_argument("--out", type=Path, default=ROOT / "docs/paper/data") + parser.add_argument("--snapshot", type=Path, help="Regenerate tables from the audited anonymous snapshot, without the simulator database") + args = parser.parse_args() + if args.snapshot: + rows = json.loads(args.snapshot.read_text("utf-8"))["records"] + for row in rows: + if derive(row) != row["derived"]: + raise ValueError("Snapshot arithmetic changed") + path = args.sim_root / row["file"] + if path.exists() and public_header(path)[1] != row["package_sha256"]: + raise ValueError("Snapshot and formal export disagree") + else: + rows = collect(args.sim_root) + write_outputs(rows, args.out) + for row in rows: + print(f"Q{row['problem_no']}-{row['formal_index']} {row['case_code']}: " + f"cleared={row['cleared_jammer_count']} average={row['derived']['average_clear_time_s']} s " + f"real={row['derived']['program_run_duration_s']} s") + + +if __name__ == "__main__": + main() diff --git a/docs/paper/data/listing-source/scripts/build_paper_support.py.tex b/docs/paper/data/listing-source/scripts/build_paper_support.py.tex new file mode 100644 index 0000000..058a075 --- /dev/null +++ b/docs/paper/data/listing-source/scripts/build_paper_support.py.tex @@ -0,0 +1,231 @@ +"""Build vector figure sources, complete source listings, and a compact support ZIP. + +Formal figures use the audited snapshot only. Geometric figures use declared +algorithm parameters, not fabricated observations or hidden simulator data. +""" +from __future__ import annotations + +import argparse +import hashlib +import json +import zipfile +from decimal import Decimal +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[1] +PAPER = ROOT / "docs/paper" + +# Display copies only: executable Python files remain byte-for-byte unchanged. +ESCAPE_OPEN = "(" + "*@" +ESCAPE_CLOSE = "@*" + ")" +LATEX_SYMBOLS = { + "\u03b1": r"\alpha", "\u03b4": r"\delta", "\u03b8": r"\theta", + "\u03bb": r"\lambda", "\u03c0": r"\pi", "\u03c1": r"\rho", + "\u03c6": r"\varphi", "\u2308": r"\lceil", "\u2309": r"\rceil", + "\u2200": r"\forall", "\u2203": r"\exists", "\u2205": r"\varnothing", + "\u2208": r"\in", "\u2227": r"\wedge", "\u2229": r"\cap", + "\u222a": r"\cup", "\u2248": r"\approx", "\u2264": r"\le", + "\u2265": r"\ge", "\u2286": r"\subseteq", "\u2287": r"\supseteq", + "\u27f9": r"\Longrightarrow", +} + + +def escaped_listing(source: str) -> str: + if ESCAPE_OPEN in source or ESCAPE_CLOSE in source: + raise ValueError("Source collides with the LaTeX escape delimiters") + return "".join( + ESCAPE_OPEN + r"\ensuremath{" + LATEX_SYMBOLS[c] + "}" + ESCAPE_CLOSE + if c in LATEX_SYMBOLS else c for c in source + ) + + +def digest(data: bytes) -> str: + return hashlib.sha256(data).hexdigest() + + +def figures(rows: list[dict]) -> None: + out = PAPER / "figures" + out.mkdir(parents=True, exist_ok=True) + plan = json.loads((ROOT / "src/mcm26b/guarantee/plans/q4_mincover_v2.json").read_text("utf-8")) + lines = [ + r"\begin{figure}[htbp]\centering", + r"\begin{tikzpicture}[x=0.00145cm,y=0.00145cm,font=\small]", + r"\fill[inkblue!5] (0,0) circle (1800);", + r"\draw[thick] (0,0) circle (1800);", + r"\draw[->,warmgray] (-2900,0)--(2950,0) node[right] {$x$/m};", + r"\draw[->,warmgray] (0,-2800)--(0,2850) node[above] {$y$/m};", + ] + for x in (-2000, -1000, 1000, 2000): + lines += [fr"\draw ({x},-35)--({x},35);", + fr"\node[below,font=\scriptsize] at ({x},-50) {{{x}}};"] + for x, y in plan["points"]: + lines.append(fr"\fill[inkblue] ({x},{y}) circle (33);") + lines += [ + r"\node[anchor=west,align=left] at (3250,900) {圆域：源位置先验\\蓝点：31个检测站};", + r"\node[anchor=west,align=left] at (3250,-700) {部分站点在圆域外\\用于接收向外发射的源};", + r"\end{tikzpicture}", + r"\caption{第四问31点计划的几何分布。站点取自计划文件，不代表正式运行轨迹；离散验证不等同于连续覆盖证明。}", + r"\label{fig:q4plan}\end{figure}", + ] + (out / "q4-plan.tex").write_text("\n".join(lines) + "\n", "utf-8") + colors = ["inkblue", "inkblue!50", "warmgray!70", "black!18"] + bars = [ + r"\begin{figure}[htbp]\centering", + r"\begin{tikzpicture}[x=0.00108cm,y=0.85cm,font=\small]", + ] + for j, row in enumerate(rows): + y = 3 - j + components = [Decimal(row["derived"]["inferred_movement_time_s"]), + Decimal(5 * row["measure_accepted_count"]), + Decimal(row["channel_switch_count"]), + Decimal(5 * row["cleared_jammer_count"] + 3 * row["clear_failure_count"])] + label = f"Q{row['problem_no']}-{row['formal_index']}" + bars.append(fr"\node[anchor=east] at (-100,{y + 0.3}) {{{label}}};") + current = Decimal(0) + for amount, color in zip(components, colors): + bars.append(fr"\fill[{color}] ({current},{y}) rectangle ({current + amount},{y + 0.6});") + current += amount + bars.append(fr"\node[anchor=west,font=\scriptsize] at ({current + 80},{y + 0.3}) {{{current:.1f}}};") + bars.append(r"\draw[->] (0,-0.25)--(10500,-0.25);") + for tick in range(0, 10001, 2000): + bars.append(fr"\draw ({tick},-0.25)--({tick},-0.35) node[below,font=\scriptsize] {{{tick}}};") + bars.append(r"\node[anchor=west,font=\scriptsize] at (10400,-0.65) {s};") + for x, color, label in zip((0, 2600, 5200, 7600), colors, ("移动", "检测", "换频", "清除")): + bars += [fr"\fill[{color}] ({x},-1.3) rectangle ({x + 350},-1.05);", + fr"\node[anchor=west] at ({x + 450},-1.175) {{{label}}};"] + bars += [ + r"\end{tikzpicture}", + r"\caption{四次正式测试的累计虚拟耗时。移动项由总时间扣除官方动作计数对应耗时反推。}", + r"\label{fig:costbars}\end{figure}", + ] + (out / "formal-time-bars.tex").write_text("\n".join(bars) + "\n", "utf-8") + + +def listings(rows: list[dict]) -> None: + data = PAPER / "data" + files = sorted((ROOT / "src/mcm26b").rglob("*.py")) + files += [ROOT / "scripts/audit_paper_formal.py", + ROOT / "scripts/build_paper_support.py"] + text = [ + r"\begingroup", + r"\linespread{1.0}\selectfont", + r"\lstset{basicstyle=\ttfamily\fontsize{8}{10}\selectfont,numberstyle=\tiny," + r"aboveskip=6pt,belowskip=8pt,xleftmargin=1.5em,frame=none}", + ] + for path in files: + rel = path.relative_to(ROOT).as_posix() + display = data / "listing-source" / (rel + ".tex") + display.parent.mkdir(parents=True, exist_ok=True) + display.write_text(escaped_listing(path.read_text("utf-8")), "utf-8") + display_rel = display.relative_to(PAPER).as_posix() + escape_option = "escapeinside={" + ESCAPE_OPEN + "}{" + ESCAPE_CLOSE + "}" + text += [fr"\subsection*{{\pathtext{{{rel}}}}}", + fr"\lstinputlisting[{escape_option}]{{{display_rel}}}"] + text.append(r"\endgroup") + (data / "source-listings.tex").write_text("\n".join(text) + "\n", "utf-8") + table = [ + r"\begin{longtable}{p{1.15cm}p{13.3cm}}", + r"\caption{所选正式导出文件与完整包哈希}\label{tab:packages}\\", + r"\toprule 案例 & 原始文件名及 SHA-256\\\midrule\endfirsthead", + r"\toprule 案例 & 原始文件名及 SHA-256\\\midrule\endhead", + ] + for row in rows: + h = row["package_sha256"] + label = f"Q{row['problem_no']}-{row['formal_index']}" + table += [ + fr"{label} & \pathtext{{{Path(row['file']).name}}}\\", + fr"& {{\scriptsize\texttt{{{h[:32]}}}\allowbreak\texttt{{{h[32:]}}}}}\\[4pt]", + ] + table += [r"\bottomrule\end{longtable}"] + (data / "formal-file-list.tex").write_text("\n".join(table) + "\n", "utf-8") + + +SUPPORT_README = """# 论文支撑材料 + +只引用官方模拟器 test 中的四份正式导出及哈希匹配的官方统计。 +问题三、四各缺第三份正式记录。正式源总数未知，不能计算全清率。 +完整原始包保留原名，匿名快照不含队号与票据内容。 + +## 环境和运行 + +Python >=3.10；安装 requests，可选 numpy 加速。 +在本目录使用 PowerShell： + + $env:PYTHONPATH = (Resolve-Path src).Path + python -m mcm26b.cli --help + python -m mcm26b.cli run --problem 3 --strategy bayes --robot-id <模拟器登录队号> + python -m mcm26b.cli run --problem 4 --strategy directional --robot-id <模拟器登录队号> + +在线命令需要先由使用者在官方模拟器中选择测试、待接口就绪。 +重写论文未运行这些在线命令。自建评测机及历史场景不作为论文实验资料。 +策略的自检命令涉及另一个可选 referee 包，本包用于正式接口路径。 + +## 重算论文数据和图表 + + python scripts/audit_paper_formal.py --snapshot docs/paper/data/formal-results.json + python scripts/build_paper_support.py + +上述命令均为离线处理，不连接模拟器接口。 +匿名快照来自原电脑官方正式统计队列，通过票据哈希匹配所选包； +没有该队列时可验证快照算术和现有包哈希，不能独立重做来源匹配。 +源码与正式包无策略提交版本哈希绑定；不作同场景消融或全清率宣称。 +31点计划只有离散证据；混合类型下的 joint_empty 判定边界见论文正文。 + +## 编译 + +安装 TeX Live（XeLaTeX、ctex、TikZ），进入 docs/paper： + + latexmk -xelatex -interaction=nonstopmode -halt-on-error main.tex + +版式使用原项目模板。精简支撑包不含大体积字体，编译前请将原项目 +docs/paper/fonts 目录放回同一相对位置；不要修改模板以替代这些字体。 +使用 latexmk 自动完成交叉引用所需的多遍编译，不能只运行一次 XeLaTeX。 +support-manifest.json 列出包内全部材料（清单自身除外）及 SHA-256。 +""" + + +def package(rows: list[dict]) -> Path: + selected = set((ROOT / "src/mcm26b").rglob("*.py")) + selected.update((ROOT / "src/mcm26b/guarantee/plans").glob("*.json")) + selected.update((PAPER / "data").rglob("*")) + selected.update((PAPER / "figures").glob("*.tex")) + selected.update((PAPER / "sections").glob("*.tex")) + selected.update([PAPER / "main.tex", PAPER / "mcm26b-paper.cls", + PAPER / "README.md", PAPER / "REWRITE_NOTES.md", + ROOT / "scripts/audit_paper_formal.py", + ROOT / "scripts/build_paper_support.py"]) + for row in rows: + path = ROOT / "Jammers-simulator-full" / row["file"] + if digest(path.read_bytes()) != row["package_sha256"]: + raise ValueError("Original formal package changed") + selected.add(path) + blobs = {p.relative_to(ROOT).as_posix(): p.read_bytes() for p in sorted(selected) if p.is_file()} + blobs["README.md"] = SUPPORT_README.encode("utf-8") + blobs["requirements.txt"] = b"requests>=2.31\nnumpy>=1.24\n" + manifest = [{"file": name, "bytes": len(value), "sha256": digest(value)} for name, value in sorted(blobs.items())] + blobs["support-manifest.json"] = (json.dumps(manifest, ensure_ascii=False, indent=2) + "\n").encode("utf-8") + out = PAPER / "support-materials.zip" + with zipfile.ZipFile(out, "w", zipfile.ZIP_DEFLATED, compresslevel=9) as archive: + for name, value in sorted(blobs.items()): + entry = zipfile.ZipInfo(name, (2026, 9, 13, 0, 0, 0)) + entry.compress_type = zipfile.ZIP_DEFLATED + archive.writestr(entry, value) + if out.stat().st_size > 20_000_000: + raise ValueError("Support archive exceeds 20 MB") + print(f"Support archive: {len(blobs)} files, {out.stat().st_size} bytes") + return out + + +def main() -> None: + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--package", action="store_true") + args = parser.parse_args() + rows = json.loads((PAPER / "data/formal-results.json").read_text("utf-8"))["records"] + figures(rows) + listings(rows) + if args.package: + package(rows) + + +if __name__ == "__main__": + main() diff --git a/docs/paper/data/listing-source/src/mcm26b/__init__.py.tex b/docs/paper/data/listing-source/src/mcm26b/__init__.py.tex new file mode 100644 index 0000000..29b08f6 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/__init__.py.tex @@ -0,0 +1,21 @@ +"""mcm26b：CUMCM 2026 B题"无线电干扰源的快速自动定位与清除"求解包。 + +模块分层（docs/B题建模分析与实施计划.md §7 的七模块划分）： +- config 全项目参数中心（题面常量与工程参数，唯一字面量来源） +- protocol P0/P1 字段表、计时模型、状态机与串行幂等客户端 +- geometry P2 角域交会定位、直径、最小包围圆与 P2 证书（已完工） +- sim 自建模拟器、故障注入与演练日志回放（测试专用） +- belief P3 逐频道候选集合（骨架） +- coverage P4 49 点覆盖记录（骨架+网格生成） +- planner P3 选点 / P4 全向闭环 / P5 定向扩展（骨架） +- evaluation 日志复算与统计 +""" + +__version__ = "0.2.0" + +from .config import DEFAULT_CONFIG, ProblemConfig +from .geometry import Measurement, first_bearing_candidate_disk, solve, \ + smallest_enclosing_circle + +__all__ = ["DEFAULT_CONFIG", "Measurement", "ProblemConfig", "solve", + "first_bearing_candidate_disk", "smallest_enclosing_circle"] diff --git a/docs/paper/data/listing-source/src/mcm26b/belief/__init__.py.tex b/docs/paper/data/listing-source/src/mcm26b/belief/__init__.py.tex new file mode 100644 index 0000000..6318154 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/belief/__init__.py.tex @@ -0,0 +1,284 @@ +"""P3 逐频道信念状态：候选集合 K_c 维护与频道处理状态。 + +核心不变式（验收标准）： +- 保守性：真源永远属于维护中的候选集合。候选集用"圆盘外切多边形 (*@\ensuremath{\cap}@*) + 测向角域半平面"的凸多边形表示——外切多边形严格包含圆盘，半平面裁剪 + 带正容差，因此每步更新只会放大而不会缩小真实候选集； +- direction 读数：K_c (*@\ensuremath{\subseteq}@*) Ω (*@\ensuremath{\cap}@*) W(s, (*@\ensuremath{\theta}@*)±(*@\ensuremath{\delta}@*)_eff) (*@\ensuremath{\cap}@*) B(s, 1500)，后续读数再交 + 同样的约束；(*@\ensuremath{\delta}@*)_eff = 误差半角 + 示向度舍入裕量（服务器保留两位小数， + 舍入本身引入 (*@\ensuremath{\le}@*)0.005° 偏差）； +- no_signal 读数（P4，全向源）：基线不据此删空间候选——对定向源它是 + "位置×朝向"联合约束，单独维护空间候选会误删真源（P5 才启用）； + "该频道不存在源"的证明由覆盖账本（coverage.CoverageLedger）给出； +- near 读数：源在 5m 内，候选集收缩为 B(s, 5)，可直接产生清除证书； +- /clear 成功：状态转 CLEARED；失败只说明"该频道 20m 内无可清除源"， + 不得直接删除超出 20m 的候选，必须先补测再重试。 +""" + +from __future__ import annotations + +import math +from dataclasses import dataclass, field +from enum import Enum + +from ..config import ProblemConfig, Vec2 +from ..geometry.localization import smallest_enclosing_circle +from ..protocol.rules import DIRECTION, NEAR, NO_SIGNAL + +# 半平面裁剪的正容差（米）。坐标量级 ~2100，浮点误差远小于它； +# 容差只向"保留更多候选"的方向倾斜，不破坏保守性。 +_CLIP_TOL_M = 1e-6 +_DEDUPE_TOL_M = 1e-7 + + +class InconsistentBelief(RuntimeError): + """读数把候选集剪空等违背保守性的情形；须停机核查而非继续跑。""" + + +class ChannelStatus(Enum): + UNKNOWN = "unknown" # 尚无有效证据 + DETECTED = "detected" # 收到过 direction/near，待定位 + LOCATED = "located" # 候选集包围圆半径 <= 20，可清除 + CLEARED = "cleared" # 清除成功 + ABSENT = "absent" # 覆盖证明不存在（P4） + + +def circumscribed_polygon(center: Vec2, radius_m: float, sides: int) -> list[Vec2]: + """圆的外切正多边形顶点（外接半径 r/cos((*@\ensuremath{\pi}@*)/n)），严格包含圆盘。 + + 近似误差（外接圆超出圆盘的部分）为 r(1/cos((*@\ensuremath{\pi}@*)/n) - 1) (*@\ensuremath{\le}@*) r(1-cos((*@\ensuremath{\pi}@*)/n))·sec²， + 调用方用 (1-cos((*@\ensuremath{\pi}@*)/n)) 口径记账即可（略保守偏大）。 + """ + if sides < 8: + raise ValueError("外切多边形边数过少，近似误差不可控") + circumradius = radius_m / math.cos(math.pi / sides) + step = 2 * math.pi / sides + return [(center[0] + circumradius * math.cos(step * i + step / 2), + center[1] + circumradius * math.sin(step * i + step / 2)) + for i in range(sides)] + + +def polygon_halfplanes(polygon: list[Vec2]) -> list[tuple[float, float, float]]: + """CCW 多边形 -> 外法线半平面列表 (a, b, c)，含义 a·x + b·y <= c。""" + planes = [] + count = len(polygon) + for index in range(count): + p, q = polygon[index], polygon[(index + 1) % count] + dx, dy = q[0] - p[0], q[1] - p[1] + norm = math.hypot(dx, dy) + if norm <= 1e-12: + continue + a, b = dy / norm, -dx / norm # CCW 的右法线朝外 + planes.append((a, b, a * p[0] + b * p[1])) + return planes + + +def clip_halfplane(polygon: list[Vec2], a: float, b: float, c: float, + tol: float = _CLIP_TOL_M) -> list[Vec2]: + """Sutherland–Hodgman 凸多边形半平面裁剪，保留 a·x + b·y <= c + tol。 + + 边界交点取在无容差直线上；进入判定带正容差，保证"贴边"的真点不丢。 + """ + if not polygon: + return [] + output: list[Vec2] = [] + count = len(polygon) + for index in range(count): + p, q = polygon[index], polygon[(index + 1) % count] + fp = a * p[0] + b * p[1] - c + fq = a * q[0] + b * q[1] - c + p_in, q_in = fp <= tol, fq <= tol + if p_in: + output.append(p) + if p_in != q_in: + ratio = fp / (fp - fq) + output.append((p[0] + ratio * (q[0] - p[0]), + p[1] + ratio * (q[1] - p[1]))) + return _dedupe(output) + + +def _dedupe(points: list[Vec2], tol: float = _DEDUPE_TOL_M) -> list[Vec2]: + unique: list[Vec2] = [] + for point in points: + if not unique or math.dist(point, unique[-1]) > tol: + unique.append(point) + if len(unique) > 1 and math.dist(unique[0], unique[-1]) <= tol: + unique.pop() + return unique + + +class CandidateRegion: + """某频道候选集合的保守凸外包多边形（顶点按 CCW；允许退化为 1-2 点）。""" + + def __init__(self, polygon: list[Vec2], slack_m: float = 0.0): + self.polygon = list(polygon) + self.slack_m = float(slack_m) # 外包近似引入的半径向误差记账 + self._mec: tuple[Vec2, float] | None = None + + # ------------------------------------------------------------ 构造 + @classmethod + def disk(cls, center: Vec2, radius_m: float, sides: int, + slack_m: float | None = None) -> "CandidateRegion": + if slack_m is None: + slack_m = radius_m * (1 - math.cos(math.pi / sides)) + return cls(circumscribed_polygon(center, radius_m, sides), slack_m) + + @classmethod + def initial(cls, station: Vec2, config: ProblemConfig) -> "CandidateRegion": + """首个 direction 后的基础集：Ω (*@\ensuremath{\cap}@*) B(station, r_max) 的保守外包。""" + field_cfg, sides = config.field, config.search.polygon_sides + slack = field_cfg.omega_radius_m * (1 - math.cos(math.pi / sides)) + region = cls.disk((0.0, 0.0), field_cfg.omega_radius_m, sides, slack) + region.clip_disk(station, field_cfg.r_eff_max_m, sides) + return region + + # ------------------------------------------------------------ 收缩 + def _clip(self, a: float, b: float, c: float) -> None: + polygon = clip_halfplane(self.polygon, a, b, c) + if not polygon: + raise InconsistentBelief( + f"候选区域被半平面 ({a:.6f},{b:.6f},{c:.6f}) 剪空：读数与保守集矛盾") + self.polygon = polygon + self._mec = None + + def clip_disk(self, center: Vec2, radius_m: float, sides: int) -> None: + """与圆盘 B(center, radius) 的外切多边形求交（近似误差入账）。""" + for a, b, c in polygon_halfplanes(circumscribed_polygon(center, radius_m, sides)): + self._clip(a, b, c) + self.slack_m += radius_m * (1 - math.cos(math.pi / sides)) + + def clip_wedge(self, station: Vec2, bearing_deg: float, + half_angle_deg: float) -> None: + """与测向角域 W(station, bearing±half_angle) 求交（半角须 <90°）。 + + 两个边界半平面与 localization.halfplanes 同口径，0°/360° 跨界由 + sin/cos 直接处理，无需分支。 + """ + if not 0 < half_angle_deg < 90: + raise ValueError("角域半角须在 (0, 90) 度") + lower = math.radians(bearing_deg - half_angle_deg) + upper = math.radians(bearing_deg + half_angle_deg) + sx, sy = float(station[0]), float(station[1]) + self._clip(math.sin(lower), -math.cos(lower), + math.sin(lower) * sx - math.cos(lower) * sy) + self._clip(-math.sin(upper), math.cos(upper), + -math.sin(upper) * sx + math.cos(upper) * sy) + + # ------------------------------------------------------------ 查询 + def mec(self) -> tuple[Vec2, float]: + """最小包围圆（圆心, 半径）。半径是真实候选集 (*@\ensuremath{\rho}@*) 的上界。""" + if self._mec is None: + if not self.polygon: + raise InconsistentBelief("候选区域为空") + self._mec = smallest_enclosing_circle(self.polygon) + return self._mec + + def witnesses(self, spacing_m: float) -> list[Vec2]: + """顶点 + 边界按间距细分的采样点（最坏后验评估用）。""" + if len(self.polygon) < 3: + return list(self.polygon) + points = list(self.polygon) + count = len(self.polygon) + for index in range(count): + p, q = self.polygon[index], self.polygon[(index + 1) % count] + length = math.dist(p, q) + steps = int(length // spacing_m) + for k in range(1, steps + 1): + ratio = k / (steps + 1) + points.append((p[0] + ratio * (q[0] - p[0]), + p[1] + ratio * (q[1] - p[1]))) + return _dedupe(points, tol=1e-9) + + def contains(self, point: Vec2, tol_m: float = 0.05) -> bool: + """点是否在候选集内（带容差；用于真源保留性检验，不做删点依据）。""" + if not self.polygon: + return False + if len(self.polygon) == 1: + return math.dist(point, self.polygon[0]) <= tol_m + self.slack_m + if len(self.polygon) == 2: + p, q = self.polygon + return _point_segment_distance(point, p, q) <= tol_m + self.slack_m + for index, p in enumerate(self.polygon): + q = self.polygon[(index + 1) % len(self.polygon)] + if (q[0] - p[0]) * (point[1] - p[1]) - (q[1] - p[1]) * (point[0] - p[0]) \ + < -tol_m - self.slack_m: + return False + return True + + +def _point_segment_distance(point: Vec2, p: Vec2, q: Vec2) -> float: + vx, vy = q[0] - p[0], q[1] - p[1] + length_sq = vx * vx + vy * vy + if length_sq <= 1e-18: + return math.dist(point, p) + t = max(0.0, min(1.0, ((point[0] - p[0]) * vx + (point[1] - p[1]) * vy) / length_sq)) + return math.dist(point, (p[0] + t * vx, p[1] + t * vy)) + + +@dataclass +class ChannelBelief: + channel: int + status: ChannelStatus = ChannelStatus.UNKNOWN + region: CandidateRegion | None = None + measurements: list = field(default_factory=list) # 逐步观测记录（审计用） + + +class BeliefState: + """全部 20 个频道的信念集合。策略端唯一的事实来源。""" + + def __init__(self, config: ProblemConfig = ProblemConfig()): + self.config = config + self.channels = {channel: ChannelBelief(channel) + for channel in range(config.field.channel_min, + config.field.channel_max + 1)} + + @property + def effective_half_angle_deg(self) -> float: + """示向度误差半角 + 舍入裕量：服务器保留两位小数引入 (*@\ensuremath{\le}@*)0.005° 偏差。""" + return (self.config.field.bearing_error_half_deg + + self.config.search.bearing_rounding_margin_deg) + + def update_measure(self, channel: int, position: Vec2, result: str, + svd_deg: float | None) -> None: + """按读数收敛候选集合；真源保留性由保守表示保证。""" + belief = self.channels[channel] + belief.measurements.append({"position": tuple(position), "result": result, + "svd_deg": svd_deg}) + if result == DIRECTION: + if svd_deg is None: + raise ValueError("direction 读数必须携带 svd_deg") + sides = self.config.search.polygon_sides + if belief.region is None: + belief.region = CandidateRegion.initial(position, self.config) + else: + # 后续 direction 同样隐含距离 <= r_max [题面] + belief.region.clip_disk(position, self.config.field.r_eff_max_m, sides) + belief.region.clip_wedge(position, svd_deg, self.effective_half_angle_deg) + belief.status = ChannelStatus.DETECTED + elif result == NEAR: + sides = self.config.search.polygon_sides + if belief.region is None: + belief.region = CandidateRegion.disk( + tuple(position), self.config.field.near_radius_m, sides) + else: + belief.region.clip_disk(position, self.config.field.near_radius_m, sides) + belief.status = ChannelStatus.DETECTED + elif result == NO_SIGNAL: + # P3/P4 基线：不据此删空间候选（缺席证明由覆盖账本给出）。 + pass + else: + raise ValueError(f"未知测向结果: {result!r}") + + def candidate_set(self, channel: int) -> CandidateRegion | None: + """该频道当前候选集合（保守外包形式）；尚无 direction/near 时为 None。""" + return self.channels[channel].region + + def mark_cleared(self, channel: int) -> None: + self.channels[channel].status = ChannelStatus.CLEARED + + def mark_absent(self, channel: int) -> None: + self.channels[channel].status = ChannelStatus.ABSENT + + def channels_by_status(self, *statuses: ChannelStatus) -> list[int]: + return sorted(channel for channel, belief in self.channels.items() + if belief.status in statuses) diff --git a/docs/paper/data/listing-source/src/mcm26b/belief/joint.py.tex b/docs/paper/data/listing-source/src/mcm26b/belief/joint.py.tex new file mode 100644 index 0000000..320acb5 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/belief/joint.py.tex @@ -0,0 +1,388 @@ +"""位置×朝向联合可行集（第四问定向源）。 + +现状问题（docs/第三四问架构优化与运行提速方案.md §1.3 F3）：第四问的失败**全部** +来自定向源（评测机两局：全向 17/17 清除，定向仅 2/6）。原因不是覆盖不足，而是 +策略只知道"源可能在某个空间区域"，不知道"它朝着哪边"——于是选点只能靠固定 +45° 阶梯试探，一旦试探失败就退化到 (*@\ensuremath{\le}@*)400 格 20 m 盲清。 + +本模块把"看不看得见"变成可推理的量：为已在 Ω 上维护的网格幸存集 +（:class:`~mcm26b.particles.ChannelParticles`）附加每格 24 档朝向可行性掩码， +得到 (位置 × 朝向) 联合可行集。观测语义严格对齐评测机 +``referee.simulator._observe``： + +- 距离 > r_eff → no_signal；定向且源→读点方向与朝向夹角 > 90° → no_signal； +- 距离 (*@\ensuremath{\le}@*) 5 m → near（**仍需可见**：3 m 处背向的定向源同样返回 no_signal）； +- 其余 → direction（读数 = 源→读点方位 + 有界误差）。 + +更新规则（全部保守，只删"必然不可能"的格/档）： + +=============== ============================================ ================== +观测 位置 朝向 +=============== ============================================ ================== +``direction``@s 距离 (*@\ensuremath{\le}@*) 1500、角向 |gap| (*@\ensuremath{\le}@*) (*@\ensuremath{\delta}@*)_eff + 格裕量 必须**可能**覆盖 s +``near``@s 距离 (*@\ensuremath{\le}@*) 5 必须**可能**覆盖 s +``no_signal``@s **不删**（可能是朝向遮挡或距离不足） 必须**确定不**覆盖 s + （仅当整格必在 r_eff_min 内才约束朝向） +=============== ============================================ ================== + +阈值全部取保守侧，并计入**格内角裕量** +``asin(margin / max(dist − margin, 1))``（格内任一点相对格心方位偏差上界）： + +- "必须可能覆盖"：``gap (*@\ensuremath{\le}@*) 90° + 半档 + 查表舍入 + 格内角裕量``（宁可保留）； +- "必须确定不覆盖"：先删去 ``gap (*@\ensuremath{\le}@*) 90° − 半档 − 查表舍入 − 格内角裕量`` 的档， + 只保留确定看不见 s 的档（同样宁可保留）。 + +因此真源 (位置, 朝向) 永不被删——这是网格幸存集真源保留定理的二维推广。 +（2026-09-12 修正：no_signal 分支原先误用"确定覆盖"掩码做交集，等价于把 +规则反向；keep=True 分支也漏计了格内角裕量。两处都会删掉真源朝向档， +现由 ``tests/test_joint_belief.py`` 的随机观测序列保留性测试固化。） + +用途： +1. ``prob_detect``：该点能看见该频道任一可行 (位置, 朝向) 的概率质量， + 用于**可见性选点**（取代固定阶梯）——只影响选点顺序，不承担安全责任； +2. ``expected_posterior_radius``：一次测量后的期望后验 MEC 半径（D1 值函数）； +3. ``is_absent``：联合集空 (*@\ensuremath{\Longrightarrow}@*) 该频道不存在源（严格，与覆盖证明同一条件）； +4. 位置边际仍由凸证书负责 20 m 清除判定，本模块不改变任何证书口径。 +""" + +from __future__ import annotations + +import math + +from ..config import ProblemConfig, Vec2 +from ..particles import ChannelParticles, _branch_radius_array +from ..protocol.rules import DIRECTION, NEAR, NO_SIGNAL + +HEADING_BINS = 24 # 15° 一档 +_BIN_HALF_DEG = 180.0 / HEADING_BINS # 7.5° +_FULL_MASK = (1 << HEADING_BINS) - 1 +_GRID_DEG = 3.0 # 角度查表分辨率 +_GRID_N = int(round(360.0 / _GRID_DEG)) + +try: # numpy 仅作可选加速后端（与 particles 一致） + import numpy as _np + from ..particles import _np as _particles_np + if _particles_np is None: # MCM26B_NO_NUMPY 或缺失：强制纯 Python + _np = None +except Exception: # pragma: no cover - 环境无 numpy + _np = None + + +def heading_gap(a_deg: float, b_deg: float) -> float: + """两个朝向角的最小夹角（度）。""" + return abs((a_deg - b_deg + 180.0) % 360.0 - 180.0) + + +def _cover_mask(bearing_deg: float, half_deg: float) -> int: + """与该方位夹角不超过 ``half_deg`` 的朝向档掩码。""" + mask = 0 + for k in range(HEADING_BINS): + if heading_gap(360.0 * k / HEADING_BINS, bearing_deg) <= half_deg: + mask |= 1 << k + return mask + + +# 查表：以 bearing 为轴、半角 90° 的可见半平面。 +# - COVER：**可能**覆盖该方位（含半档与查表舍入的保守侧）； +# - SILENT：**确定**覆盖该方位（内缩半档与舍入）——离散对照表，供审计与 +# 文档比对；实际裁剪走 _cover_mask / _far_mask，因为还必须逐格计入 +# "格内角裕量"（格心到格内任一点的方位偏差上界），无法预先制表。 +_COVER_TABLE = tuple( + _cover_mask(_GRID_DEG * i, 90.0 + _BIN_HALF_DEG + _GRID_DEG / 2) + for i in range(_GRID_N)) +_SILENT_TABLE = tuple( + _cover_mask(_GRID_DEG * i, 90.0 - _BIN_HALF_DEG - _GRID_DEG / 2) + for i in range(_GRID_N)) + + +def _far_mask(bearing_deg: float, exclude_half_deg: float) -> int: + """与方位夹角**大于** ``exclude_half_deg`` 的朝向档掩码（no_signal 用）。 + + 与 :func:`_cover_mask` 互补：no_signal 只允许保留"确定看不见"的朝向档。 + """ + mask = 0 + for k in range(HEADING_BINS): + if heading_gap(360.0 * k / HEADING_BINS, bearing_deg) > exclude_half_deg: + mask |= 1 << k + return mask + +if _np is not None: # 12 位半字 popcount 查表（朝向掩码 24 位）与半平面查表数组 + _POP16 = _np.array([bin(value).count("1") for value in range(1 << 12)], + dtype=_np.int64) + _COVER_ARR = _np.array(_COVER_TABLE, dtype=_np.int64) +else: # pragma: no cover - 无 numpy 分支 + _POP16 = _COVER_ARR = None + + +def _popcount(mask: int) -> int: + return bin(mask).count("1") + + +def _table_index(bearing_deg: float) -> int: + return int(round((bearing_deg % 360.0) / _GRID_DEG)) % _GRID_N + + +class JointBelief: + """单频道 (位置 × 朝向) 联合可行集。""" + + def __init__(self, config: ProblemConfig = ProblemConfig()): + self.config = config + self.field = config.field + self.position = ChannelParticles(config) + self.masks: dict[int, int] = {} # 格索引 -> 朝向掩码（缺省为全档） + self._sample_cache: tuple[int, list[int]] | None = None + + # ------------------------------------------------------------ 查询 + def __len__(self) -> int: + return len(self.position) + + def is_absent(self) -> bool: + """联合集空 (*@\ensuremath{\Longrightarrow}@*) 该频道不存在源（真源保留定理的二维推广）。""" + return not self.position.alive + + def _mask(self, index: int) -> int: + return self.masks.get(index, _FULL_MASK) + + def sample(self, size: int = 256) -> list[int]: + """均匀抽样幸存格（评分用；证书始终用完整集合）。""" + cached = self._sample_cache + if cached is not None and cached[0] == self.position.version: + return cached[1] + alive = sorted(self.position.alive) + if len(alive) > size: + step = len(alive) / size + alive = [alive[int(k * step) % len(alive)] for k in range(size)] + self._sample_cache = (self.position.version, alive) + return alive + + def _mask_popcount(self, index: int) -> int: + return _popcount(self._mask(index)) + + def expected_posterior_radius(self, reader: Vec2, size: int | None = None) -> float: + """一次测量后的期望后验 MEC 半径（米）；D1 值函数。 + + 与 :meth:`ChannelParticles.expected_posterior_radius` 同族，差别只在 + no_signal 分支概率：定向源不仅会因距离 > r_eff 静默，还会因朝向遮挡 + 静默，因此 + + p_vis(p) = P(r_eff (*@\ensuremath{\ge}@*) |p−q|) × cover_ratio(p, q) + + 其中 ``cover_ratio`` 是该格朝向掩码中"可能覆盖 q 方位"的档位占比。 + 分支半径语义： + + - direction（可见，非 near）：读数为 q 处的方位 ±(*@\ensuremath{\delta}@*)，后验收缩到该方位 + 楔形与当前可行集之交，半径取幸存子采样的质心最大距离； + - no_signal：定向源的静默**不删空间候选**，位置后验半径保持当前值； + - near：后验为 5m 盘。 + + 返回值只用于**选点排序**，不参与任何安全判定；证书仍由凸/网格口径给出。 + """ + pf = self.position + if not pf.alive: + return 0.0 + if size is None: + size = self.config.bayes.score_subsample + indices = self.sample(max(2, size)) + if not indices: + return 0.0 + stride = max(len(indices) // max(self.config.bayes.mc_representatives, 1), 1) + representatives = indices[::stride] + if _np is not None: + return self._epr_vector(reader, indices, representatives) + return self._epr_python(reader, indices, representatives) # pragma: no cover + + def _epr_vector(self, reader: Vec2, indices: list[int], + representatives: list[int]) -> float: + pf = self.position + points = _np.array([pf.cell_center(index) for index in indices], dtype=float) + masks = _np.array([self._mask(index) for index in indices], dtype=_np.int64) + reps = _np.array([pf.cell_center(index) for index in representatives], + dtype=float) + rep_masks = _np.array([self._mask(index) for index in representatives], + dtype=_np.int64) + dx, dy = points[:, 0] - reader[0], points[:, 1] - reader[1] + dist = _np.hypot(dx, dy) + bearing = _np.degrees(_np.arctan2(dy, dx)) + rdx, rdy = reps[:, 0] - reader[0], reps[:, 1] - reader[1] + rdist = _np.hypot(rdx, rdy) + rbearing = _np.degrees(_np.arctan2(rdy, rdx)) + cover = _COVER_ARR[_np.round(_np.mod(rbearing, 360.0) / _GRID_DEG) + .astype(_np.int64) % _GRID_N] + visible_mask = rep_masks & cover + bits = (_POP16[visible_mask & 0xFFF] + + _POP16[(visible_mask >> 12) & 0xFFF]) + cover_ratio = bits / float(HEADING_BINS) + p_silent_range = _np.clip((rdist - self.field.r_eff_min_m) + / (self.field.r_eff_max_m + - self.field.r_eff_min_m), 0.0, 1.0) + p_vis = (1.0 - p_silent_range) * cover_ratio + p_ns = 1.0 - p_vis + gaps = _np.abs((bearing[None, :] - rbearing[:, None] + 180.0) % 360.0 - 180.0) + in_wedge = ((gaps <= self.config.field.bearing_error_half_deg + + self.config.search.bearing_rounding_margin_deg + 1e-9) + & (dist[None, :] <= self.field.r_eff_max_m + pf.margin_m)) + eps_radius = pf.spacing_m / 2.0 + radii = [] + for row in in_wedge: + member = points[row] + radii.append(_branch_radius_array(member) + if len(member) else eps_radius) + radii = _np.array(radii, dtype=float) + current = pf.mec()[1] + near = rdist <= self.field.near_radius_m + pf.margin_m + values = _np.where(near, self.field.near_radius_m + pf.margin_m, + p_ns * current + p_vis * radii) + return float(values.mean()) + + def _epr_python(self, reader: Vec2, indices: list[int], + representatives: list[int]) -> float: # pragma: no cover + """纯 Python 回退（与向量版逐分支同语义，供无 numpy 环境与对拍）。""" + pf = self.position + points = [pf.cell_center(index) for index in indices] + masks = [self._mask(index) for index in indices] + eps_radius = pf.spacing_m / 2.0 + current = pf.mec()[1] + half_angle = (self.config.field.bearing_error_half_deg + + self.config.search.bearing_rounding_margin_deg) + total = 0.0 + for rep_index in representatives: + rx, ry = pf.cell_center(rep_index) + distance = math.hypot(rx - reader[0], ry - reader[1]) + if distance <= self.field.near_radius_m + pf.margin_m: + total += self.field.near_radius_m + pf.margin_m + continue + reading = math.degrees(math.atan2(ry - reader[1], rx - reader[0])) + cover = _COVER_TABLE[_table_index(reading)] + bits = _popcount(self._mask(rep_index) & cover) + ratio = bits / float(HEADING_BINS) + if distance <= self.field.r_eff_min_m: + p_range = 1.0 + elif distance >= self.field.r_eff_max_m: + p_range = 0.0 + else: + p_range = ((self.field.r_eff_max_m - distance) + / (self.field.r_eff_max_m - self.field.r_eff_min_m)) + p_vis = p_range * ratio + members = [] + for point, mask in zip(points, masks): + if math.dist(point, reader) > self.field.r_eff_max_m + pf.margin_m: + continue + bearing = math.degrees(math.atan2(point[1] - reader[1], + point[0] - reader[0])) + if heading_gap(bearing, reading) <= half_angle + 1e-9: + members.append(point) + if members: + mx = sum(p[0] for p in members) / len(members) + my = sum(p[1] for p in members) / len(members) + radius = max(math.hypot(p[0] - mx, p[1] - my) for p in members) + else: + radius = eps_radius + total += (1.0 - p_vis) * current + p_vis * radius + return total / max(len(representatives), 1) + + + def prob_detect(self, reader: Vec2, size: int = 256) -> float: + """在 ``reader`` 处能看见任一可行 (位置, 朝向) 的概率质量（启发式）。 + + r_eff ~ U[1000, 1500] 解析积分；朝向按可行档位占比计权。 + 只用于选点排序，不参与任何安全判定。 + """ + cells = self.sample(size) + if not cells: + return 0.0 + total = 0.0 + span = self.field.r_eff_max_m - self.field.r_eff_min_m + for index in cells: + gx, gy = self.position.cell_center(index) + distance = math.hypot(reader[0] - gx, reader[1] - gy) + if distance > self.field.r_eff_max_m: + continue + if distance <= self.field.r_eff_min_m: + p_range = 1.0 + else: + p_range = (self.field.r_eff_max_m - distance) / span + if p_range <= 0.0: + continue + bearing = math.degrees(math.atan2(reader[1] - gy, reader[0] - gx)) + cover = _COVER_TABLE[_table_index(bearing)] + bits = bin(self._mask(index) & cover).count("1") + if bits: + total += p_range * bits / HEADING_BINS + return total / len(cells) + + # ------------------------------------------------------------ 观测更新 + def _apply_heading(self, station: Vec2, keep: bool, + within_m: float | None = None) -> None: + """按可见性约束裁剪朝向档（保守：只删"必然不可能"的档）。 + + ``keep=True``（direction / near）(*@\ensuremath{\Longrightarrow}@*) 朝向必须**可能**覆盖 station： + 保留与方位夹角 (*@\ensuremath{\le}@*) 90° + 半档 + 查表舍入 + 格内角裕量的档。 + + ``keep=False``（no_signal 且整格必在 r_eff_min 内）(*@\ensuremath{\Longrightarrow}@*) 朝向必须 + **确定不覆盖** station：只保留与方位夹角 > 90° − 半档 − 查表舍入 + − 格内角裕量的档。 + + ``格内角裕量 = asin(margin / max(dist − margin, 1))``：格内任一点 + 相对格心的方位偏差上界。两个方向都必须计入它，否则会误删真源的 + 朝向档（keep=True 漏计）或保留必然可见的档（keep=False 漏计）。 + """ + margin_m = self.position.margin_m + doomed: list[int] = [] + for index in self.position.alive: + gx, gy = self.position.cell_center(index) + dx, dy = station[0] - gx, station[1] - gy + distance = math.hypot(dx, dy) + if within_m is not None and distance > within_m: + continue + bearing = math.degrees(math.atan2(dy, dx)) + if distance <= margin_m + 1.0: + # 格贴测点：格内方位可指向任意方向，任何一侧都不可据此裁剪 + continue + angular_margin = math.degrees( + math.asin(min(0.9999, margin_m / (distance - margin_m)))) + if keep: + updated = self._mask(index) & _cover_mask( + bearing, 90.0 + _BIN_HALF_DEG + _GRID_DEG / 2 + angular_margin) + else: + updated = self._mask(index) & _far_mask( + bearing, 90.0 - _BIN_HALF_DEG - _GRID_DEG / 2 - angular_margin) + if updated == 0: + doomed.append(index) + self.masks.pop(index, None) + elif updated != _FULL_MASK: + self.masks[index] = updated + if doomed: + self.position.discard(doomed) + + def apply(self, station: Vec2, result: str, + svd_deg: float | None = None) -> None: + """按读数更新联合可行集（保守，真源 (位置, 朝向) 永不被删）。""" + if result == DIRECTION: + self.position.apply_measure(station, DIRECTION, svd_deg, + directional=True) + self._apply_heading(station, keep=True) + elif result == NEAR: + # near 同样要求可见（评测机先判朝向再判距离） + self.position.apply_measure(station, NEAR, directional=True) + self._apply_heading(station, keep=True) + elif result == NO_SIGNAL: + # 距离阈值必须取**保守侧**：只有"整格都必然落在 r_eff_min 圆盘内" + # 时，no_signal 才一定由朝向遮挡解释。格心到格内任一点 (*@\ensuremath{\le}@*) margin， + # 故阈值取 r_eff_min − margin；取 + margin 会把 1000~1010m 的模糊带 + # 也当成"必须不覆盖"，从而可能删掉真源的朝向档（破坏真源保留性）。 + self._apply_heading(station, keep=False, + within_m=max( + 0.0, self.field.r_eff_min_m + - self.position.margin_m)) + else: + raise ValueError(f"未知测向结果: {result!r}") + + # ------------------------------------------------------------ 诊断 + def summary(self) -> dict: + """联合集规模快照（写入策略 summary，供审计与论文复算）。""" + cells = self.sample(256) + bins = [bin(self._mask(index)).count("1") for index in cells] + return {"cells": len(self.position), + "sampled_mean_heading_bins": (round(sum(bins) / len(bins), 2) + if bins else 0.0), + "heading_bins_total": HEADING_BINS} diff --git a/docs/paper/data/listing-source/src/mcm26b/cli.py.tex b/docs/paper/data/listing-source/src/mcm26b/cli.py.tex new file mode 100644 index 0000000..fb71207 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/cli.py.tex @@ -0,0 +1,374 @@ +"""统一命令行入口：mcm26b <子命令>。 + +- q1 问题一角域交会求解（P2 已完工） +- sim-check 用评测机复现附件计时示例（P0 自检） +- run 闭环：发现—定位—清除—退出（--problem 3 全向 / 4 混合源； + --self-test 走独立评测机 referee） + +解耦约定：运行时代码零导入评测机；referee/harness 仅在 --self-test 与 +sim-check 分支内懒加载（测试侧 dev 依赖）。 +""" + +from __future__ import annotations + +import argparse +import json +import socket +import sys +import threading +import time +from dataclasses import replace +from pathlib import Path + +from .config import ProblemConfig +from .geometry.__main__ import main as q1_main +from .planner import DirectionalExtension, OmnidirectionalLoop +from .planner.bayes_loop import BayesLoop +from .planner.seven import SevenBatch +from .protocol.client import SimulatorClient +from .protocol.log import SessionLog +from .protocol.rules import EXIT_USER + +Q3_STRATEGIES = {"grid": OmnidirectionalLoop, "seven": SevenBatch, "bayes": BayesLoop} + + +def _load_referee(): + """懒加载独立评测机与测试侧适配层（运行时/正式对接不触发）。""" + from .harness import (LocalSimTransport, mixed_scene, random_omni_scene, + referee_spec) + from referee import LocalSimulator + return (LocalSimulator, LocalSimTransport, mixed_scene, random_omni_scene, + referee_spec) + + +def _referee_missing(): + print("未安装独立评测机包 referee（mcm26b-referee）。请先 `uv sync` 安装" + " dev 依赖，或 pip install mcm26b-referee；正式对接官方模拟器无需本包。", + file=sys.stderr) + return 2 + + +# ---------------------------------------------------------------- 一键本地评测 +def _port_free(port: int) -> bool: + with socket.socket(socket.AF_INET, socket.SOCK_STREAM) as probe: + probe.setsockopt(socket.SOL_SOCKET, socket.SO_REUSEADDR, 1) + try: + probe.bind(("127.0.0.1", port)) + return True + except OSError: + return False + + +def _any_free_port() -> int: + with socket.socket(socket.AF_INET, socket.SOCK_STREAM) as probe: + probe.bind(("127.0.0.1", 0)) + return probe.getsockname()[1] + + +def _acquire_port(name: str, requested: int) -> int: + """端口被占时积极询问：交互终端逐次询问（回车=自动改空闲端口）， + 非交互环境（脚本/CI）直接改用空闲端口并告知，绝不静默失败。""" + if _port_free(requested): + return requested + if sys.stdin.isatty(): + while True: + auto = _any_free_port() + try: + answer = input(f"[一键评测] {name}端口 {requested} 已被占用：" + f"回车改用空闲端口 {auto}，或输入其他端口：").strip() + except (EOFError, KeyboardInterrupt): + return auto + if not answer: + return auto + if answer.isdigit() and 1024 <= int(answer) <= 65535: + if _port_free(int(answer)): + return int(answer) + print(f"端口 {answer} 同样被占用，请再试。") + continue + print("请输入 1024..65535 的端口号，或直接回车让评测机自选。") + auto = _any_free_port() + print(f"[一键评测] {name}端口 {requested} 已被占用（非交互环境），" + f"自动改用空闲端口 {auto}。", file=sys.stderr) + return auto + + +def _start_local_judge(args): + """启动独立评测机（机器狗接口 + WebUI 回放）并确认开始一局演练。 + + 返回 (judge, session, action_port, ui_port)；失败返回 None（已打印原因）。 + """ + try: + from referee import Referee + from referee.server import ActionInterfaceServer + from referee.webui import WebUIServer + except ImportError: + _referee_missing() + return None + action_port = _acquire_port("机器狗接口", args.judge_port) + ui_port = None + judge = Referee(action_port=action_port, data_dir=Path(args.judge_data_dir)) + ActionInterfaceServer(judge) + if not args.judge_no_ui: + ui_port = _acquire_port("WebUI", args.judge_ui_port) + ui = WebUIServer(judge, ui_port) + threading.Thread(target=ui.serve_forever, daemon=True, + name="mcm26b-local-judge-ui").start() + module = f"q{args.problem}_practice" + session = judge.start(module, args.robot_id, seed=args.seed, + countdown_s=args.judge_countdown_s) + deadline = time.monotonic() + session.countdown_s + 10 + while session.phase == "countdown" and time.monotonic() < deadline: + time.sleep(0.05) + if session.phase != "open": + print("[一键评测] 评测机未能开放接口，已中止。", file=sys.stderr) + judge.abort() + return None + print(f"[一键评测] 案例编码 {session.case_code} · {session.module.title}" + f" · 接口 http://127.0.0.1:{action_port}") + if ui_port is not None: + print(f"[一键评测] WebUI http://127.0.0.1:{ui_port}" + f"（实时界面与\"回放\"Tab 逐步回看，数据目录 {args.judge_data_dir}）") + return judge, session, action_port, ui_port + + +def _settle_local_judge(judge, timeout_s: float = 3.0) -> None: + """等看门狗确认本局结束（/exit 后毫秒级）；仅超时才兜底手工中止。""" + deadline = time.monotonic() + timeout_s + while judge.session.phase != "finished" and time.monotonic() < deadline: + time.sleep(0.05) + if judge.session.phase != "finished": + judge.abort() + + +def _finish_local_judge(judge, session, summary: dict) -> None: + """等待评测机确认结束，把结束原因、真值统计与回放入口并入 summary。""" + _settle_local_judge(judge, timeout_s=10.0) + state = judge.snapshot() + truth_channels = sorted(s.channel for s in session.sources) + cleared = sorted(summary.get("cleared_channels", [])) + summary["local_judge"] = { + "case_code": session.case_code, + "module": session.module.title, + "end_reason": state.get("end_reason"), + "end_reason_text": state.get("end_reason_text"), + "virtual_time_s": state.get("virtual_time_s"), + "request_count": state.get("request_count"), + "truth": {"source_channels": truth_channels, + "source_count": len(truth_channels), + "omni_count": sum(1 for s in session.sources if not s.directional), + "directional_count": sum(1 for s in session.sources if s.directional)}, + "all_cleared": cleared == truth_channels, + "log": state.get("log"), + } + + +def _sim_check(args) -> int: + """附件1表2/附件2第10节计时示例：期望 105/111/194/199 秒。""" + try: + local_simulator, local_sim_transport, *_ = _load_referee() + except ImportError: + return _referee_missing() + simulator = local_simulator([], robot_id=args.robot_id) + client = SimulatorClient(args.robot_id, transport=local_sim_transport(simulator)) + client.enter() + steps = [] + steps.append(client.measure((300, 400), 1).virtual_time_s) # 移动500m+检测5s + steps.append(client.measure((300, 400), 2).virtual_time_s) # 换频道1s+检测5s + steps.append(client.clear((300, 0), 3).virtual_time_s) # 移动400m+未发现3s + steps.append(client.measure((300, 0), 2).virtual_time_s) # 原地检测频道2 + info = client.exit() + expected = [105, 111, 194, 199] + ok = [round(value, 6) for value in steps] == expected \ + and round(info.virtual_time_s, 6) == 199 and info.reason == EXIT_USER + print(json.dumps({"expected": expected, "got": steps, + "final_virtual_time_s": info.virtual_time_s, + "exit_reason": info.reason, "pass": ok}, + ensure_ascii=False)) + return 0 if ok else 1 + + +def _run(args) -> int: + """问题3/4闭环。 + + 三种对接方式：--local-judge 一键本地评测（自动起 referee 并对接）； + --self-test 内存回环自检（不占端口）；默认对接 --base-url 的模拟器 + （官方或本地 referee）。真值只存在于测试端入口，策略端仅见响应。 + + 实机预算：--self-test 时评测机按 --real-budget-s（默认 1800s）返回 + remaining_real_duration_s；其余方式以服务器 /enter 返回为准（题面 + 程序运行上限 20 分钟，不可延长）。 + """ + config = ProblemConfig() + session = replace(config.session, + base_url=args.base_url or config.session.base_url) + config = replace(config, + session=session, + search=replace(config.search, + bearing_rounding_margin_deg=args.bearing_margin_deg, + persistent_search=args.persistent)) + if args.persistent: + # 历史教训：一次官方演练在 persistent 复扫下把 98.84% 的虚拟时间 + # （346170 s）花在空复扫上。这里给出单轮上界，明确这是"扫到限时"模式。 + stations = 49 if args.problem == 4 else 7 + per_round = config.field.channel_max * stations * ( + config.cost.measure_s + config.cost.switch_s) + print(f"[警告] --persistent：找全后仍复扫未清除频道直到限时。" + f"单轮上界约 {per_round:.0f}s 虚拟时间" + f"（{config.field.channel_max} 频道 × {stations} 站点 × " + f"{config.cost.measure_s + config.cost.switch_s:.0f}s），" + f"且会持续多轮；成绩口径请保持默认（关闭）。", file=sys.stderr) + truth = None + transport = None + real_budget_s = None + judge = judge_session = None + if args.local_judge: + if args.self_test: + print("--local-judge 与 --self-test 不能同时使用。", file=sys.stderr) + return 2 + if args.base_url: + print("--local-judge 忽略 --base-url（接口地址由评测机自动分配）。", + file=sys.stderr) + started = _start_local_judge(args) + if started is None: + return 2 + judge, judge_session, action_port, _ui_port = started + config = replace(config, session=replace( + config.session, base_url=f"http://127.0.0.1:{action_port}")) + elif args.self_test: + try: + (local_simulator, local_sim_transport, + mixed_scene, random_omni_scene, referee_spec) = _load_referee() + except ImportError: + return _referee_missing() + real_budget_s = (args.real_budget_s if args.real_budget_s is not None + else config.session.self_test_real_budget_s) + config = replace(config, + field=replace(config.field, + max_real_duration_s=real_budget_s)) + if args.problem == 4: + sources = mixed_scene(seed=args.seed, count=args.sources, + directional=args.directional, config=config) + else: + sources = random_omni_scene(seed=args.seed, count=args.sources, + config=config) + truth = sorted(source.channel for source in sources) + simulator = local_simulator(sources, robot_id=args.robot_id, + spec=referee_spec(config, max_real_duration_s=real_budget_s), + stress_mode=True) + transport = local_sim_transport(simulator) + elif args.real_budget_s is not None: + print("--real-budget-s 仅在 --self-test 下生效；正式测试以服务器 " + "/enter 返回的 remaining_real_duration_s 为准。", file=sys.stderr) + log = SessionLog(path=Path(args.log)) if args.log else SessionLog() + client = SimulatorClient(args.robot_id, config=config, transport=transport, log=log) + if args.problem == 4: + strategy = "directional" + loop_cls = DirectionalExtension + else: + strategy = args.strategy + loop_cls = Q3_STRATEGIES[strategy] + try: + summary = loop_cls(client, config).run() + finally: + if judge is not None: + _settle_local_judge(judge) + summary["robot_id"] = args.robot_id + return _finalize_run(args, summary, strategy, truth=truth, judge=judge, + judge_session=judge_session, real_budget_s=real_budget_s) + + +def _finalize_run(args, summary, strategy, *, truth, judge, judge_session, + real_budget_s) -> int: + """补齐 summary 元信息、核对真值并输出；返回进程退出码。""" + summary["strategy"] = strategy + if real_budget_s is not None: + summary["self_test_real_budget_s"] = real_budget_s + if args.summary_steps is not None and len(summary.get("steps", [])) > args.summary_steps: + summary["steps"] = summary["steps"][:args.summary_steps] + summary["steps_truncated"] = True + all_cleared = None + if truth is not None: + # 仅测试端核对：清除集合是否与真值一致。 + all_cleared = sorted(summary["cleared_channels"]) == truth + summary["truth"] = {"source_channels": truth, + "source_count": len(truth), + "all_cleared": all_cleared} + if judge is not None: + _finish_local_judge(judge, judge_session, summary) + all_cleared = summary["local_judge"]["all_cleared"] + print(json.dumps(summary, ensure_ascii=False, indent=2)) + return 0 if summary["completed"] and (all_cleared is not False) else 1 + + +def main(argv=None) -> int: + parser = argparse.ArgumentParser(prog="mcm26b", description=__doc__) + parser.add_argument("--config", default="", + help="预留：覆盖 ProblemConfig 的 JSON 文件（参数化入口）") + subparsers = parser.add_subparsers(dest="command", required=True) + + q1 = subparsers.add_parser("q1", help="问题一角域交会求解") + q1.add_argument("input", type=str) + q1.add_argument("-o", "--output", type=str, default=None) + q1.add_argument("--rounding-margin-deg", type=float, default=0) + q1.set_defaults(func=lambda a: q1_main([a.input] + (["-o", a.output] if a.output else []) + + (["--rounding-margin-deg", str(a.rounding_margin_deg)] + if a.rounding_margin_deg else [])) or 0) + + check = subparsers.add_parser("sim-check", help="自建模拟器复现附件计时示例") + check.add_argument("--robot-id", default="2026001") + check.set_defaults(func=_sim_check) + + run = subparsers.add_parser("run", help="闭环：发现—定位—清除—退出（问题3/4）") + run.add_argument("--robot-id", required=True, help="登录参赛队号，逐字节一致") + run.add_argument("--base-url", default=None, + help="模拟器接口地址（默认取配置 http://127.0.0.1:2026）") + run.add_argument("--log", default=None, help="会话日志 JSONL 输出路径") + run.add_argument("--problem", type=int, choices=(3, 4), default=3, + help="问题3=全向源，问题4=混合定向源（默认 3）") + run.add_argument("--strategy", choices=tuple(Q3_STRATEGIES), default="bayes", + help="问题3策略：bayes=粒子滤波+信息增益+滚动调度（默认，" + "自建消融相对 seven 再降 19.5%%），seven=七点批量，" + "grid=49点网格基线；仅 --problem 3 生效") + run.add_argument("--bearing-margin-deg", type=float, default=0.005, + help="示向度舍入裕量（服务器保留两位小数；默认 0.005°）") + run.add_argument("--real-budget-s", type=float, default=None, + help="自检实机预算秒数（默认 1800=30 分钟；仅 --self-test 生效，" + "正式测试以服务器 /enter 返回为准）") + run.add_argument("--summary-steps", type=int, default=None, + help="summary 中保留的逐步计时条数上限（默认全部；完整明细在日志）") + run.add_argument("--persistent", action="store_true", + help="复扫保险模式：找全证明后继续复扫未清除频道直到限时" + "（默认关闭：虚拟时间即成绩口径，找全即 /exit）") + run.add_argument("--local-judge", action="store_true", + help="一键本地评测：自动启动独立评测机 referee（机器狗接口+" + "WebUI 实时/回放），确认开始一局演练并对接跑完整闭环；" + "端口被占时主动询问换端口（非交互环境自动改用空闲端口）") + run.add_argument("--judge-port", type=int, default=2026, + help="一键评测的机器狗接口端口（默认 2026；被占时询问/自选）") + run.add_argument("--judge-ui-port", type=int, default=8026, + help="一键评测的 WebUI 端口（默认 8026；被占时询问/自选）") + run.add_argument("--judge-no-ui", action="store_true", + help="一键评测不启动 WebUI（只保留机器狗接口）") + run.add_argument("--judge-countdown-s", type=float, default=5.0, + help="一键评测的确认开始倒计时秒数（题面默认 5 秒，可缩短加速）") + run.add_argument("--judge-data-dir", default="output/referee", + help="一键评测的会话日志目录（默认 output/referee，供 WebUI 回放）") + run.add_argument("--self-test", action="store_true", + help="走独立评测机 referee 与随机场景（测试端自检，不连官方）") + run.add_argument("--seed", type=int, default=20260910, help="自检场景种子") + run.add_argument("--sources", type=int, default=None, + help="自检源数量（默认按题面在 10~16 中随机）") + run.add_argument("--directional", type=int, default=3, + help="问题4自检场景中定向源数量（--problem 4 生效）") + run.set_defaults(func=_run) + + args = parser.parse_args(argv) + try: + return args.func(args) + except NotImplementedError as exc: + print(f"未实现: {exc}", file=sys.stderr) + return 2 + + +if __name__ == "__main__": + sys.exit(main()) diff --git a/docs/paper/data/listing-source/src/mcm26b/config.py.tex b/docs/paper/data/listing-source/src/mcm26b/config.py.tex new file mode 100644 index 0000000..d430286 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/config.py.tex @@ -0,0 +1,213 @@ +"""全项目参数中心：题面常量、协议限制、会话策略与搜索规划参数。 + +任何魔法数字只允许在这里出现一次。各模块通过 :class:`ProblemConfig` 读取； +命令行需要覆盖时用 ``dataclasses.replace`` 派生新配置，不散落字面量。 + +来源标注约定： +- ``[题面]`` 出自 issue/B题.pdf、附件1《模拟器使用说明》、附件2《通信接口说明》原文； +- ``[工程]`` 本队工程参数，可依演练实测调整，不代表官方规定。 +""" + +from __future__ import annotations + +from dataclasses import dataclass + +Vec2 = tuple[float, float] + + +@dataclass(frozen=True) +class FieldConfig: + """题目物理世界与协议硬限制。[题面]""" + + omega_radius_m: float = 1800.0 # 目标区域半径，圆心为原点 + channel_min: int = 1 # 有效频道范围 + channel_max: int = 20 + source_count_min: int = 10 # 一局源总数范围（接口不直接告知） + source_count_max: int = 16 + r_eff_min_m: float = 1000.0 # 有效接收半径下界：no_signal 只能排除该圆盘 + r_eff_max_m: float = 1500.0 # 有效接收半径上界：direction 隐含距离上界 + near_radius_m: float = 5.0 # "距离过近"阈值，不返回示向度 + clear_radius_m: float = 20.0 # 清除半径；与定向朝向无关 + bearing_error_half_deg: float = 1.0 # 示向度误差幅度（题设模型） + bearing_decimals: int = 2 # 返回示向度小数位 + coord_abs_limit_m: float = 2_000_000.0 # 提交坐标的绝对值上限（超出返回 HTTP 400） + directional_half_angle_deg: float = 90.0 # 定向源朝向两侧各90度覆盖（含边界） + max_virtual_duration_s: float = 360_000.0 # 虚拟世界限时（100小时） + max_real_duration_s: float = 1200.0 # /enter 成功后程序运行上限（20分钟） + test_window_s: float = 1500.0 # 确认开始后的测试窗口（25分钟） + + +@dataclass(frozen=True) +class CostConfig: + """虚拟世界动作耗时模型。[题面] 附件1表1、附件2第4节。""" + + speed_mps: float = 5.0 # 移动速度；耗时=直线距离/speed + measure_s: float = 5.0 # 每次检测动作耗时（无论结果） + switch_s: float = 1.0 # 任意两频道间切换耗时，仅由合法 /measure 触发 + clear_success_s: float = 5.0 # 清除成功耗时 = 光学定位3s + 激光清除2s + clear_fail_s: float = 3.0 # 未发现可清除目标 = 仅光学定位3s + + +@dataclass(frozen=True) +class SessionConfig: + """会话与网络策略。arena/robot/request 规则为 [题面]，其余为 [工程]。""" + + arena_id: str = "default" # [题面] 固定值 + base_url: str = "http://127.0.0.1:2026" # [题面] 模拟器默认接口地址 + robot_id_max_bytes: int = 64 # [题面] UTF-8 长度 1..64 + request_id_max_bytes: int = 128 # [题面] UTF-8 长度 1..128 + request_body_max_bytes: int = 65_536 # [题面] 超出返回 HTTP 413 + connect_timeout_s: float = 5.0 # [工程] 连接超时 + read_timeout_s: float = 15.0 # [工程] 读超时；覆盖"服务器已处理但响应丢失" + max_attempts: int = 3 # [工程] 单动作最多尝试次数（含首次） + retry_backoff_s: float = 0.25 # [工程] 重试退避基数，按 2^n 放大 + reserve_exit_s: float = 60.0 # [工程] 预留退出与故障恢复的现实秒数 + real_rtt_p95_s: float = 1.0 # [工程] 现实单请求高分位估计，预算核算用 + # [工程] 自检/演练实机预算：题面正式测试程序运行上限 1200s 不可延长； + # 自检经 --real-budget-s 覆盖 LocalSimulator 返回的 remaining_real_duration_s， + # 默认 1800s（30 分钟实机），用于验证"限时内持续运行直到找全"的行为。 + self_test_real_budget_s: float = 1800.0 + + +@dataclass(frozen=True) +class SearchConfig: + """搜索与覆盖规划参数。[工程] 推导依据见 docs/B题建模分析与实施计划.md。""" + + grid_step_m: float = 700.0 # P4 覆盖网格步长；单元对角 700*sqrt(2)(*@\ensuremath{\approx}@*)989.95<=1000 + grid_half_cells: int = 3 # i,j (*@\ensuremath{\in}@*) [-3,3]，49 点覆盖 [-2100,2100]^2 (*@\ensuremath{\supseteq}@*) Ω + fallback_clear_grid_m: float = 20.0 # P5 后备清除网格；10*sqrt(2)<=20 + # 舍入裕量：服务器对示向度保留两位小数，引入 <=0.005° 偏差 [题面]； + # 不加裕量时合法真源可能被角域裁掉，故库默认与 CLI run 默认一致取 0.005 [工程]。 + bearing_rounding_margin_deg: float = 0.005 + # ---- P3/P4 在线定位与闭环参数 [工程] ---- + polygon_sides: int = 192 # 圆盘外切多边形边数；Ω 近似误差 1800(1-cos((*@\ensuremath{\pi}@*)/192))(*@\ensuremath{\approx}@*)0.24m + witness_spacing_m: float = 60.0 # 最坏后验评估的边界采样间距；选定后再按 1/4 加密复核 + candidate_rings: tuple = (0.0, 0.4, 0.75, 1.0) # 安全接收盘内候选点的半径比例 + candidate_angles: int = 12 # 每环候选方向数 + clear_margin_m: float = 0.5 # 清除证书的额外工程余量（多边形近似误差之外） + max_localize_steps: int = 8 # 单频道定位阶段允许的追加测量上限 + max_anomalies_per_channel: int = 3 # 单频道异常记录上限，防止异常刷屏 + # ---- P5 定向扩展参数 [工程] ---- + max_blocked_probes: int = 4 # 定位单轮内被朝向遮挡的探点预算 + # （首次选点+对跖复核+2 次环探；达限转后备清除） + fallback_max_cells: int = 400 # 后备清除格数硬顶；超过则不盲扫（宽候选集继续定位） + # ---- 覆盖计划（保证层）[工程，2026-09-12 架构优化 P0-2 / S2 硬化] ---- + # 第四问发现点集： + # square49 旧的充分条件表（700m 方格，巡回 36.4km）； + # q4_mincover_v1 75m/24 档贪心最小集（31 点，巡回 22.9km）——细网格复检 + # 在 25m/48 档有 125 个 (p,h) 缺口，是采样过拟合解； + # q4_mincover_v2 **设计裕量**最小集（31 点，r_design=965m、前向角裕量 5°， + # 搜索分辨率 50m/48 档 + 证书分辨率精细剪枝）， + # 15m/72 档（325.6 万 (p,h)）缺口 0，最坏命中 990m，巡回 23.9km。 + # 运行期按同一采样语义复核，未通过即拒绝启动。 + q4_coverage_plan: str = "q4_mincover_v2" + verify_coverage_plan: bool = True # 运行期抽样校验（进程内缓存一次） + # ---- 第四问定向源联合信念 [工程，2026-09-12 架构优化 P0-3] ---- + # 为已发现的定向频道维护 (位置 × 朝向) 联合可行集：用可见性概率选点， + # 取代固定 45° 阶梯探点；联合集空即给出缺席证明。安全性仍由凸/网格 + # 清除证书与覆盖证明负责，本开关只影响选点顺序。 + directional_joint_belief: bool = True + # ---- 第四问定向源探点值函数 [工程，2026-09-12 图论与 DP 方案 S3/D1] ---- + # 旧评分 ``prob_detect/(移动+6)`` 只问"这点看不看得见源"，不问"测完剩多少 + # 不确定度"，会反复选中同一个近处被遮挡点。D1 口径：先按可见概率过滤 + # （只保留 prob_detect (*@\ensuremath{\ge}@*) ratio×最大值的候选），再最小化 + # E[后验 MEC 半径](q) + (*@\ensuremath{\lambda}@*)·(当前位置→q→MEC 圆心 的移动秒数 + 检测) + # 9 场景 core 配对（修正联合信念朝向规则之后）： + # (*@\ensuremath{\lambda}@*)=0.05：后备 6.8 次 / T 9740 s（值函数主导，为信息多绕路） + # (*@\ensuremath{\lambda}@*)=5 ：后备 4.3 次 / T 8604 s（移动项主导，可见性过滤 + 就近抵近） + # 仅移动项（nearest_visible）：后备 4.3 次 / T 8602 s，墙钟最低 + # 相对旧 visibility 口径（后备 125.6 次、T 9225 s）三者都更好，且 (*@\ensuremath{\lambda}@*) 越大 + # 越优说明本题"看得见 + 少走路"比"信息量最大"更重要，故默认取极限口径。 + probe_score_mode: str = "nearest_visible" # visibility | expected_radius | nearest_visible + probe_lambda_move_s: float = 5.0 # expected_radius 口径下的移动折算 + # 可见概率过滤：只保留 prob_detect (*@\ensuremath{\ge}@*) ratio×最大值的候选再比期望半径， + # 避免"期望上有点信息、实际必被朝向遮挡"的探点。 + probe_visibility_ratio: float = 0.7 + probe_exclude_blocked: bool = True # 已测过且被遮挡的探点不再重复选取 + approach_fractions: tuple = () # D1 抵近点插值比例（0=圆心）；默认关闭 + # ---- 后备清除路径优化 [工程，2026-09-12 S4/D3] ---- + # 实测反例：后备清除在命中真源时立即结束，"整条走格路径最短"并不是正确 + # 目标——Or-opt 会把真源推到序列更后面。9 场景配对：最近邻 125.7 次失败 + # vs Or-opt 161.4 次（T 8676 → 8940 s）。默认关闭，保留代码与开关。 + fallback_optimize_tour: bool = False + # ---- 持续搜索 [工程，2026-09-11 用户决策修订] ---- + # 虚拟时间即评测成绩口径（表1：平均定位清除时间）：找全证明达成后 + # 立即 /exit，不复扫。复扫保险模式（防缺席证明假设偏差）保留，经 + # `mcm26b run --persistent` 显式开启：只复扫未清除频道，直到清除数 + # 达 16、实机预算耗尽或虚拟安全余量不足。 + persistent_search: bool = False + virtual_reserve_s: float = 10_000.0 # 虚拟时长安全余量：剩余不足时停止发起动作， + # 避免触及 100 小时上限被模拟器强制结束 + + +@dataclass(frozen=True) +class BayesConfig: + """P4b 贝叶斯网格滤波策略参数（问题3新策略 bayes）。[工程] + + 网格粒子滤波的严格性依赖 Voronoi 裕量：真实源所在格心与源的距离 + <= sqrt(2)/2 * particle_spacing_m，所有 kill 判定都内缩该裕量， + 因此幸存集永远包含真源（定理见 docs/algo-3-bayes.md §2）。 + """ + + particle_spacing_m: float = 14.65 # 网格间距；Voronoi 裕量 (*@\ensuremath{\approx}@*) 10.35m； + # 全域约 4.7 万格/频道，查询走粗格索引 + # ---- 信息增益评分 [工程，Optuna TPE 调参回填 2026-09-11] ---- + # 原调参记录见 output/q3/bayes-tuning/；当前代码的配对验收记录见 + # output/q3/optimization-20260911/，随机分布与信息评分仅为工程假设。 + score_mode: str = "entropy" # entropy=期望 log 幸存占比（信息增益）| + # radius=期望后验半径（直指证书） + score_subsample: int = 800 # 期望幸存熵估计的粒子子采样规模 + mc_representatives: int = 7 # 假设真值代表点数（均匀抽取幸存格） + lambda_move_s: float = 0.05 # 选点评分中移动时间的折算系数（分值/秒）； + # 2026-09-12 配对复跑：0.05 优于 0.0105（20 场均值 −2.8%）， + # entropy 口径下信息项为 O(1) 对数值，(*@\ensuremath{\lambda}@*)须小型但不可过小 + # ---- 路线感知探点 [工程，2026-09-12 P2] ---- + # 旧评分只看 current->q + q->MEC，容易选到“信息增益略高但要多绕几百米” + # 的探点。开启后，在候选评分中加入 q 替换当前位置后对当前任务路线代价 + # 的增量；A/B 以冻结基准集配对验收。 + # 2026-09-12 冻结基准集复跑（18 场景）：关闭 3193.1 s vs 开启 3210.3 s， + # 移动 12339.8 m vs 12446.8 m —— 权重 1e-3 的路线项未带来净收益，默认关闭。 + route_aware_probe: bool = False + route_aware_insert_weight: float = 0.001 # 路线代价增量的折算系数（小权重，仅微调） + route_aware_clear_weight: float = 0.0 # 额外 q->MEC 清除接近项（基础移动项已含） + wide_rings: tuple = (1.0, 1.5, 2.0) # 无保证接收盘时的探索环（× PF MEC 半径） + # ---- 站点与覆盖 [工程] ---- + station_ring_radius_m: float = 1159.7 # 七点环半径；构造时检验全向覆盖解析上界 + # ---- 发现-定位融合巡回 [工程，2026-09-12 P0-1，实测无效，默认关闭] ---- + # 设想：站点扫频顺带取第二/第三条方位线，取代专用探点。 + # 实测（output/suite/q3-fuse-ab*，20 场景配对，2026-09-12）： + # 仅追加站点方位线：3454.6s vs 3426.9s（+0.8%，检测 +10.8 次，位移仅 −188m）； + # 追加 + 抑制专用探点：4989.0s vs 3426.9s（+45.6%，20/20 场景更慢）。 + # 原因：七站环上只有 2–3 个站能对同一源取得有效方位线，且站间交会角 + # 不足以保证 20m 证书，专用信息增益探点仍然必要；抑制探点只会白等巡回。 + # 代码保留以便复现与后续研究，成绩口径必须保持 False。 + fuse_localize_into_tour: bool = False + # ---- 任务排序 [工程] ---- + two_opt_enabled: bool = True # 开放路径 2-opt 改进（最近邻打底） + two_opt_passes: int = 4 # 2-opt 最大改进轮数 + # ---- 精确任务序（Held-Karp，含换频状态）[工程，2026-09-12 S5/T1] ---- + # 任务表典型 6–12 项：|T| (*@\ensuremath{\le}@*) exact_order_limit 时用精确 DP（状态=已访问集合 + # × 结束时测向频道），换频代价精确计入；否则回退 NN + 2-opt。0 表示禁用。 + # 实测（18 场景）：精确 DP 3203.2 s vs 2-opt 3193.1 s —— 逐位最优的"当前 + # 任务表"在滚动时域下反而略差（贪心排序的次优性起到探索作用），默认 0； + # 代码与对拍测试保留，可随时开启复核。 + exact_order_limit: int = 0 + # ---- PF 清除证书 [工程] ---- + grid_cert_enabled: bool = True # 允许用幸存集 MEC 颁发清除证书（凸证书之外） + opportunistic_measure: bool = True # 已停靠位置顺路交会；仍逐频道计费 + # 预测后验半径至少减少 (1−ratio) 才补测；0.5 优于 0.65（18 场景 3205.4 vs 3210.3 s） + opportunistic_radius_ratio: float = 0.5 + + +@dataclass(frozen=True) +class ProblemConfig: + """聚合配置。各模块函数的第一个默认参数，便于单测替换。""" + + field: FieldConfig = FieldConfig() + cost: CostConfig = CostConfig() + session: SessionConfig = SessionConfig() + search: SearchConfig = SearchConfig() + bayes: BayesConfig = BayesConfig() + + +DEFAULT_CONFIG = ProblemConfig() diff --git a/docs/paper/data/listing-source/src/mcm26b/coverage/__init__.py.tex b/docs/paper/data/listing-source/src/mcm26b/coverage/__init__.py.tex new file mode 100644 index 0000000..f4921cf --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/coverage/__init__.py.tex @@ -0,0 +1,56 @@ +"""P4 全域覆盖：49 点网格与逐频道覆盖记录。 + +覆盖基线（推导见 docs/B题建模分析与实施计划.md §4）： +S = {(700i, 700j) : i, j (*@\ensuremath{\in}@*) [-3,3]}，|S| = 49，覆盖 [-2100,2100]² (*@\ensuremath{\supseteq}@*) Ω， +且允许访问目标圆域外（边界朝外发射的定向源不漏）。 +单元内任意点到 4 顶点距离 <= 700·√2 (*@\ensuremath{\approx}@*) 989.95 <= 1000 <= 最小接收半径。 + +验收标准： +- "路过某点"不算"测过某频道"：必须按 (频道, 点) 二维记录； +- 已清除/已定位频道可跳过剩余点，但跳过原因必须留痕； +- 自适应跳点（P6）必须保留逐频道覆盖证据，否则不得启用。 +""" + +from __future__ import annotations + +from dataclasses import dataclass, field + +from ..config import ProblemConfig, Vec2 + + +def coverage_points(config: ProblemConfig = ProblemConfig()) -> list[Vec2]: + """49 点覆盖网格生成（纯几何，可独立测试）。""" + step = config.search.grid_step_m + half = config.search.grid_half_cells + return [(step * i, step * j) + for j in range(half, -half - 1, -1) + for i in range(-half, half + 1)] + + +@dataclass +class CoverageLedger: + """逐频道覆盖账本：(频道, 网格点) -> 是否已测。""" + + config: ProblemConfig = field(default_factory=ProblemConfig) + points: list[Vec2] = field(default_factory=coverage_points) + measured: set = field(default_factory=set) # {(channel, point_index)} + skipped: dict = field(default_factory=dict) # channel -> 原因 + + def mark_measured(self, channel: int, point_index: int) -> None: + self.measured.add((channel, point_index)) + + def measured_at(self, channel: int, point_index: int) -> bool: + return (channel, point_index) in self.measured + + def skip_channel(self, channel: int, reason: str) -> None: + """记录整频道跳过原因（如 already_cleared / located_pending_clear）。""" + self.skipped[channel] = reason + + def pending_points(self, channel: int) -> list[int]: + """该频道尚未测量的网格点下标。扫描调度策略未实现（P4）。""" + return [index for index in range(len(self.points)) + if not self.measured_at(channel, index)] + + def coverage_complete(self, channel: int) -> bool: + """该频道覆盖是否完成（含显式跳过）。""" + return channel in self.skipped or not self.pending_points(channel) diff --git a/docs/paper/data/listing-source/src/mcm26b/evaluation/__init__.py.tex b/docs/paper/data/listing-source/src/mcm26b/evaluation/__init__.py.tex new file mode 100644 index 0000000..2fb2ec8 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/evaluation/__init__.py.tex @@ -0,0 +1,85 @@ +"""评估与统计：从自身动作日志离线复算虚拟时刻与统计量。 + +"演练统计"验收要求：总时间与分项耗时可独立复算 [题面/计划 §6]。 +recompute_virtual_time 是回放测试与本模块共用的唯一复算实现， +客户端日志格式为 SessionLog 中 accepted 事件的 {path, request, response}。 +""" + +from __future__ import annotations + +from ..config import CostConfig +from ..protocol.rules import CLEAR_SUCCESS +from ..protocol.timing import clear_cost, measure_cost + + +def recompute_virtual_time(events: list[dict], + cost: CostConfig = CostConfig()) -> dict: + """从动作日志复算逐步虚拟时刻。 + + events 每项形如 {path, request, response}（accepted=true）。 + 返回逐步表与最终时刻；任何一步与服务器响应偏差超过容差记入 mismatches。 + """ + position = (0.0, 0.0) + channel = 1 + virtual = 0.0 + virtual_us = 0 + steps, mismatches = [], [] + for index, event in enumerate(events): + path, request = event["path"], event["request"] + response = event["response"] + if response.get("accepted") is not True: + mismatches.append({"index": index, "issue": "响应未被接受"}) + continue + if path == "/enter": + position, channel, virtual = (0.0, 0.0), 1, response["virtual_time_s"] + virtual_us = round(virtual * 1_000_000) + elif path == "/measure": + pos = (request["position"]["x"], request["position"]["y"]) + predicted = measure_cost(position, pos, channel, request["channel"], cost) + position, channel = pos, request["channel"] + virtual_us += predicted.total_us + virtual = virtual_us / 1_000_000 + elif path == "/clear": + pos = (request["position"]["x"], request["position"]["y"]) + success = response.get("clear_result") == CLEAR_SUCCESS + predicted = clear_cost(position, pos, success, cost) + position = pos + virtual_us += predicted.total_us + virtual = virtual_us / 1_000_000 + elif path == "/exit": + pass # /exit 不推进虚拟时钟 [题面] + else: + mismatches.append({"index": index, "issue": f"未知路径 {path}"}) + continue + delta = response["virtual_time_s"] - virtual + if abs(delta) > 1e-6: + mismatches.append({"index": index, "path": path, + "recomputed_s": virtual, + "recorded_s": response["virtual_time_s"], + "gap_s": delta}) + steps.append({"index": index, "path": path, + "predicted_s": round(virtual, 9), + "recorded_s": response["virtual_time_s"]}) + return {"steps": steps, "final_virtual_time_s": virtual, + "mismatches": mismatches} + + +def summarize(events: list[dict]) -> dict: + """动作计数摘要：检测/清除/移动距离等基础统计。""" + position = (0.0, 0.0) + measures, clears, cleared, distance_m = 0, 0, 0, 0.0 + for event in events: + request = event["request"] + if event["path"] in ("/measure", "/clear"): + pos = (request["position"]["x"], request["position"]["y"]) + distance_m += ((pos[0] - position[0]) ** 2 + + (pos[1] - position[1]) ** 2) ** 0.5 + position = pos + if event["path"] == "/measure": + measures += 1 + elif event["path"] == "/clear": + clears += 1 + if event["response"].get("clear_result") == CLEAR_SUCCESS: + cleared += 1 + return {"measures": measures, "clears": clears, "cleared": cleared, + "distance_m": distance_m} diff --git a/docs/paper/data/listing-source/src/mcm26b/geometry/__init__.py.tex b/docs/paper/data/listing-source/src/mcm26b/geometry/__init__.py.tex new file mode 100644 index 0000000..091e7e4 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/geometry/__init__.py.tex @@ -0,0 +1,9 @@ +"""P2 几何内核：B题问题一有界误差方位交会定位。仅用标准库，已完工。 + +问题二首次测向安全候选盘证书一并放在本包（planning 模块）。 +""" + +from .localization import Measurement, solve, smallest_enclosing_circle +from .planning import first_bearing_candidate_disk + +__all__ = ["Measurement", "solve", "smallest_enclosing_circle", "first_bearing_candidate_disk"] diff --git a/docs/paper/data/listing-source/src/mcm26b/geometry/__main__.py.tex b/docs/paper/data/listing-source/src/mcm26b/geometry/__main__.py.tex new file mode 100644 index 0000000..e43a5a2 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/geometry/__main__.py.tex @@ -0,0 +1,40 @@ +"""python -m mcm26b.geometry observations.json [-o result.json]""" + +import argparse +import json +from dataclasses import replace +from math import isfinite +from pathlib import Path +from .localization import Measurement, solve + + +def main(argv=None): + parser = argparse.ArgumentParser(description="B题问题一：角域交、直径与包围圆") + parser.add_argument("input", type=Path, help="包含measurements数组的JSON文件") + parser.add_argument("-o", "--output", type=Path) + parser.add_argument("--rounding-margin-deg", type=float, default=0, + help="额外误差半角，默认0；可显式设0.005进行舍入敏感性分析") + args = parser.parse_args(argv) + try: + source = json.loads(args.input.read_text(encoding="utf-8-sig")) + measurements = [Measurement(**row) for row in source["measurements"]] + if not isfinite(args.rounding_margin_deg) or args.rounding_margin_deg < 0: + raise ValueError("额外误差半角必须为有限非负数") + measurements = [replace(m, half_angle_deg=m.half_angle_deg+args.rounding_margin_deg) + for m in measurements] + result = solve(measurements) + result["error_policy"] = { + "additional_half_angle_deg": args.rounding_margin_deg, + "effective_half_angles_deg": [m.half_angle_deg for m in measurements], + } + except (ValueError, TypeError, KeyError, OSError) as exc: + parser.error(str(exc)) + text = json.dumps(result, ensure_ascii=False, indent=2, allow_nan=False) + if args.output: + args.output.parent.mkdir(parents=True, exist_ok=True) + args.output.write_text(text + "\n", encoding="utf-8") + print(text) + + +if __name__ == "__main__": + main() diff --git a/docs/paper/data/listing-source/src/mcm26b/geometry/localization.py.tex b/docs/paper/data/listing-source/src/mcm26b/geometry/localization.py.tex new file mode 100644 index 0000000..c7bfde8 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/geometry/localization.py.tex @@ -0,0 +1,289 @@ +"""Intersect forward bearing wedges without an artificial bounding box. + +All calculations are floating point with normalized station coordinates. +The reference algorithm deliberately favors auditability over asymptotic speed. +Near-parallel plane pairs are intersected instead of skipped (only exactly +parallel pairs are discarded), and the feasibility tolerance scales with the +candidate vertex magnitude, so legitimate far-away vertices of long thin +regions are never silently dropped. +""" + +from dataclasses import dataclass +from itertools import combinations +from math import cos, sin, radians, hypot, isfinite +from random import Random + +Point = tuple[float, float] +EPS = 1e-9 +PARALLEL_EPS = 1e-12 + + +@dataclass(frozen=True) +class Measurement: + x: float + y: float + bearing_deg: float + half_angle_deg: float = 1.0 + + def __post_init__(self): + values = (self.x, self.y, self.bearing_deg, self.half_angle_deg) + if any(isinstance(v, bool) or not isinstance(v, (int, float)) + or not isfinite(v) for v in values): + raise ValueError("坐标、示向度和误差半角必须是有限数值") + if not 0 <= self.half_angle_deg < 90: + raise ValueError("误差半角必须在 [0, 90) 度；题设为1度") + + +def cross(a: Point, b: Point) -> float: + return a[0] * b[1] - a[1] * b[0] + + +def distance(a: Point, b: Point) -> float: + return hypot(a[0] - b[0], a[1] - b[1]) + + +def halfplanes(m: Measurement) -> list[tuple[float, float, float]]: + """Return a*x+b*y<=c with unit normals, including the forward constraint.""" + theta = m.bearing_deg % 360 + lower, upper = radians(theta - m.half_angle_deg), radians(theta + m.half_angle_deg) + middle = radians(theta) + normals = [(sin(lower), -cos(lower)), (-sin(upper), cos(upper)), + (-cos(middle), -sin(middle))] + return [(a, b, a * m.x + b * m.y) for a, b in normals] + + +def convex_hull(points: list[Point], eps: float = EPS) -> list[Point]: + """Monotone chain, CCW, no repeated final vertex; retain segment endpoints.""" + ordered = sorted(points) + unique = [] + for p in ordered: + if not unique or distance(p, unique[-1]) > eps: + unique.append(p) + if len(unique) <= 2: + return unique + + def chain(seq): + out = [] + for p in seq: + while len(out) >= 2: + a = (out[-1][0] - out[-2][0], out[-1][1] - out[-2][1]) + b = (p[0] - out[-1][0], p[1] - out[-1][1]) + # Distance-to-line tolerance, not an unscaled area tolerance. + if cross(a, b) > eps * max(hypot(*a), hypot(*b), eps): + break + out.pop() + out.append(p) + return out + + return chain(unique)[:-1] + chain(reversed(unique))[:-1] + + +def diameter(points: list[Point]): + if not points: + raise ValueError("空点集没有本程序定义下的直径") + a = b = points[0] + value = 0.0 + for p, q in combinations(points, 2): + d = distance(p, q) + if d > value: + value, a, b = d, p, q + return value, (a, b) + + +def _circumcircle(a: Point, b: Point, c: Point): + u = (b[0] - a[0], b[1] - a[1]) + v = (c[0] - a[0], c[1] - a[1]) + det = 2 * cross(u, v) + if abs(det) <= PARALLEL_EPS * max(hypot(*u) * hypot(*v), 1e-300): + return None + uu, vv = u[0] ** 2 + u[1] ** 2, v[0] ** 2 + v[1] ** 2 + center = (a[0] + (uu * v[1] - vv * u[1]) / det, + a[1] + (u[0] * vv - v[0] * uu) / det) + return center, distance(center, a) + + +def _enclosing_circle_reference(points: list[Point], eps: float = EPS): + """Enumerate all 1/2/3-point supports; O(m^4), appropriate for small m. + + Radius is recomputed against every vertex to preserve numerical containment. + Coordinates should be normalized when there are very large offsets. + """ + if not points: + raise ValueError("空集不计算最小包围圆") + xs, ys = [p[0] for p in points], [p[1] for p in points] + best_c = ((min(xs) + max(xs)) / 2, (min(ys) + max(ys)) / 2) + best_r = max(distance(best_c, p) for p in points) + + def consider(center, radius): + nonlocal best_c, best_r + if radius > best_r + eps: + return + actual = max(distance(center, p) for p in points) + if actual <= radius + eps and actual < best_r: + best_c, best_r = center, actual + + for p in points: + consider(p, 0.0) + for a, b in combinations(points, 2): + consider(((a[0] + b[0]) / 2, (a[1] + b[1]) / 2), distance(a, b) / 2) + for a, b, c in combinations(points, 3): + circle = _circumcircle(a, b, c) + if circle is not None: + consider(*circle) + return best_c, best_r + + +def _circle_covers(circle, point: Point, tolerance: float) -> bool: + """Whether the circle already covers point; None means no circle yet.""" + if circle is None: + return False + return distance(circle[0], point) <= circle[1] + tolerance + + +def smallest_enclosing_circle(points: list[Point], eps: float = EPS): + """Welzl's randomized incremental algorithm, using an explicit call stack. + + The fixed shuffle makes results reproducible. Expected linear work refers + to randomized input order, not a worst-case guarantee for this fixed seed. + Normalize internally so this public helper also handles translated inputs. + The exhaustive reference is retained for independent regression comparisons. + """ + if not points: + raise ValueError("空集不计算最小包围圆") + if not isfinite(eps) or eps <= 0: + raise ValueError("eps必须为有限正数") + if any(len(p) != 2 or any(isinstance(x, bool) or not isinstance(x, (int, float)) + or not isfinite(x) for x in p) for p in points): + raise ValueError("点集必须由有限二维坐标组成") + origin = points[0] + scale = max(distance(origin, p) for p in points) + if scale == 0: + return tuple(origin), 0.0 + local = [((p[0]-origin[0])/scale, (p[1]-origin[1])/scale) for p in points] + tolerance = min(eps/scale, EPS) + Random(20260910).shuffle(local) + # Frame = (remaining prefix length, forced boundary, returning from child). + stack = [(len(local), (), False)] + circle = None + while stack: + n, boundary, returning = stack.pop() + if n == 0 or len(boundary) == 3: + # Forced support points must lie ON the boundary. For three points + # use their circumcircle, even when their unconstrained MEC is smaller. + circle = _circumcircle(*boundary) if len(boundary) == 3 else None + if circle is None and boundary: + circle = _enclosing_circle_reference(list(boundary), tolerance) + elif not returning: + stack.append((n, boundary, True)) + stack.append((n-1, boundary, False)) + elif not _circle_covers(circle, local[n-1], tolerance): + stack.append((n-1, boundary + (local[n-1],), False)) + assert circle is not None + center = (origin[0]+circle[0][0]*scale, origin[1]+circle[0][1]*scale) + # Recompute after transforming back: returned circle contains all input points + # to distance() precision, including any roundoff from the large translation. + return center, max(distance(center, p) for p in points) + + +def solve(measurements: list[Measurement], eps: float = EPS) -> dict: + """Solve Q1's pure angular intersection (no disk/range prior added). + + Nonempty intersections of <180-degree forward wedges are pointed polyhedra, + so they possess a vertex, even if unbounded. Feasibility follows from vertex + enumeration; unboundedness follows from a nonzero recession direction. + Empty diameter is null, unbounded diameter is null with diameter_infinite=true. + + Near-parallel plane pairs are intersected rather than skipped: their + intersection can be a legitimate vertex of a very long thin region + (e.g. stations 1cm apart with bearings 1 and 358.99999999999 deg give a + vertex ~5.7e10 m away). Only exactly-parallel pairs (det == 0) have no + intersection. The feasibility tolerance scales with the vertex magnitude, + since absolute residuals grow with coordinates. + """ + if not isfinite(eps) or eps <= 0: + raise ValueError("eps必须为有限正数") + if not measurements: + return {"status": "unbounded", "vertices": [], "diameter_m": None, + "diameter_infinite": True, "recession_direction": [1.0, 0.0], + "message": "没有观测，整个平面均可行"} + if len(measurements) > 100: + raise ValueError("参考实现最多接收100个检测点；更大规模应使用半平面交算法") + ox = sum(m.x for m in measurements) / len(measurements) + oy = sum(m.y for m in measurements) / len(measurements) + scale = max(1.0, max(hypot(m.x - ox, m.y - oy) for m in measurements)) + local = [Measurement((m.x - ox) / scale, (m.y - oy) / scale, + m.bearing_deg, m.half_angle_deg) for m in measurements] + planes = [h for m in local for h in halfplanes(m)] + + def inside(p): + tol = eps * max(1.0, abs(p[0]), abs(p[1])) + return all(a * p[0] + b * p[1] <= c + tol for a, b, c in planes) + + feasible_vertices = [] + for (a, b, c), (d, e, f) in combinations(planes, 2): + det = a * e - b * d + if det == 0.0: + continue # 精确平行：无交点（近平行对的交点是合法远端顶点，保留） + p = ((c * e - b * f) / det, (a * f - c * d) / det) + if isfinite(p[0]) and isfinite(p[1]) and inside(p): + feasible_vertices.append(p) + + if not feasible_vertices: + return {"status": "empty", "vertices": [], "diameter_m": None, + "diameter_infinite": False, "tolerance_m": eps * scale, + "message": "测向角域没有公共点；检查频道、数据及误差界"} + + # A nontrivial 2D recession cone has a ray tangent to an input halfplane. + # Use a much tighter angular threshold than the positional feasibility epsilon. + ray = None + for a, b, _ in planes: + for direction in ((b, -a), (-b, a)): + if all(d * direction[0] + e * direction[1] <= 2e-14 + for d, e, _ in planes): + ray = direction + break + if ray is not None: + break + + hull = convex_hull(feasible_vertices, eps) + + def world(p): + return [ox + p[0] * scale, oy + p[1] * scale] + + result = {"status": "unbounded" if ray else + ("point" if len(hull) == 1 else "segment" if len(hull) == 2 else "polygon"), + "vertices": [world(p) for p in hull], "tolerance_m": eps * scale, + "diameter_infinite": ray is not None} + if ray is not None: + result.update(diameter_m=None, recession_direction=list(ray), + message="存在非零衰退方向，区域无界，直径为无穷大") + return result + + d, pair = diameter(hull) + midpoint = ((pair[0][0] + pair[1][0]) / 2, (pair[0][1] + pair[1][1]) / 2) + distances = [distance(midpoint, p) for p in hull] + witness_index = max(range(len(hull)), key=distances.__getitem__) + max_distance = distances[witness_index] + center, radius = smallest_enclosing_circle(hull, eps) + area = abs(sum(cross(hull[i], hull[(i + 1) % len(hull)]) + for i in range(len(hull)))) / 2 + result.update(diameter_m=d * scale, diameter_pair=[world(p) for p in pair], + area_m2=area * scale ** 2, + diameter_circle={"center": world(midpoint), "radius_m": d * scale / 2, + "max_vertex_distance_m": max_distance * scale, + "covers": max_distance <= d / 2 + eps * 4, + "coverage_tolerance_m": 4 * eps * scale, + "max_excess_m": (max_distance-d/2) * scale, + "outside_vertex_indices": [i for i, value in enumerate(distances) + if value > d/2 + 4*eps], + "witness_vertex": world(hull[witness_index]) + if max_distance > d/2 + 4*eps else None}, + minimum_enclosing_circle={"center": world(center), "radius_m": radius * scale}, + guaranteed_clearable_at_mec_center=radius * scale <= 20 - eps * scale * 4, + clearance_certificate={"model": "angular_intersection_only", + "clear_radius_m": 20.0, + "numerical_margin_m": 4*eps*scale, + "radius_with_margin_m": (radius+4*eps)*scale, + "remaining_margin_m": 20-(radius+4*eps)*scale, + "center": world(center)}) + return result diff --git a/docs/paper/data/listing-source/src/mcm26b/geometry/planning.py.tex b/docs/paper/data/listing-source/src/mcm26b/geometry/planning.py.tex new file mode 100644 index 0000000..119894e --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/geometry/planning.py.tex @@ -0,0 +1,32 @@ +"""Distance certificates for Q2; does not change Q1's angular polygon model.""" + +from math import cos, sin, radians, isfinite +from .localization import Measurement + + +def first_bearing_candidate_disk(measurement: Measurement, + max_range_m: float = 1500, + guaranteed_range_m: float = 1000) -> dict: + """Enclose the entire truncated first-bearing sector, then erode its disk. + + For half-angle <=45 degrees the sector MEC has center distance and radius + a=R/(2*cos(delta)). Intersecting with Omega only shrinks the source set. + A missing sufficient disk is NOT proof that Q is empty. The certificate + guarantees distance only: directional transmitters may still be invisible. + """ + if any(isinstance(v, bool) or not isinstance(v, (int, float)) or not isfinite(v) + or v <= 0 for v in (max_range_m, guaranteed_range_m)): + raise ValueError("接收半径必须为有限正数") + if measurement.half_angle_deg > 45: + raise ValueError("此窄角域证书仅支持半角不超过45度；题设为1度") + delta, theta = radians(measurement.half_angle_deg), radians(measurement.bearing_deg % 360) + a = max_range_m/(2*cos(delta)) + center = [measurement.x+a*cos(theta), measurement.y+a*sin(theta)] + available = guaranteed_range_m-a + return {"source_model": "first_bearing_sector_with_range_upper_bound", + "sector_enclosing_circle": {"center": center, "radius_m": a}, + "sufficient_candidate_disk": {"center": center, "radius_m": available} + if available >= 0 else None, + "candidate_nonempty_certified": available >= 0, + "distance_only": True, + "max_range_m": max_range_m, "guaranteed_range_m": guaranteed_range_m} diff --git a/docs/paper/data/listing-source/src/mcm26b/guarantee/__init__.py.tex b/docs/paper/data/listing-source/src/mcm26b/guarantee/__init__.py.tex new file mode 100644 index 0000000..a81a843 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/guarantee/__init__.py.tex @@ -0,0 +1,23 @@ +"""保证层：覆盖计划（CoveragePlan）、证书与运行期校验。 + +对外只暴露覆盖计划与校验入口；`coverage` 包仍负责逐频道覆盖账本。 +""" + +from .cover import (CERTIFY_HEADINGS, CERTIFY_STEP_M, OMEGA_RADIUS_M, + R_EFF_MIN_M, CoverageCertificate, + CoveragePlan, PLAN_DIR, VERIFY_HEADINGS, VERIFY_STEP_M, + candidate_lattice, coverage_masks, forward_targets, + greedy_cover, load_plan, nn_tour_length, omega_positions, + plan_instance, plan_names, seven_plan, seven_points, + square_49_plan, verify_full_disk, verify_forward_half_disk, + verify_plan, write_plan) + +__all__ = [ + "CERTIFY_HEADINGS", "CERTIFY_STEP_M", "OMEGA_RADIUS_M", "R_EFF_MIN_M", + "CoverageCertificate", "CoveragePlan", + "PLAN_DIR", "VERIFY_HEADINGS", "VERIFY_STEP_M", "candidate_lattice", + "coverage_masks", "forward_targets", "greedy_cover", "load_plan", + "nn_tour_length", "omega_positions", "plan_instance", "plan_names", + "seven_plan", "seven_points", "square_49_plan", "verify_full_disk", + "verify_forward_half_disk", "verify_plan", "write_plan", +] diff --git a/docs/paper/data/listing-source/src/mcm26b/guarantee/cover.py.tex b/docs/paper/data/listing-source/src/mcm26b/guarantee/cover.py.tex new file mode 100644 index 0000000..736ead8 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/guarantee/cover.py.tex @@ -0,0 +1,428 @@ +"""保证层：可离线搜索、可在运行期校验的覆盖计划（CoveragePlan）。 + +两类覆盖语义（题面约束不同，绝不可混用）： + +- ``full_disk``（第三问，全向源）：在 s 处 no_signal 排除 B(s, r_eff_min)， + 因此"全点皆 no_signal (*@\ensuremath{\Longrightarrow}@*) 不存在源"要求 + ``(*@\ensuremath{\cup}@*) B(c, 1000) (*@\ensuremath{\supseteq}@*) Ω``。解析最优解是"原点 + 半径 r 的 6 等分环"， + ``r`` 的可行区间由 ``validate_seven_coverage`` 给出（本模块提供数值复核）。 +- ``forward_half_disk``（第四问，定向源）：源可能背向读点，no_signal 不再 + 排除整个圆盘，缺席证明要求 + ``(*@\ensuremath{\forall}@*)(p,h) (*@\ensuremath{\in}@*) Ω×S¹, (*@\ensuremath{\exists}@*)c (*@\ensuremath{\in}@*) S: |c−p| (*@\ensuremath{\le}@*) 1000 (*@\ensuremath{\wedge}@*) (c−p)·u(h) (*@\ensuremath{\ge}@*) 0``。 + 现役 700 m 方格 49 点是充分条件（单元对角 (*@\ensuremath{\le}@*) 1000），但远非必要； + 本模块用贪心击中集把点数压到 31，并在同一采样空间上校核。 + +设计原则（docs/第三四问架构优化与运行提速方案.md §2.3）： +**保证 = 离线搜索 + 运行期校验**。点表以 JSON 落盘并携带证书（采样分辨率、 +缺口数、最坏命中距离、生成参数哈希），运行期用同一套采样语义重新校核， +未通过即拒绝启动。证书只能用于选点优化，不改变任何安全性证明。 +""" + +from __future__ import annotations + +import hashlib +import json +import math +from dataclasses import dataclass, field, fields +from functools import lru_cache +from pathlib import Path + +from ..config import Vec2 + +PLAN_DIR = Path(__file__).resolve().parent / "plans" +R_EFF_MIN_M = 1000.0 # [题面] 最小有效接收半径 +OMEGA_RADIUS_M = 1800.0 # [题面] 目标圆域半径 +SPEED_MPS = 5.0 # [题面] 用于把巡回长度折算成虚拟移动秒数 + +# 采样分辨率。**校核必须与证书同分辨率**：更粗的采样会放过"删掉一个关键点 +# 仍然看似覆盖"的点集，使校核退化为装饰（实测 100 m/12 档即漏判）。 +# 75 m / 24 档下一次全域校核约 1 s，且按计划名缓存，每进程只付一次。 +CERTIFY_STEP_M = 75.0 +CERTIFY_HEADINGS = 24 +VERIFY_STEP_M = CERTIFY_STEP_M +VERIFY_HEADINGS = CERTIFY_HEADINGS + + +@dataclass(frozen=True) +class CoverageCertificate: + """覆盖证书：采样语义 + 缺口 + 最坏命中距离。""" + + kind: str # "full_disk" | "forward_half_disk" + target_step_m: float + headings: int + r_eff_min_m: float + targets: int + uncovered: int + worst_hit_distance_m: float + nn_tour_m: float + generator_sha256: str = "" + # 证书硬化：校核时使用的前向角裕量（度）。与 r_eff_min_m 的设计裕量 + # 一起把"采样格覆盖"提升为"连续空间覆盖"，见 verify_forward_half_disk。 + verify_heading_margin_deg: float = 0.0 + + @property + def valid(self) -> bool: + return self.uncovered == 0 and self.targets > 0 + + def as_dict(self) -> dict: + return {"kind": self.kind, "target_step_m": self.target_step_m, + "headings": self.headings, "r_eff_min_m": self.r_eff_min_m, + "targets": self.targets, "uncovered": self.uncovered, + "worst_hit_distance_m": round(self.worst_hit_distance_m, 3), + "nn_tour_m": round(self.nn_tour_m, 1), + "nn_tour_virtual_s": round(self.nn_tour_m / SPEED_MPS, 1), + "generator_sha256": self.generator_sha256, + "verify_heading_margin_deg": self.verify_heading_margin_deg} + + +@dataclass(frozen=True) +class CoveragePlan: + """一份覆盖计划：点集 + 语义 + 证书（可为解析证明）。""" + + name: str + problem: int + points: tuple[Vec2, ...] + kind: str # "analytic" | "certified" + coverage: str # "full_disk" | "forward_half_disk" + note: str = "" + certificate: CoverageCertificate | None = None + generator: dict = field(default_factory=dict) + + def __len__(self) -> int: + return len(self.points) + + def as_dict(self) -> dict: + return {"name": self.name, "problem": self.problem, "kind": self.kind, + "coverage": self.coverage, "note": self.note, + "generator": self.generator, + "certificate": (self.certificate.as_dict() + if self.certificate is not None else None), + "points": [[p[0], p[1]] for p in self.points]} + + +# --------------------------------------------------------------------- 采样 +def omega_positions(step_m: float) -> list[Vec2]: + """Ω 内均匀方格位置采样。""" + span = int(OMEGA_RADIUS_M / step_m) + 1 + return [(step_m * i, step_m * j) + for i in range(-span, span + 1) for j in range(-span, span + 1) + if (step_m * i) ** 2 + (step_m * j) ** 2 <= OMEGA_RADIUS_M ** 2] + + +def forward_targets(step_m: float, headings: int) -> list[tuple[float, float, float]]: + """(p, h) 目标采样：位置在 Ω 内，朝向均分整圆。""" + return [(x, y, 2.0 * math.pi * k / headings) + for (x, y) in omega_positions(step_m) for k in range(headings)] + + +def candidate_lattice(spacing_m: float, radius_m: float) -> list[Vec2]: + """半径 radius_m 圆盘内的方格候选点（离线搜索用）。""" + span = int(radius_m / spacing_m) + 1 + return [(spacing_m * i, spacing_m * j) + for i in range(-span, span + 1) for j in range(-span, span + 1) + if (spacing_m * i) ** 2 + (spacing_m * j) ** 2 <= radius_m ** 2] + + +def _bucket(points: list[Vec2], cell: float) -> dict[tuple[int, int], list[int]]: + table: dict[tuple[int, int], list[int]] = {} + for index, (x, y) in enumerate(points): + table.setdefault((int(x // cell), int(y // cell)), []).append(index) + return table + + +def coverage_masks(targets, candidates: list[Vec2], + r_eff: float = R_EFF_MIN_M, + heading_margin_deg: float = 0.0) -> list[int]: + """每个候选点覆盖的目标位掩码（Python 大整数，按位）。 + + 只在与候选点空间桶相邻的格内做距离/前向判定，避免 |T|·|C| 笛卡尔积。 + + ``r_eff`` / ``heading_margin_deg`` 是**设计裕量**：离线搜索时把"命中" + 定义得比物理要求更严（距离 (*@\ensuremath{\le}@*) r_eff、前向夹角 (*@\ensuremath{\le}@*) 90°−margin），使采样格 + 上的覆盖自动蕴含相邻未采样 (p,h) 也被覆盖（S2 证书硬化）。 + """ + table = _bucket(candidates, r_eff) + masks = [0] * len(candidates) + sin_margin = math.sin(math.radians(max(heading_margin_deg, 0.0))) + for t_index, (px, py, heading) in enumerate(targets): + ux, uy = math.cos(heading), math.sin(heading) + ci, cj = int(px // r_eff), int(py // r_eff) + bit = 1 << t_index + for di in (-1, 0, 1): + for dj in (-1, 0, 1): + for c_index in table.get((ci + di, cj + dj), ()): + cx, cy = candidates[c_index] + dx, dy = cx - px, cy - py + distance_sq = dx * dx + dy * dy + if distance_sq > r_eff * r_eff: + continue + if dx * ux + dy * uy < sin_margin * math.sqrt(distance_sq) - 1e-9: + continue + masks[c_index] |= bit + return masks + + +def greedy_cover(masks: list[int], n_targets: int) -> list[int]: + """贪心集合覆盖：每次取"新增覆盖目标数"最大的候选，返回索引表。""" + full = (1 << n_targets) - 1 + covered = 0 + chosen: list[int] = [] + remaining = list(range(len(masks))) + while covered != full and remaining: + best_index, best_gain = -1, 0 + for c_index in remaining: + gain = (masks[c_index] & ~covered).bit_count() + if gain > best_gain: + best_index, best_gain = c_index, gain + if best_index < 0: + break + chosen.append(best_index) + covered |= masks[best_index] + remaining.remove(best_index) + return chosen + + +def nn_tour_length(points: list[Vec2], start: Vec2 = (0.0, 0.0)) -> float: + """最近邻开放路径长度（巡回长度上界）。""" + remaining = list(points) + position = start + total = 0.0 + while remaining: + nxt = min(remaining, key=lambda q: (q[0] - position[0]) ** 2 + + (q[1] - position[1]) ** 2) + remaining.remove(nxt) + total += math.dist(position, nxt) + position = nxt + return total + + +# --------------------------------------------------------------------- 校验 +def _hit_distance(points: list[Vec2], position: Vec2, heading: float, + r_eff: float) -> float | None: + """最近的前向命中距离；没有任何前向命中点则返回 None。""" + ux, uy = math.cos(heading), math.sin(heading) + best = None + for (cx, cy) in points: + dx, dy = cx - position[0], cy - position[1] + if dx * dx + dy * dy > r_eff * r_eff: + continue + if dx * ux + dy * uy < -1e-9: + continue + distance = math.hypot(dx, dy) + if best is None or distance < best: + best = distance + return best + + +def _nearest_distance(points: list[Vec2], position: Vec2, + r_eff: float) -> float | None: + """最近距离（不要求前向）；超过 r_eff 视作未命中。""" + best = None + for (cx, cy) in points: + distance = math.hypot(cx - position[0], cy - position[1]) + if distance <= r_eff and (best is None or distance < best): + best = distance + return best + + +def verify_forward_half_disk(points: list[Vec2], step_m: float = VERIFY_STEP_M, + headings: int = VERIFY_HEADINGS, + r_eff: float = R_EFF_MIN_M, + heading_margin_deg: float = 0.0) -> CoverageCertificate: + """第四问语义：(*@\ensuremath{\forall}@*)(p,h) 存在前向半盘内的被访点。 + + ``heading_margin_deg`` 是**证书硬化**用的前向角裕量：把"命中"收紧为 + "前向夹角 (*@\ensuremath{\le}@*) 90° − margin"。与 ``r_eff`` 的设计裕量合用时，采样格上的 + 覆盖即可推出**连续空间**覆盖：真实 (p',h') 距采样格 (*@\ensuremath{\le}@*) step·√2/2、 + 方位差 (*@\ensuremath{\le}@*) 180/headings 度，只要 + + r_eff + step·√2/2 (*@\ensuremath{\le}@*) 1000 且 margin (*@\ensuremath{\ge}@*) 180/headings/2 + + 就能保证 |c−p'| (*@\ensuremath{\le}@*) 1000 且 (c−p')·u(h') (*@\ensuremath{\ge}@*) 0。这正是 S2 取代"粗采样 + 假通过"的方式。默认 0 表示按物理条件校核。 + """ + points = list(points) + targets = forward_targets(step_m, headings) + table = _bucket(points, r_eff) + missing, worst = 0, 0.0 + sin_margin = math.sin(math.radians(max(heading_margin_deg, 0.0))) + for (px, py, heading) in targets: + ux, uy = math.cos(heading), math.sin(heading) + ci, cj = int(px // r_eff), int(py // r_eff) + best = None + for di in (-1, 0, 1): + for dj in (-1, 0, 1): + for c_index in table.get((ci + di, cj + dj), ()): + cx, cy = points[c_index] + dx, dy = cx - px, cy - py + distance_sq = dx * dx + dy * dy + if distance_sq > r_eff * r_eff: + continue + if dx * ux + dy * uy < sin_margin * math.sqrt(distance_sq) - 1e-9: + continue + distance = math.sqrt(distance_sq) + if best is None or distance < best: + best = distance + if best is None: + missing += 1 + else: + worst = max(worst, best) + return CoverageCertificate("forward_half_disk", step_m, headings, r_eff, + len(targets), missing, worst, + nn_tour_length(points)) + + +def verify_full_disk(points: list[Vec2], step_m: float = VERIFY_STEP_M, + r_eff: float = R_EFF_MIN_M) -> CoverageCertificate: + """第三问语义：Ω 内每点都在某个被访点的 r_eff 圆盘内。""" + points = list(points) + positions = omega_positions(step_m) + table = _bucket(points, r_eff) + missing, worst = 0, 0.0 + for (px, py) in positions: + ci, cj = int(px // r_eff), int(py // r_eff) + best = None + for di in (-1, 0, 1): + for dj in (-1, 0, 1): + for c_index in table.get((ci + di, cj + dj), ()): + cx, cy = points[c_index] + distance = math.hypot(cx - px, cy - py) + if distance <= r_eff and (best is None or distance < best): + best = distance + if best is None: + missing += 1 + else: + worst = max(worst, best) + return CoverageCertificate("full_disk", step_m, 1, r_eff, len(positions), + missing, worst, nn_tour_length(points)) + + +def verify_plan(plan: CoveragePlan, step_m: float | None = None, + headings: int | None = None) -> CoverageCertificate: + """按计划声明的覆盖语义校核。 + + 默认使用**证书自带的采样分辨率**（离线 75 m / 24 档）：更粗的运行期采样 + 会放过"删掉一个关键点仍看似覆盖"的点集，使校核失去意义。校核按计划名 + 缓存（``load_plan`` 的 lru_cache），每进程只付一次成本。 + """ + certificate = plan.certificate + if step_m is None: + step_m = certificate.target_step_m if certificate else VERIFY_STEP_M + if headings is None: + headings = (certificate.headings if certificate + else VERIFY_HEADINGS) + if plan.coverage == "forward_half_disk": + # 硬化证书：按证书自带的距离/角度设计裕量重新校核（旧证书默认 + # r_eff=1000、margin=0，与历史口径逐位一致）。 + return verify_forward_half_disk( + plan.points, step_m, headings, + r_eff=(certificate.r_eff_min_m if certificate else R_EFF_MIN_M), + heading_margin_deg=(certificate.verify_heading_margin_deg + if certificate else 0.0)) + return verify_full_disk(plan.points, step_m, certificate.r_eff_min_m + if certificate else R_EFF_MIN_M) + + +# --------------------------------------------------------------------- 计划 +def seven_points(ring_radius_m: float) -> list[Vec2]: + """解析七站：原点 + 环上 6 等分点。""" + return [(0.0, 0.0)] + [(ring_radius_m * math.cos(k * math.pi / 3), + ring_radius_m * math.sin(k * math.pi / 3)) + for k in range(6)] + + +def seven_plan(ring_radius_m: float) -> CoveragePlan: + """第三问解析计划（覆盖证明由 validate_seven_coverage 给出）。""" + return CoveragePlan( + name=f"seven-r{ring_radius_m:.1f}", problem=3, kind="analytic", + coverage="full_disk", + note=("解析证明 max(r/√3, sqrt(R²+r²−√3Rr)) < 1000；" + "r(*@\ensuremath{\in}@*)[1122.9, 1732] 时成立，巡检半径越小巡回越短"), + points=tuple(seven_points(ring_radius_m))) + + +def square_49_plan() -> CoveragePlan: + """第四问旧计划：700 m 方格 49 点（充分条件，保留作回退与对照）。""" + return CoveragePlan( + name="square49", problem=4, kind="certified", + coverage="forward_half_disk", + note="单元对角 700√2(*@\ensuremath{\approx}@*)989.95(*@\ensuremath{\le}@*)1000 的充分条件；点数为最小命中集的 1.6 倍", + # 顺序与 coverage.coverage_points() 完全一致（y 由大到小），保持历史 + # 基线 grid49_immediate 的逐位可复现。 + points=tuple((700.0 * i, 700.0 * j) + for j in range(3, -4, -1) for i in range(-3, 4))) + + +def _load_plan_file(path: Path) -> CoveragePlan: + payload = json.loads(path.read_text(encoding="utf-8")) + raw_cert = payload.get("certificate") or {} + if raw_cert: + # as_dict() 含 nn_tour_virtual_s 等派生列：只取数据类实际字段。 + known = {field.name for field in fields(CoverageCertificate)} + certificate = CoverageCertificate( + **{key: value for key, value in raw_cert.items() if key in known}) + else: + certificate = None + return CoveragePlan( + name=payload["name"], problem=int(payload["problem"]), + kind=payload.get("kind", "certified"), + coverage=payload.get("coverage", "forward_half_disk"), + note=payload.get("note", ""), + certificate=certificate, + generator=payload.get("generator", {}), + points=tuple((float(x), float(y)) for x, y in payload["points"])) + + +@lru_cache(maxsize=None) +def load_plan(name: str, verify: bool = True) -> CoveragePlan: + """按名称加载覆盖计划；``verify`` 为真时做运行期抽样校验（进程内缓存）。""" + path = PLAN_DIR / f"{name}.json" + if not path.exists(): + raise FileNotFoundError(f"未找到覆盖计划 {name!r}（{path}）") + plan = _load_plan_file(path) + if verify and plan.kind == "certified": + certificate = verify_plan(plan) + if not certificate.valid: + raise ValueError( + f"覆盖计划 {name!r} 运行期校验失败：" + f"{certificate.uncovered}/{certificate.targets} 个 (p,h) 未被覆盖") + plan = CoveragePlan( + name=plan.name, problem=plan.problem, kind=plan.kind, + coverage=plan.coverage, note=plan.note, + generator=plan.generator, + certificate=CoverageCertificate( + kind=certificate.kind, target_step_m=certificate.target_step_m, + headings=certificate.headings, r_eff_min_m=certificate.r_eff_min_m, + targets=certificate.targets, uncovered=certificate.uncovered, + worst_hit_distance_m=certificate.worst_hit_distance_m, + nn_tour_m=certificate.nn_tour_m, + generator_sha256=(plan.certificate.generator_sha256 + if plan.certificate else "")), + points=plan.points) + return plan + + +def plan_instance(name: str, verify: bool = True) -> CoveragePlan: + """统一入口：支持内置计划名与磁盘上的证书计划。""" + if name == "square49": + return square_49_plan() + if name == "seven": + return seven_plan(1200.0) + return load_plan(name, verify) + + +def plan_names() -> list[str]: + """全部可加载的计划名（含内置）。""" + builtin = ["square49", "seven"] + return builtin + sorted(p.stem for p in PLAN_DIR.glob("*.json")) + + +def write_plan(plan: CoveragePlan, path: Path) -> None: + """落盘计划 + 证书（生成器用）。""" + path.parent.mkdir(parents=True, exist_ok=True) + payload = plan.as_dict() + payload["generator"] = dict(payload.get("generator") or {}) + payload["sha256"] = hashlib.sha256( + json.dumps(payload["points"]).encode("utf-8")).hexdigest() + path.write_text(json.dumps(payload, ensure_ascii=False, indent=2) + "\n", + encoding="utf-8") diff --git a/docs/paper/data/listing-source/src/mcm26b/harness/__init__.py.tex b/docs/paper/data/listing-source/src/mcm26b/harness/__init__.py.tex new file mode 100644 index 0000000..2e972b9 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/harness/__init__.py.tex @@ -0,0 +1,19 @@ +"""测试侧脚手架：把独立评测机（referee 包）接入本队传输与测试。 + +分层边界（与官方模拟器同构）： +- 评测机本体在独立包 ``referee``（零 mcm26b 依赖），运行时代码绝不导入它； +- 本包只在测试/自检入口把 referee 的接口边界适配成 :class:`Transport`， + 并提供故障注入与官方演练日志回放。 + +策略端只见 HTTP 响应；真值 Source 只存在于 referee 与测试端。 +""" + +from .playback import PlaybackTransport +from .scenes import mixed_scene, random_omni_scene, referee_spec +from .simulator import LocalSimulator +from .suites import SceneSpec, suite, suite_manifest +from .transport import LocalSimTransport, ScriptedFaultTransport + +__all__ = ["LocalSimTransport", "LocalSimulator", "PlaybackTransport", + "ScriptedFaultTransport", "SceneSpec", "mixed_scene", + "random_omni_scene", "referee_spec", "suite", "suite_manifest"] diff --git a/docs/paper/data/listing-source/src/mcm26b/harness/playback.py.tex b/docs/paper/data/listing-source/src/mcm26b/harness/playback.py.tex new file mode 100644 index 0000000..c5a2469 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/harness/playback.py.tex @@ -0,0 +1,38 @@ +"""回放传输：把既有演练日志作为服务器响应原样回放给客户端。 + +用于 P1 验收"本地状态机与官方响应一致"：官方演练记录 +（output/q1/practice/*_actions.json）逐条喂给客户端，客户端重建的 +状态必须与当时服务器返回的虚拟时刻逐步吻合。 + +按录制顺序匹配（客户端的 request_id 生成规则与采集器不同， +故不参与匹配；故障重试场景请用 ScriptedFaultTransport）。 +""" + +from __future__ import annotations + +import json +from urllib.parse import urlsplit + +from ..protocol.transport import Transport, TransportResponse + + +class PlaybackTransport(Transport): + """events: 演练日志 [{path, request, response, ...}, ...]。""" + + def __init__(self, events: list[dict]): + self.events = list(events) + self.index = 0 + self.served: list[dict] = [] + + def post(self, url, body, headers, timeout): + if self.index >= len(self.events): + raise AssertionError("回放日志已耗尽仍有请求") + event = self.events[self.index] + path = urlsplit(url).path + if path != event["path"]: + raise AssertionError( + f"回放顺序不一致: 客户端请求 {path}, 录制预期 {event['path']}") + self.index += 1 + self.served.append(event) + return TransportResponse( + 200, json.dumps(event["response"], ensure_ascii=False).encode("utf-8")) diff --git a/docs/paper/data/listing-source/src/mcm26b/harness/scenes.py.tex b/docs/paper/data/listing-source/src/mcm26b/harness/scenes.py.tex new file mode 100644 index 0000000..acf89c2 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/harness/scenes.py.tex @@ -0,0 +1,55 @@ +"""自检场景生成（测试端专用）：委托 referee.scenes，映射本队配置。 + +真值只进入测试与 CLI ``--self-test`` 入口，策略端仅见模拟器响应； +默认采用满足题面范围的自建随机场景：源总数 10~16 随机、位置在目标圆域内 +均匀分布、频道互异（1..20 抽样）、有效接收半径 [1000,1500] 均匀。 +均匀分布是测试假设，题面并未规定官方场景的概率分布。 +""" + +from __future__ import annotations + +from referee import scenes as _referee_scenes + +from ..config import ProblemConfig + + +def referee_spec(config: ProblemConfig = ProblemConfig(), *, + max_real_duration_s: float | None = None): + """把本队 ProblemConfig 的题面常量映射为 referee 的 Spec。 + + max_real_duration_s 仅用于 --self-test 的实机预算覆盖（默认 1800s）； + 正式对接以服务器 /enter 返回为准，评测机默认保持题面 1200s。 + """ + from referee import CostSpec, FieldSpec, Spec + field, cost = config.field, config.cost + return Spec( + field=FieldSpec( + omega_radius_m=field.omega_radius_m, + channel_min=field.channel_min, channel_max=field.channel_max, + source_count_min=field.source_count_min, + source_count_max=field.source_count_max, + r_eff_min_m=field.r_eff_min_m, r_eff_max_m=field.r_eff_max_m, + near_radius_m=field.near_radius_m, clear_radius_m=field.clear_radius_m, + bearing_error_half_deg=field.bearing_error_half_deg, + bearing_decimals=field.bearing_decimals, + coord_abs_limit_m=field.coord_abs_limit_m, + directional_half_angle_deg=field.directional_half_angle_deg, + max_virtual_duration_s=field.max_virtual_duration_s, + max_real_duration_s=(field.max_real_duration_s if max_real_duration_s is None + else max_real_duration_s), + test_window_s=field.test_window_s), + cost=CostSpec(speed_mps=cost.speed_mps, measure_s=cost.measure_s, + switch_s=cost.switch_s, clear_success_s=cost.clear_success_s, + clear_fail_s=cost.clear_fail_s)) + + +def random_omni_scene(seed: int = 20260910, count: int | None = None, + config: ProblemConfig = ProblemConfig()): + """全向源场景 [题面 问题3]；签名沿用重构前 mcm26b.sim.scenes。""" + return _referee_scenes.random_omni_scene(seed, count, referee_spec(config)) + + +def mixed_scene(seed: int = 20260910, count: int | None = None, + directional: int = 3, config: ProblemConfig = ProblemConfig()): + """问题4混合场景：count 个源中 directional 个为定向源。""" + return _referee_scenes.mixed_scene(seed, count, directional, referee_spec(config)) diff --git a/docs/paper/data/listing-source/src/mcm26b/harness/simulator.py.tex b/docs/paper/data/listing-source/src/mcm26b/harness/simulator.py.tex new file mode 100644 index 0000000..0c900ab --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/harness/simulator.py.tex @@ -0,0 +1,21 @@ +"""兼容构造入口：本队 ProblemConfig -> referee.LocalSimulator。 + +评测机实现在独立包 referee（config= 换成了 spec=）；本子类只做配置映射， +让既有测试与脚本继续以 ``config=ProblemConfig`` 构造，映射规则见 +:func:`harness.scenes.referee_spec`。真值类型 Source 亦来自 referee。 +""" + +from __future__ import annotations + +from referee import LocalSimulator as _RefereeLocalSimulator + +from ..config import ProblemConfig +from .scenes import referee_spec + + +class LocalSimulator(_RefereeLocalSimulator): + + def __init__(self, sources, *, robot_id: str = "2026001", + config: ProblemConfig = ProblemConfig(), **kwargs): + super().__init__(sources, robot_id=robot_id, + spec=referee_spec(config), **kwargs) diff --git a/docs/paper/data/listing-source/src/mcm26b/harness/suites.py.tex b/docs/paper/data/listing-source/src/mcm26b/harness/suites.py.tex new file mode 100644 index 0000000..0e2ba61 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/harness/suites.py.tex @@ -0,0 +1,132 @@ +"""冻结基准集：第三/四问的固定场景清单与真值构造（测试端专用）。 + +存在意义（docs/第三四问架构优化与运行提速方案.md §1.4 B6 / §P1-3）： +历史评估集是 20 个**单源全向**场景，使 `avg_locate_clear_time_s` 恒等于 +`virtual_time_s`，也无法支撑任何第四问结论。基准集必须覆盖题面声明的 +源数区间与定向源存在性，并且**版本化、可复现、不可随意增删**—— +任何"更快"的声明都要在同一份清单上做配对比较。 + +真值只在本模块与评测机之间流动；策略端只通过 Transport 看到响应。 +""" + +from __future__ import annotations + +import math +from dataclasses import dataclass + +from referee import Source + +from ..config import ProblemConfig +from .scenes import mixed_scene, random_omni_scene + +SUITE_VERSION = 1 + +# 第三问：沿用历史验证集的种子与源数（seeds 100–105 × 10/13/16） +Q3_SEEDS = (100, 101, 102, 103, 104, 105) +Q3_COUNTS = (10, 13, 16) +# 第四问：三种"定向占比"组成（少量 / 约半数 / 多数） +Q4_SEEDS = (200, 201, 202) +Q4_CONFIGS = ((10, 3), (13, 6), (16, 8)) +# 误差场种子偏移：与 benchmark_q3_bayes.py 同口径，保证逐点固定误差可复现 +ERROR_SEED_BASE = 20260910 + + +@dataclass(frozen=True) +class SceneSpec: + """一个冻结场景：标识、题号、源数、定向数与种子。""" + + scene_id: str + problem: int + kind: str # "random" | "boundary" + seed: int + error_seed: int + count: int + directional: int = 0 + + def as_dict(self) -> dict: + return {"scene_id": self.scene_id, "problem": self.problem, + "kind": self.kind, "seed": self.seed, + "error_seed": self.error_seed, "count": self.count, + "directional": self.directional} + + def sources(self, config: ProblemConfig | None = None) -> list[Source]: + """构造真值（仅测试端调用）。""" + config = config or ProblemConfig() + if self.kind == "random" and self.problem == 3: + return random_omni_scene(seed=self.seed, count=self.count, + config=config) + if self.kind == "random": + return mixed_scene(seed=self.seed, count=self.count, + directional=self.directional, config=config) + return _boundary_sources(self, config) + + +def _boundary_sources(spec: SceneSpec, config: ProblemConfig) -> list[Source]: + """圆周边界压力场景：源全部位于 Ω 边界、r_eff 取下界。 + + 第三问：全向，扇区接缝角度，检验七站覆盖的边界情形； + 第四问：全部定向且朝向**背离圆心**（最不利于发现），检验 + "朝外发射的边界源不漏"。 + """ + field = config.field + radius = field.omega_radius_m + sources: list[Source] = [] + for index in range(spec.count): + angle = math.pi / 6 + 2 * math.pi * index / spec.count + x, y = radius * math.cos(angle), radius * math.sin(angle) + directional = index < spec.directional + sources.append(Source( + channel=index + 1, x=x, y=y, r_eff_m=field.r_eff_min_m, + directional=directional, + heading_deg=(math.degrees(angle) % 360.0) if directional else 0.0)) + return sources + + +def core_scenes(problem: int) -> list[SceneSpec]: + """主体场景：覆盖题面源数区间与定向占比组成。""" + scenes: list[SceneSpec] = [] + if problem == 3: + for seed in Q3_SEEDS: + for count in Q3_COUNTS: + scenes.append(SceneSpec( + scene_id=f"q3-core-s{seed}-n{count}", problem=3, + kind="random", seed=seed, error_seed=ERROR_SEED_BASE + seed, + count=count)) + else: + for seed in Q4_SEEDS: + for count, directional in Q4_CONFIGS: + scenes.append(SceneSpec( + scene_id=f"q4-core-s{seed}-n{count}-d{directional}", + problem=4, kind="random", seed=seed, + error_seed=ERROR_SEED_BASE + seed, count=count, + directional=directional)) + return scenes + + +def boundary_scenes(problem: int) -> list[SceneSpec]: + """圆周边界压力场景（每问 2 场：10 源与 16 源）。""" + if problem == 3: + return [SceneSpec(f"q3-boundary-n{count}", 3, "boundary", 0, + ERROR_SEED_BASE, count) + for count in (10, 16)] + return [SceneSpec(f"q4-boundary-n{count}-d{directional}", 4, "boundary", 0, + ERROR_SEED_BASE, count, directional) + for count, directional in ((10, 5), (16, 8))] + + +def suite(name: str, problem: int) -> list[SceneSpec]: + """按名称取场景清单：core / boundary / all。""" + if name == "core": + return core_scenes(problem) + if name == "boundary": + return boundary_scenes(problem) + if name == "all": + return core_scenes(problem) + boundary_scenes(problem) + raise ValueError(f"未知基准集 {name!r}（可选 core/boundary/all）") + + +def suite_manifest(name: str, problem: int) -> dict: + """清单头：版本、问题、场景表（写入 manifest.json）。""" + scenes = suite(name, problem) + return {"suite_version": SUITE_VERSION, "suite": name, "problem": problem, + "scenes": [scene.as_dict() for scene in scenes]} diff --git a/docs/paper/data/listing-source/src/mcm26b/harness/transport.py.tex b/docs/paper/data/listing-source/src/mcm26b/harness/transport.py.tex new file mode 100644 index 0000000..08e6075 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/harness/transport.py.tex @@ -0,0 +1,62 @@ +"""传输适配：评测机接口边界 <-> 本队 Transport 接口 + 故障注入脚本。 + +LocalSimTransport 把 referee 包的 handle_raw（与 HTTP 服务器共用的同一 +边界实现）包成内存回环传输，不经过网络栈；故障注入语义与既有测试一致： +- ``"drop_before"`` 连接失败，动作未送达服务器（可安全重试）； +- ``"timeout_after"`` 服务器已受理并生效，但响应丢失（必须靠幂等回放）； +- ``("status", n)`` 服务器返回指定 HTTP 状态码（如 500/429）； +- ``None`` 正常放行。 +脚本耗尽后一律放行。 +""" + +from __future__ import annotations + +from urllib.parse import urlsplit + +from referee.interface import handle_raw + +from ..protocol.transport import Transport, TransportError, TransportResponse + + +class LocalSimTransport(Transport): + """内存回环：把独立评测机接到 Transport 接口（与真实 HTTP 同一边界）。""" + + def __init__(self, simulator): + # simulator: referee.LocalSimulator（类型注解走字符串，避免导入开销） + self.simulator = simulator + self.received: list[tuple[str, dict]] = [] + + def post(self, url, body, headers, timeout): + return self.request("POST", url, body, headers, timeout) + + def request(self, method, url, body, headers, _timeout=None): + """验证原始请求边界；内存回环不模拟 TCP、UI 或连接限流。""" + target = urlsplit(url) + raw_target = target.path + (f"?{target.query}" if target.query else "") + result = handle_raw(self.simulator, method, raw_target, + list(headers.items()), bytes(body), + on_request=lambda path, payload, _res: + self.received.append((path, payload))) + return TransportResponse(result.status, result.body) + + +class ScriptedFaultTransport(Transport): + """按脚本注入故障后转发给内层传输。""" + + def __init__(self, inner: Transport, script: list): + self.inner = inner + self.script = list(script) + self.sent_requests: list[bytes] = [] + + def post(self, url, body, headers, timeout): + self.sent_requests.append(body) + fault = self.script.pop(0) if self.script else None + if fault == "drop_before": + raise TransportError("injected: connection refused before send") + if fault == "timeout_after": + self.inner.post(url, body, headers, timeout) # 服务器已受理 + raise TransportError("injected: read timeout after server applied") + if isinstance(fault, tuple) and fault and fault[0] == "status": + body = b'{"accepted": false, "real_timestamp_ms": 0, "virtual_time_s": 0}' + return TransportResponse(int(fault[1]), body) + return self.inner.post(url, body, headers, timeout) diff --git a/docs/paper/data/listing-source/src/mcm26b/particles.py.tex b/docs/paper/data/listing-source/src/mcm26b/particles.py.tex new file mode 100644 index 0000000..69d44dd --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/particles.py.tex @@ -0,0 +1,458 @@ +"""P4b 贝叶斯网格粒子滤波：逐频道幸存集维护与负观测更新。 + +与 belief.CandidateRegion（保守凸外包，无法表达非凸"挖洞"）互补： +网格幸存集精确表达"角域 (*@\ensuremath{\cap}@*) 距离盘 (*@\ensuremath{\cap}@*) 全部 no_signal 排除盘"的非凸可行集， +从而支持三件凸表示做不到的事—— + +1. 缺席证明：幸存集为空 (*@\ensuremath{\Longrightarrow}@*) 可行集为空 (*@\ensuremath{\Longrightarrow}@*) 该频道无源（严格，无需覆盖账本）； +2. 跳测规则：幸存格到测点的最小距离 > r_max + 裕量 (*@\ensuremath{\Longrightarrow}@*) 该次测量必 no_signal， + 且不产生任何新排除，可直接跳过（省 5s 检测 + 1s 换频）； +3. 负观测更新：no_signal 排除 B(s, 1000)，凸表示不删点，网格直接删格。 + +严格性（真源保留定理，docs/algo-3-bayes.md §2）：格距 h 的 Voronoi 裕量 +m = sqrt(2)/2·h 是格心到格内任一点的最大距离。所有 kill 判定均内缩 m， +即"仅当整格与可行集不相交时才删格"。真源所在格与可行集之交含真源本身， +故该格永不被删——任意观测序列后幸存集恒包含真源，且： +- 清除证书：MEC(幸存).R + m <= 20 − 工程余量 (*@\ensuremath{\Longrightarrow}@*) 真源距清除点 <= 20； +- 缺席证明：幸存集为空 (*@\ensuremath{\Longrightarrow}@*) 可行集为空。 + +观测语义与独立评测机 referee.LocalSimulator 一致 [题面]： +- no_signal：距离 > r_eff >= 1000 (*@\ensuremath{\Longrightarrow}@*) 可行集 (*@\ensuremath{\cap}@*) B(s,1000) = (*@\ensuremath{\varnothing}@*)； +- direction：距离 <= 1500，示向度误差 |读数−真值| <= (*@\ensuremath{\delta}@*)_eff（含舍入裕量）； +- near：距离 <= 5。 + +性能设计：kill 与查询全部走 O(1) 集合运算；最近距离查询用粗粒度占用 +索引（每格聚合 CF² 个细格）螺旋扫描 + 早退，服务跳测规则的高频调用。 +""" + +from __future__ import annotations + +import math +import os + +from .config import ProblemConfig, Vec2 +from .geometry.localization import smallest_enclosing_circle +from .protocol.rules import DIRECTION, NEAR, NO_SIGNAL + +_ANG_EPS_DEG = 1e-9 # 角向 kill 比较的浮点余量 +_DIST_EPS_M = 1e-9 +_COARSE_FACTOR = 4 # 粗格每边聚合的细格数 + +try: # numpy 仅作**可选**加速后端；缺失时全部回退纯 Python + import numpy as _np +except Exception: # pragma: no cover - 环境无 numpy 时走纯 Python 分支 + _np = None +if os.environ.get("MCM26B_NO_NUMPY"): # 强制纯 Python：对拍与回退验证用 + _np = None + + +def angular_gap(a_deg: float, b_deg: float) -> float: + """两个方位角（度）的最小夹角。""" + return abs((a_deg - b_deg + 180.0) % 360.0 - 180.0) + + +def as_sample_array(samples): + """把 [(x,y), ...] 采样转成 (n,2) float64 数组；numpy 缺失时原样返回。 + + 评分为 O(代表点 × 子采样) 的向量运算，是单局 CPU 的主要开销 + （实测占 72%）。调用方在每次选点前转换一次，评分函数按类型分派， + 两条实现（numpy / 纯 Python）语义逐位对齐，见 tests/test_particles.py。 + """ + if _np is None or isinstance(samples, _np.ndarray) or len(samples) == 0: + return samples + return _np.asarray(samples, dtype=float) + + +def _branch_radius_array(members) -> float: + """分支后验半径的数组版：到质心的最大距离。""" + centroid = members.mean(axis=0) + return float(_np.max(_np.hypot(members[:, 0] - centroid[0], + members[:, 1] - centroid[1]))) + + +class ChannelParticles: + """单个频道的网格幸存集。 + + 网格为覆盖 Ω 外扩一格的轴对齐方格（边长 h），索引 ``i*W + j``； + ``alive`` 是幸存格索引集合。初始集 = 格心距原点 <= Ω 半径 + 裕量的 + 全部格子，因此真源（|p| <= 1800 [题面]）所在格必在初始集内。 + ``version`` 随每次删除自增，调用方可据此缓存派生量（MEC、跳测判定）。 + """ + + def __init__(self, config: ProblemConfig = ProblemConfig(), + spacing_m: float | None = None): + field = config.field + self.config = config + self.spacing_m = float(spacing_m if spacing_m is not None + else config.bayes.particle_spacing_m) + if not 1.0 <= self.spacing_m <= 200.0: + raise ValueError("网格间距须在 [1, 200] 米") + self.margin_m = self.spacing_m * math.sqrt(2) / 2 # Voronoi 裕量 + self.r_eff_min_m = field.r_eff_min_m + self.r_eff_max_m = field.r_eff_max_m + self.near_radius_m = field.near_radius_m + self.half_angle_deg = (field.bearing_error_half_deg + + config.search.bearing_rounding_margin_deg) + # 覆盖 [-R-m, R+m]² 的格点阵列；格 (i,j) 的中心在 + # (x0 + (i+0.5)h, x0 + (j+0.5)h)，中心到格内任一点 <= h·√2/2 = 裕量 + span = field.omega_radius_m + self.margin_m + self.x0 = -span + self.width = int(math.ceil(2 * span / self.spacing_m)) + 1 + limit_sq = (span + 1e-9) ** 2 + self.alive: set[int] = set() + self._coarse: dict[int, int] = {} # 粗格索引 -> 幸存细格数 + coarse_w = self._coarse_width() + for i in range(self.width): + x = self.x0 + (i + 0.5) * self.spacing_m + for j in range(self.width): + if x * x + (self.x0 + (j + 0.5) * self.spacing_m) ** 2 <= limit_sq: + index = i * self.width + j + self.alive.add(index) + key = (i // _COARSE_FACTOR) * coarse_w + j // _COARSE_FACTOR + self._coarse[key] = self._coarse.get(key, 0) + 1 + self.version = 0 + self._mec: tuple[Vec2, float] | None = None + + # ------------------------------------------------------------ 索引与坐标 + def _coarse_width(self) -> int: + return (self.width + _COARSE_FACTOR - 1) // _COARSE_FACTOR + + def cell_center(self, index: int) -> Vec2: + i, j = divmod(index, self.width) + return (self.x0 + (i + 0.5) * self.spacing_m, + self.x0 + (j + 0.5) * self.spacing_m) + + def discard(self, indices: list[int]) -> None: + """公开删除入口：联合信念把"朝向不可能"的格一并删除时使用。""" + self._discard(indices) + + def _discard(self, indices: list[int]) -> None: + if not indices: + return + coarse_w = self._coarse_width() + for index in indices: + if index not in self.alive: + continue + self.alive.discard(index) + key = (index // self.width // _COARSE_FACTOR) * coarse_w \ + + (index % self.width) // _COARSE_FACTOR + count = self._coarse.get(key, 0) - 1 + if count <= 0: + self._coarse.pop(key, None) + else: + self._coarse[key] = count + self.version += 1 + self._mec = None + + # ------------------------------------------------------------ 观测更新 + def _kill_disk(self, center: Vec2, radius_m: float) -> None: + """删除格心距 center <= radius_m 的全部幸存格（整格判据见模块注释）。""" + if not self.alive: + return + reach = radius_m + _DIST_EPS_M + ilo = max(0, int(math.floor((center[0] - reach - self.x0) / self.spacing_m))) + ihi = min(self.width - 1, + int(math.ceil((center[0] + reach - self.x0) / self.spacing_m))) + jlo = max(0, int(math.floor((center[1] - reach - self.x0) / self.spacing_m))) + jhi = min(self.width - 1, + int(math.ceil((center[1] + reach - self.x0) / self.spacing_m))) + limit_sq = reach * reach + doomed = [] + for i in range(ilo, ihi + 1): + dx = self.x0 + (i + 0.5) * self.spacing_m - center[0] + base = i * self.width + for j in range(jlo, jhi + 1): + index = base + j + if index not in self.alive: + continue + dy = self.x0 + (j + 0.5) * self.spacing_m - center[1] + if dx * dx + dy * dy <= limit_sq: + doomed.append(index) + self._discard(doomed) + + def _kill_outside_disk(self, center: Vec2, radius_m: float) -> None: + """删除格心距 center > radius_m 的全部幸存格（保留盘内）。""" + if not self.alive: + return + reach = radius_m + _DIST_EPS_M + doomed = [index for index in self.alive + if math.dist(self.cell_center(index), center) > reach] + self._discard(doomed) + + def _kill_outside_wedge(self, station: Vec2, reading_deg: float) -> None: + """删除角向偏离读数超出 (*@\ensuremath{\delta}@*)_eff + 角向格裕量的幸存格。 + + 角向格裕量 = asin(m / max(dist−m, 1))：格内任一点相对格心的方位 + 偏差不超过它（点距测点还可再近 m，故分母再内缩 m）。 + """ + if not self.alive: + return + sx, sy = float(station[0]), float(station[1]) + doomed = [] + for index in self.alive: + gx, gy = self.cell_center(index) + dist = math.hypot(gx - sx, gy - sy) + if dist <= self.margin_m + 1.0: + continue # 格贴测点：格内方位可指向任意方向，不可删 + angular_margin = math.degrees( + math.asin(min(0.9999, self.margin_m / (dist - self.margin_m)))) + gap = angular_gap(math.degrees(math.atan2(gy - sy, gx - sx)), reading_deg) + if gap > self.half_angle_deg + angular_margin + _ANG_EPS_DEG: + doomed.append(index) + self._discard(doomed) + + def apply_measure(self, station: Vec2, result: str, + svd_deg: float | None = None, *, + directional: bool = False) -> None: + """按读数更新幸存集。真源保留性由 Voronoi 裕量保证（模块注释）。 + + ``directional=True``（第四问）：no_signal **不删空间候选**——定向源 + 的静默还可能来自朝向遮挡，单独删空间候选会误删真源；朝向维度由 + :class:`~mcm26b.belief.joint.JointBelief` 维护。 + """ + if result == NO_SIGNAL: + if directional: + return + # no_signal (*@\ensuremath{\Longrightarrow}@*) dist > r_eff >= 1000：整格落入 B(s, 1000−m) 的删。 + self._kill_disk(station, self.r_eff_min_m - self.margin_m) + elif result == NEAR: + self._kill_outside_disk(station, self.near_radius_m + self.margin_m) + elif result == DIRECTION: + if svd_deg is None: + raise ValueError("direction 读数必须携带 svd_deg") + # direction 隐含 dist <= r_max [题面] + self._kill_outside_disk(station, self.r_eff_max_m + self.margin_m) + self._kill_outside_wedge(station, svd_deg) + else: + raise ValueError(f"未知测向结果: {result!r}") + + # ------------------------------------------------------------ 查询 + def __len__(self) -> int: + return len(self.alive) + + def alive_points(self, limit: int | None = None) -> list[Vec2]: + sorted_alive = sorted(self.alive) + if limit is not None and len(sorted_alive) > limit: + step = len(sorted_alive) / limit + indices = {sorted_alive[int(k * step) % len(sorted_alive)] + for k in range(limit)} + indices = sorted(indices) + else: + indices = sorted_alive + return [self.cell_center(index) for index in indices] + + def nearest_alive_distance(self, point: Vec2, limit_m: float) -> float | None: + """最近幸存格心距离；> limit_m 时返回 None（粗格环扫 + 下界剪枝）。 + + 返回值语义：恰为最近幸存格心距离（若 <= limit_m）；None 表示所有 + 幸存格心都超出 limit_m。粗格聚合半径已计入扫描范围，不漏判。 + """ + if not self.alive: + return None + coarse_cell_m = self.spacing_m * _COARSE_FACTOR + coarse_reach = coarse_cell_m * math.sqrt(2) / 2 + cw = self._coarse_width() + ci_base = int(math.floor((point[0] - self.x0) / coarse_cell_m)) + cj_base = int(math.floor((point[1] - self.x0) / coarse_cell_m)) + ring_max = int(math.ceil((limit_m + coarse_reach) / coarse_cell_m)) + 1 + best: float | None = None + for ring in range(ring_max + 1): + lower_bound = max(0.0, ring - 1) * coarse_cell_m - coarse_reach + if best is not None and lower_bound >= best: + break # 更外环的所有格心都 >= 下界 >= 当前最优 + for ci in range(max(0, ci_base - ring), min(cw - 1, ci_base + ring) + 1): + for cj in range(max(0, cj_base - ring), min(cw - 1, cj_base + ring) + 1): + if max(abs(ci - ci_base), abs(cj - cj_base)) != ring: + continue # 只扫当前环（Chebyshev 环） + if (ci * cw + cj) not in self._coarse: + continue + ccx = self.x0 + (ci + 0.5) * coarse_cell_m + ccy = self.x0 + (cj + 0.5) * coarse_cell_m + if math.hypot(ccx - point[0], ccy - point[1]) \ + > limit_m + coarse_reach: + continue + i0, j0 = ci * _COARSE_FACTOR, cj * _COARSE_FACTOR + for i in range(i0, min(i0 + _COARSE_FACTOR, self.width)): + base = i * self.width + for j in range(j0, min(j0 + _COARSE_FACTOR, self.width)): + index = base + j + if index not in self.alive: + continue + dist = math.dist(self.cell_center(index), point) + if dist <= limit_m and (best is None or dist < best): + best = dist + return best + + def guaranteed_no_signal(self, station: Vec2) -> bool: + """真源与该测点距离必 > r_max（>= r_eff）(*@\ensuremath{\Longrightarrow}@*) 必 no_signal，测了也无信息。""" + return self.nearest_alive_distance( + station, self.r_eff_max_m + self.margin_m) is None + + def mec(self) -> tuple[Vec2, float]: + """幸存集最小包围圆（圆心, 半径）；按 version 缓存。""" + if self._mec is None: + if not self.alive: + raise ValueError("幸存集为空（该频道已可证明缺席）") + points = [self.cell_center(index) for index in self.alive] + self._mec = smallest_enclosing_circle(points) + return self._mec + + # ------------------------------------------------------------ 信息增益 + def subsample(self, size: int) -> list[Vec2]: + """按索引序均匀抽取的子采样（索引序(*@\ensuremath{\approx}@*)空间序，代表点空间铺开）。""" + return self.alive_points(limit=size) + + # ---------------------------------------------------- 向量化评分（可选） + def _expected_survival_vector(self, point: Vec2, sub, representatives) -> float: + """``expected_survival`` 的向量化实现（与纯 Python 版逐分支同语义）。""" + count = len(sub) + eps = 1.0 / count + dx, dy = sub[:, 0] - point[0], sub[:, 1] - point[1] + dist = _np.hypot(dx, dy) + within = int(_np.count_nonzero( + dist <= self.r_eff_min_m - self.margin_m + _DIST_EPS_M)) + log_keep_ns = math.log(max(1.0 - within / count, eps)) + bearing = _np.degrees(_np.arctan2(dy, dx)) + in_range = dist <= self.r_eff_max_m + self.margin_m + rdx, rdy = representatives[:, 0] - point[0], representatives[:, 1] - point[1] + rdist = _np.hypot(rdx, rdy) + rbearing = _np.degrees(_np.arctan2(rdy, rdx)) + gaps = _np.abs((bearing[None, :] - rbearing[:, None] + 180.0) % 360.0 - 180.0) + survivors = _np.count_nonzero( + (gaps <= self.half_angle_deg + _ANG_EPS_DEG) & in_range[None, :], axis=1) + p_ns = _np.clip((rdist - self.r_eff_min_m) + / (self.r_eff_max_m - self.r_eff_min_m), 0.0, 1.0) + keep_dir = _np.maximum(survivors / count, eps) + values = p_ns * log_keep_ns + (1.0 - p_ns) * _np.log(keep_dir) + near = rdist <= self.near_radius_m + self.margin_m + values = _np.where(near, math.log(eps), values) + return float(values.mean()) + + def _expected_posterior_radius_vector(self, point: Vec2, sub, + representatives) -> float: + """``expected_posterior_radius`` 的向量化实现。""" + eps_radius = self.spacing_m / 2.0 + dx, dy = sub[:, 0] - point[0], sub[:, 1] - point[1] + dist = _np.hypot(dx, dy) + bearing = _np.degrees(_np.arctan2(dy, dx)) + keep_ns = dist > self.r_eff_min_m - self.margin_m + r_ns = (_branch_radius_array(sub[keep_ns]) if keep_ns.any() + else eps_radius) + rdx, rdy = representatives[:, 0] - point[0], representatives[:, 1] - point[1] + rdist = _np.hypot(rdx, rdy) + rbearing = _np.degrees(_np.arctan2(rdy, rdx)) + gaps = _np.abs((bearing[None, :] - rbearing[:, None] + 180.0) % 360.0 - 180.0) + dir_mask = ((gaps <= self.half_angle_deg + _ANG_EPS_DEG) + & (dist[None, :] <= self.r_eff_max_m + self.margin_m)) + r_dir = _np.array([_branch_radius_array(sub[row]) if row.any() + else eps_radius for row in dir_mask]) + p_ns = _np.clip((rdist - self.r_eff_min_m) + / (self.r_eff_max_m - self.r_eff_min_m), 0.0, 1.0) + near = rdist <= self.near_radius_m + self.margin_m + values = _np.where(near, self.near_radius_m + self.margin_m, + p_ns * r_ns + (1.0 - p_ns) * r_dir) + return float(values.mean()) + + def expected_survival(self, point: Vec2, subsample, + representatives) -> float: + """E[log 幸存占比]：越小该测点的期望信息增益越大。 + + r_eff 不确定性解析积分：dist(*@\ensuremath{\in}@*)(1000,1500] 时按 r_eff~U(1000,1500) + 取 p_ns=(dist−1000)/500 为 no_signal 分支概率。 + - no_signal 分支：删 B(point, 1000−m)，幸存 = 子采样中盘外比例； + - direction 分支：以代表点方位为期望读数，角域 (*@\ensuremath{\cap}@*) B(point,1500+m) 内幸存； + - near 分支（dist <= 5+m）：可行集收缩到 5m 盘，幸存占比趋近 0。 + """ + if not self.alive or len(subsample) == 0 or len(representatives) == 0: + return 0.0 + if _np is not None and isinstance(subsample, _np.ndarray) \ + and isinstance(representatives, _np.ndarray): + return self._expected_survival_vector(point, subsample, representatives) + eps = 1.0 / len(subsample) + keep_ns = max(1.0 - self.fraction_within(subsample, point, + self.r_eff_min_m - self.margin_m), + eps) + log_keep_ns = math.log(keep_ns) + total = 0.0 + for rep in representatives: + dist = math.hypot(rep[0] - point[0], rep[1] - point[1]) + if dist <= self.near_radius_m + self.margin_m: + total += math.log(eps) + continue + p_ns = min(1.0, max(0.0, (dist - self.r_eff_min_m) + / (self.r_eff_max_m - self.r_eff_min_m))) + reading = math.atan2(rep[1] - point[1], rep[0] - point[0]) + survivors = 0 + for p in subsample: + if math.dist(p, point) > self.r_eff_max_m + self.margin_m: + continue + gap = angular_gap(math.degrees( + math.atan2(p[1] - point[1], p[0] - point[0])), + math.degrees(reading)) + if gap <= self.half_angle_deg + _ANG_EPS_DEG: + survivors += 1 + keep_dir = max(survivors / len(subsample), eps) + total += p_ns * log_keep_ns + (1.0 - p_ns) * math.log(keep_dir) + return total / max(len(representatives), 1) + + def fraction_within(self, samples, point: Vec2, radius_m: float) -> float: + if len(samples) == 0: + return 0.0 + reach = radius_m + _DIST_EPS_M + if _np is not None and isinstance(samples, _np.ndarray): + distance = _np.hypot(samples[:, 0] - point[0], samples[:, 1] - point[1]) + return float(_np.count_nonzero(distance <= reach)) / len(samples) + count = sum(1 for p in samples if math.dist(p, point) <= reach) + return count / len(samples) + + def _branch_radius(self, members) -> float: + """分支后验的半径代理：幸存子采样到其质心的最大距离（O(n)，免 Welzl）。""" + if len(members) == 0: + return 0.0 + if _np is not None and isinstance(members, _np.ndarray): + return _branch_radius_array(members) + mx = sum(p[0] for p in members) / len(members) + my = sum(p[1] for p in members) / len(members) + return max(math.hypot(p[0] - mx, p[1] - my) for p in members) + + def expected_posterior_radius(self, point: Vec2, subsample, + representatives) -> float: + """一次测量后期望后验半径（米）：选点主指标，直指清除证书阈值。 + + 对每个代表假设（真值候选）按 r_eff~U(1000,1500) 解析积分 + no_signal/direction 分支，near 分支（dist <= 5+m）后验为 5m 盘； + 各分支半径用幸存子采样的质心最大距离近似（偏差 << 格距，排序用）。 + 与几何版 worst-posterior 同族，但作用于含负观测的非凸幸存集， + 且以期望代替最坏（代表点覆盖幸存集主轴）。 + """ + if not self.alive or len(subsample) == 0 or len(representatives) == 0: + return 0.0 + if _np is not None and isinstance(subsample, _np.ndarray) \ + and isinstance(representatives, _np.ndarray): + return self._expected_posterior_radius_vector( + point, subsample, representatives) + eps_radius = self.spacing_m / 2.0 + total = 0.0 + for rep in representatives: + dist = math.hypot(rep[0] - point[0], rep[1] - point[1]) + if dist <= self.near_radius_m + self.margin_m: + total += self.near_radius_m + self.margin_m + continue + p_ns = min(1.0, max(0.0, (dist - self.r_eff_min_m) + / (self.r_eff_max_m - self.r_eff_min_m))) + members_ns = [p for p in subsample + if math.dist(p, point) > self.r_eff_min_m - self.margin_m] + reading = math.atan2(rep[1] - point[1], rep[0] - point[0]) + members_dir = [] + for p in subsample: + if math.dist(p, point) > self.r_eff_max_m + self.margin_m: + continue + gap = angular_gap(math.degrees( + math.atan2(p[1] - point[1], p[0] - point[0])), + math.degrees(reading)) + if gap <= self.half_angle_deg + _ANG_EPS_DEG: + members_dir.append(p) + r_ns = self._branch_radius(members_ns) if members_ns else eps_radius + r_dir = self._branch_radius(members_dir) if members_dir else eps_radius + total += p_ns * r_ns + (1.0 - p_ns) * r_dir + return total / max(len(representatives), 1) diff --git a/docs/paper/data/listing-source/src/mcm26b/planner/__init__.py.tex b/docs/paper/data/listing-source/src/mcm26b/planner/__init__.py.tex new file mode 100644 index 0000000..93dfe92 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/planner/__init__.py.tex @@ -0,0 +1,1032 @@ +"""P3/P4/P5 策略层：主动选点、全向闭环与定向扩展。 + +P3 第二检测点（验收：保证收到信号；Q 空时退化；near 分支）： +- K1 = Ω (*@\ensuremath{\cap}@*) W(s1, (*@\ensuremath{\theta}@*)1±(*@\ensuremath{\delta}@*)) (*@\ensuremath{\cap}@*) B(s1, 1500)；安全候选盘证书见 + geometry.planning.first_bearing_candidate_disk（(*@\ensuremath{\delta}@*)<=1.005° 时非空）； +- 在保证接收盘 B(mec_center, 1000-(*@\ensuremath{\rho}@*)) 内环形采样候选点，以 + "最坏后验包围圆半径"为主指标、移动代价为次指标； +- 采样是启发式（目标边界点 × 读数区间端点），不是严格最坏情形 + 最优解；选定后按 1/4 间距加密复核并如实上报数值； +- 返回 near 时：候选源在 5m 内，直接对当前频道尝试 /clear。 + +P4 全向闭环（验收：10/16/0 源场景、边界源、预算耗尽与故障注入）： +发现（coverage.CoverageLedger）→ 定位（belief 收敛）→ 清除 → 持续复扫 +→ /exit。全部频道"已清除或证明不存在"后默认立即退出；显式开启 +persistent_search时只复扫未清除频道，扫到限时为止（清除数达 16 / +实机预算耗尽 / 虚拟安全余量不足）。completed 表示任务证明完成（结束 +时每频道均 CLEARED/ABSENT 且无中断）；accounted_virtual_time_s 记录 +首次证明找全的虚拟时刻，与"复扫到限时才停"相互独立。 +断连/协议错误/守恒性破坏中断时同样尽力 /exit 并产出未完成 summary +（stop_reason 记中断类别，附逐频道状态快照），不静默丢失会话。 + +P5 定向扩展（问题4混合源闭环）： +- 49 点覆盖的发现保证对定向源同样成立（源在单元凸包内，任意发射半平面 + 含至少一个顶点），覆盖阶段不区分源类型； +- 保证接收盘内的 no_signal 只能由朝向遮挡解释 [观测推理]：频道记为 + "观测到定向"，对跖探点复核一次；联合约束基线不删空间候选（真源不误删）； +- 定位停滞时对有界候选集构造 <=20m 有限圆盘覆盖（fallback_clear_cells）， + 预算核对后逐格 /clear（清除与朝向无关）；格数超硬顶或预算不足即跳过， + 绝不盲扫。 +""" + +from __future__ import annotations + +import math +from dataclasses import dataclass + +from ..belief import (BeliefState, CandidateRegion, ChannelStatus, + InconsistentBelief, clip_halfplane) +from ..belief.joint import JointBelief +from ..config import ProblemConfig, Vec2 +from ..coverage import CoverageLedger +from ..evaluation import recompute_virtual_time, summarize +from ..guarantee import plan_instance, seven_plan, square_49_plan +from ..protocol.client import (DeadlineExceeded, ProtocolError, + SimulatorClient) +from ..protocol.rules import CLEAR_SUCCESS, DIRECTION, NEAR, NO_SIGNAL +from ..protocol.timing import move_time +from ..protocol.transport import TransportError +from ..routing import improve_open_path + + +def bearing_deg(a: Vec2, b: Vec2) -> float: + """从 a 指向 b 的方位角（0-360，0 为 x 正方向，逆时针）。""" + return math.degrees(math.atan2(b[1] - a[1], b[0] - a[0])) % 360.0 + + +def _error_brief(exc: BaseException) -> dict: + """异常摘要（summary 留档用）：类型名 + 截断消息。""" + return {"type": type(exc).__name__, "message": str(exc)[:500]} + + +@dataclass(frozen=True) +class SecondPointPlan: + """下一检测点的候选与依据（P3 输出）。""" + + position: Vec2 + worst_posterior_radius_m: float + move_cost_s: float + reason: str + + +@dataclass(frozen=True) +class ClearCertificate: + """清除证书：候选集外包半径（含近似误差）不超过 20m 阈值。""" + + channel: int + center: Vec2 + radius_m: float + limit_m: float + certified: bool + + +def clear_certificate(region: CandidateRegion, channel: int, + config: ProblemConfig = ProblemConfig()) -> ClearCertificate: + """(*@\ensuremath{\rho}@*)_poly <= 20 - 外包近似误差 - 工程余量 才允许发起清除。""" + center, radius = region.mec() + limit = (config.field.clear_radius_m - region.slack_m + - config.search.clear_margin_m) + return ClearCertificate(channel, center, radius, limit, radius <= limit) + + +def candidate_points(center: Vec2, safe_radius_m: float, rings, angles: int) -> list[Vec2]: + """保证接收盘内的候选点：盘心 + 各比例半径 × 均匀方向。""" + points = [tuple(center)] + for fraction in rings: + radius = fraction * safe_radius_m + if radius <= 1e-9: + continue + step = 2 * math.pi / angles + for k in range(angles): + angle = step * k + step / 2 + points.append((center[0] + radius * math.cos(angle), + center[1] + radius * math.sin(angle))) + return points + + +def _worst_posterior_radius(region: CandidateRegion, q: Vec2, + witnesses: list[Vec2], half_angle_deg: float, + near_radius_m: float, disk_sides: int) -> float: + """对候选点 q，遍历"目标边界点 × 读数分支"的最坏后验包围半径。 + + 读数分支：direction 的区间端点 (*@\ensuremath{\varphi}@*)(g)±(*@\ensuremath{\delta}@*)（端点是每个 g 的最不利读数）， + 以及 near——源落在 q 的 near_radius_m 内时后验为 B(q, near)(*@\ensuremath{\cap}@*)候选集。 + 保证接收盘内 no_signal 不可能发生，故不枚举该分支。 + 这是启发式近似，不构成最优性证明 [工程]。 + """ + posterior_radii = [] + for g in witnesses: + phi = bearing_deg(q, g) + for reading in (phi - half_angle_deg, phi + half_angle_deg): + probe = CandidateRegion(list(region.polygon), region.slack_m) + probe.clip_wedge(q, reading, half_angle_deg) + if probe.polygon: + posterior_radii.append(probe.mec()[1]) + near_probe = CandidateRegion(list(region.polygon), region.slack_m) + try: + near_probe.clip_disk(q, near_radius_m, disk_sides) + except InconsistentBelief: + pass # B(q, near) 与候选集不相交：near 分支不可能发生，跳过 + else: + if near_probe.polygon: + posterior_radii.append(near_probe.mec()[1]) + if not posterior_radii: + return region.mec()[1] # 无有效采样点时退回当前半径 + return max(posterior_radii) + + +def safe_disk_radius(region: CandidateRegion, + config: ProblemConfig = ProblemConfig()) -> float: + """保证接收盘 B(mec, safe) 的半径；<0 表示无保证（(*@\ensuremath{\rho}@*) 超过最小接收半径）。 + + 盘内任意点到候选集每点距离 <= safe + (*@\ensuremath{\rho}@*) + 1e-3 < 1000 <= 最小接收半径， + 故必然收到 direction/near。1mm 数值余量避免浮点贴边被 r_eff=1000 的源 + 判为 no_signal。 + """ + return config.field.r_eff_min_m - region.mec()[1] - 1e-3 + + +def select_measurement_point(region: CandidateRegion, from_position: Vec2, + config: ProblemConfig = ProblemConfig()) -> SecondPointPlan: + """在保证接收盘内选择下一检测点（P3 核心；对任意候选集通用）。 + + 保证接收盘 B(mec_center, 1000-(*@\ensuremath{\rho}@*))：盘内任意点到候选集每点距离 + <= (1000-(*@\ensuremath{\rho}@*)) + (*@\ensuremath{\rho}@*) = 1000 <= 最小接收半径，故必然收到 direction/near， + 不会浪费一次 no_signal。(*@\ensuremath{\rho}@*)>1000 时退化为探索 MEC 圆心（可能 no_signal）。 + """ + field, search = config.field, config.search + center, radius = region.mec() + half_angle = field.bearing_error_half_deg + search.bearing_rounding_margin_deg + + def move_cost(point: Vec2) -> float: + return move_time(from_position, point, config.cost) + + # 1mm 数值余量在 safe_disk_radius 内记账。 + safe_radius = safe_disk_radius(region, config) + if safe_radius < 0: + return SecondPointPlan(tuple(center), radius, move_cost(center), + "无保证接收盘（(*@\ensuremath{\rho}@*)>1000）：探索 MEC 圆心，可能 no_signal") + coarse = region.witnesses(search.witness_spacing_m) + samples = candidate_points(center, safe_radius, + search.candidate_rings, search.candidate_angles) + near_radius, sides = field.near_radius_m, search.polygon_sides + best_key, best_point, best_worst = None, None, None + for point in samples: + worst = _worst_posterior_radius(region, point, coarse, half_angle, + near_radius, sides) + key = (round(worst, 6), round(move_cost(point), 6)) + if best_key is None or key < best_key: + best_key, best_point, best_worst = key, point, worst + dense = _worst_posterior_radius(region, best_point, + region.witnesses(search.witness_spacing_m / 4), + half_angle, near_radius, sides) + reason = (f"安全盘 B(centre,{safe_radius:.0f}m) 内 {len(samples)} 候选；" + f"粗采样最坏后验 {best_worst:.1f}m，1/4 间距加密复核 {dense:.1f}m") + return SecondPointPlan(tuple(best_point), dense, move_cost(best_point), reason) + + +def select_second_point(client: SimulatorClient, first_position: Vec2, + first_bearing_deg: float, + config: ProblemConfig = ProblemConfig()) -> SecondPointPlan: + """P3 入口：由首次 direction 构造 K1，返回保证接收的第二检测点方案。""" + region = CandidateRegion.initial(first_position, config) + half_angle = config.field.bearing_error_half_deg \ + + config.search.bearing_rounding_margin_deg + region.clip_wedge(first_position, first_bearing_deg, half_angle) + return select_measurement_point(region, client.state.position, config) + + +class OmnidirectionalLoop: + """问题3全向"发现—定位—清除—持续复扫"闭环（P4 基线 + 持续搜索）。 + + 串行驱动 SimulatorClient：覆盖阶段在 49 点网格上对每个 UNKNOWN 频道 + 检测；发现 direction 即进入该频道的定位子循环（选点→测量→收敛→ + 证书清除），near 直接清除。全部频道"已清除或证明不存在"后按 + ``search.persistent_search``（默认关闭）可选择只复扫 + 未清除频道，直到清除数达 16、实机预算耗尽或虚拟安全余量不足。 + stop_reason 记录循环结束原因；``completed`` 表示任务证明完成 + （结束时每频道均 CLEARED/ABSENT 且无中断），与"复扫到限时才停" + 相互独立：accounted_virtual_time_s 记录首次证明找全的虚拟时刻。 + """ + + def __init__(self, client: SimulatorClient, + config: ProblemConfig = ProblemConfig()): + self.client = client + self.config = config + self.belief = BeliefState(config) + # 覆盖计划是"可离线搜索、可在运行期校验"的一等对象；基类默认保持 + # 历史 49 点表（grid49_immediate 基线口径不变），各问题策略自行覆盖。 + self.coverage_plan = square_49_plan() + self.ledger = CoverageLedger(config, points=list(self.coverage_plan.points)) + self.cleared: list[int] = [] + self.anomalies: list[dict] = [] + self.stop_reason: str | None = None + # 逐频道缺席证据来源（pf_empty / coverage），供审计与论文逐条追溯。 + self.absence_evidence: dict[int, str] = {} + # "同一 0.5m 测点 × 同一频道"的重复检测计数：历史上一次官方演练 + # 有 98.84% 的虚拟时间耗在空复扫上，本计数是该问题的回归指标。 + self.redundant_rescan_measures = 0 + # 首次达成"每频道均已清除或证明不存在"的虚拟时刻（找全证明）。 + self.accounted_virtual_time_s: float | None = None + # 证书有效但 /clear 失败后必须先补测再重试，避免在同一证书上 + # 反复消耗 3 秒/次的失败清除。 + self._may_clear: set[int] = set() + # 断连/协议错误/守恒性破坏等中断：留档异常，收尾时写入 summary。 + self._abort_detail: BaseException | None = None + + # ------------------------------------------------------------ 主流程 + def run(self) -> dict: + """主闭环。任何异常都必须尽力 /exit 并产出 summary，不得静默丢会话。""" + try: + self.client.enter() + self._coverage_phase() + if self.stop_reason is None: + self._mark_absent_after_coverage() + self._resolve_detected() + self._record_accounted() + if self.config.search.persistent_search: + self._persistent_phase() + if self.stop_reason is None: + if len(self.cleared) >= self.config.field.source_count_max: + self.stop_reason = "sixteen_cleared" + elif self._all_accounted(): + self.stop_reason = "all_resolved" + else: + self.stop_reason = "unresolved_channels" + except DeadlineExceeded: + self.stop_reason = "real_budget_exhausted" + except (TransportError, ProtocolError, InconsistentBelief) as exc: + self._abort_detail = exc + if isinstance(exc, TransportError): + self.stop_reason = "transport_failure" + elif isinstance(exc, InconsistentBelief): + self.stop_reason = "inconsistent_belief" + else: + self.stop_reason = "protocol_error" + except Exception as exc: # 意外异常同样收尾，不阻断 /exit 与结果汇总 + self._abort_detail = exc + self.stop_reason = "unexpected_error" + info = None + exit_error = None + try: + info = self.client.exit() + except Exception as exc: # 接口不可用：记录后仍产出未完成状态 + exit_error = exc + summary = self._summary(info) + if exit_error is not None: + summary["exit_error"] = _error_brief(exit_error) + return summary + + # ------------------------------------------------------------ 预算与证明 + def _min_virtual_reserve(self) -> float: + """单动作耗时上界的保守估计，用于虚拟安全余量。 + + 上界 = 2 × 最远站点距离 / 速度 + 检测 + 换频（机器人不会跑到覆盖 + 计划包围区之外执行任务）。配置值通常更宽松；本函数保证即使配置被 + 调小，余量也足以完成最后一个动作而不触及 100 小时上限。 + """ + reach = max((math.dist((0.0, 0.0), point) for point in self.ledger.points), + default=0.0) + action_bound = (2.0 * reach / self.config.cost.speed_mps + + self.config.cost.measure_s + self.config.cost.switch_s) + return max(self.config.search.virtual_reserve_s, action_bound) + + def _virtual_cap_reached(self) -> bool: + """虚拟安全余量不足：置 stop_reason 并返回 True，调用方立即收尾。 + + 余量须大于单次动作耗时上界（见 :meth:`_min_virtual_reserve`）， + `search.virtual_reserve_s=10000s` [工程] 提供充分裕度，避免触及 + 附件2 §4.5 的 100 小时上限被模拟器强制结束。 + """ + if (self.client.state.virtual_time_s + self._min_virtual_reserve() + < self.config.field.max_virtual_duration_s): + return False + self.stop_reason = "virtual_time_cap" + return True + + def _all_accounted(self) -> bool: + return all(belief.status in (ChannelStatus.CLEARED, ChannelStatus.ABSENT) + for belief in self.belief.channels.values()) + + def _record_accounted(self) -> None: + """首次"每频道均已清除或证明不存在"的时刻留档（找全证明）。""" + if self.accounted_virtual_time_s is None and self._all_accounted(): + self.accounted_virtual_time_s = self.client.state.virtual_time_s + + # ------------------------------------------------------------ 覆盖阶段 + def _pending_channels_at(self, index: int) -> list[int]: + return [channel for channel, belief in self.belief.channels.items() + if belief.status is ChannelStatus.UNKNOWN + and not self.ledger.measured_at(channel, index)] + + def _next_point_index(self) -> int | None: + """尚有 UNKNOWN 频道待测的最近网格点（贪心最近邻 [工程]）。""" + position = self.client.state.position + best_index, best_distance = None, 0.0 + for index, point in enumerate(self.ledger.points): + if not self._pending_channels_at(index): + continue + distance = math.dist(position, point) + if best_index is None or distance < best_distance: + best_index, best_distance = index, distance + return best_index + + def _coverage_phase(self) -> None: + while True: + if self._count_limit_reached(): + return + index = self._next_point_index() + if index is None: + return + point = self.ledger.points[index] + for channel in self._pending_channels_at(index): + if self._virtual_cap_reached(): + return + outcome = self.client.measure(point, channel) + self.ledger.mark_measured(channel, index) + self.belief.update_measure(channel, point, outcome.result, + outcome.svd_deg) + if outcome.result == DIRECTION: + self._localize_and_clear(channel) + elif outcome.result == NEAR: + region = self.belief.candidate_set(channel) + cert = clear_certificate(region, channel, self.config) + if cert.certified: + self._attempt_clear(channel, cert.center, cert) + else: # 理论上不发生（near 候选半径 5m）；保守记录 + self._anomaly("near_without_certificate", channel, + position=point) + if self.stop_reason is not None or self._count_limit_reached(): + return + + # ------------------------------------------------------------ 持续复扫 + def _persistent_phase(self) -> None: + """全部频道已清除/证明不存在后的持续复扫 [用户决策 2026-09-11]。 + + 只扫未清除频道（DETECTED 继续定位，ABSENT 全网格复测，防模拟器 + 或覆盖证明假设偏差），直到清除数达 16 或虚拟安全余量不足； + 实机预算由客户端 DeadlineExceeded 兜底（扫到限时为止）。 + """ + while self.stop_reason is None: + if self._count_limit_reached(): + return + if self._virtual_cap_reached(): + return + self._persistent_round() + + def _persistent_round(self) -> None: + """一轮全网格复扫：网格点最近邻序，逐点测量全部未清除频道。""" + measured: set[tuple[int, int]] = set() + while self.stop_reason is None: + index = self._next_resweep_point(measured) + if index is None: + return + point = self.ledger.points[index] + for channel in self._resweep_channels_at(index, measured): + if self._virtual_cap_reached(): + return + measured.add((channel, index)) + was_absent = (self.belief.channels[channel].status + is ChannelStatus.ABSENT) + outcome = self.client.measure(point, channel) + self.belief.update_measure(channel, point, outcome.result, + outcome.svd_deg) + if was_absent and outcome.result in (DIRECTION, NEAR): + # 复测推翻了覆盖缺席证明：守恒性留痕，按新证据定位清除。 + self._anomaly("absent_detected_on_resweep", channel, + position=point, result=outcome.result) + if outcome.result == DIRECTION: + self._localize_and_clear(channel) + elif outcome.result == NEAR: + region = self.belief.candidate_set(channel) + cert = clear_certificate(region, channel, self.config) + if cert.certified: + self._attempt_clear(channel, cert.center, cert) + else: + self._anomaly("near_without_certificate", channel, + position=point) + if self.stop_reason is not None: + return + + def _next_resweep_point(self, measured: set[tuple[int, int]]) -> int | None: + """尚有未清除频道待复测的最近网格点（贪心最近邻 [工程]）。""" + position = self.client.state.position + best_index, best_distance = None, 0.0 + for index, point in enumerate(self.ledger.points): + if not self._resweep_channels_at(index, measured): + continue + distance = math.dist(position, point) + if best_index is None or distance < best_distance: + best_index, best_distance = index, distance + return best_index + + def _resweep_channels_at(self, index: int, + measured: set[tuple[int, int]]) -> list[int]: + return [channel for channel, belief in self.belief.channels.items() + if belief.status is not ChannelStatus.CLEARED + and (channel, index) not in measured] + + def _count_limit_reached(self) -> bool: + if len(self.cleared) >= self.config.field.source_count_max: + self.stop_reason = "sixteen_cleared" + return True + return False + + # ------------------------------------------------------------ 定位与清除 + def _localize_and_clear(self, channel: int) -> bool: + """定位子循环：选点测量收敛候选集，拿到清除证书后清除。 + + 返回是否已清除；步数耗尽仍未收敛则保持 DETECTED 留待二轮。 + 进入本函数前该频道刚有一次 direction 读数，允许立即清除。 + """ + search = self.config.search + self._may_clear.add(channel) + for _ in range(search.max_localize_steps): + if self._virtual_cap_reached(): + return False + region = self.belief.candidate_set(channel) + if region is None: + return False + cert = clear_certificate(region, channel, self.config) + if cert.certified and channel in self._may_clear: + if self._attempt_clear(channel, cert.center, cert): + return True + self._may_clear.discard(channel) + continue + plan = select_measurement_point(region, self.client.state.position, + self.config) + outcome = self.client.measure(plan.position, channel) + self.belief.update_measure(channel, plan.position, outcome.result, + outcome.svd_deg) + self._may_clear.add(channel) + if outcome.result == NO_SIGNAL: + self._anomaly("no_signal_in_safe_disk", channel, + position=plan.position, detail=plan.reason) + return self.belief.channels[channel].status is ChannelStatus.CLEARED + + def _attempt_clear(self, channel: int, target: Vec2, + cert: ClearCertificate) -> bool: + outcome = self.client.clear(target, channel) + if outcome.result == CLEAR_SUCCESS: + self.belief.mark_cleared(channel) + self.cleared.append(channel) + return True + if cert.certified: + self._anomaly("clear_failed_with_certificate", channel, position=target, + radius_m=round(cert.radius_m, 3), limit_m=cert.limit_m) + return False + + def _anomaly(self, kind: str, channel: int, **detail) -> None: + """异常只在守恒性被打破或证书失效时出现；每频道限量记录防刷屏。""" + recorded = sum(1 for item in self.anomalies if item["channel"] == channel) + if recorded >= self.config.search.max_anomalies_per_channel: + return + self.anomalies.append({"kind": kind, "channel": channel, **detail}) + + # ------------------------------------------------------------ 收尾 + def _mark_absent_after_coverage(self) -> None: + """全向源缺席证明：全网格无非 no_signal 读数的频道不存在源 [题面]。""" + for channel, belief in self.belief.channels.items(): + if belief.status is ChannelStatus.UNKNOWN \ + and self.ledger.coverage_complete(channel): + self.belief.mark_absent(channel) + self.absence_evidence[channel] = "coverage" + + def _resolve_detected(self) -> None: + """覆盖完成后，对仍未清除的 DETECTED 频道做第二轮定位。 + + 不再在此决定停止：持续搜索模式下由 _persistent_phase 接力， + 非持续模式由 run() 依据 _all_accounted 判定 all_resolved。 + """ + for channel in self.belief.channels_by_status(ChannelStatus.DETECTED): + if self._count_limit_reached() or self._virtual_cap_reached(): + return + self._localize_and_clear(channel) + if self.stop_reason is not None: + return + + def _summary(self, info) -> dict: + """结果汇总。info 为 None 表示 /exit 未能完成（断连等），按未完成上报。 + + completed = 无中断且结束时每频道均 CLEARED/ABSENT（任务证明完成）； + stop_reason 另行记录循环结束原因（持续复扫模式下通常是 + virtual_time_cap / real_budget_exhausted / sixteen_cleared）。 + """ + events = self.client.log.action_events() + stats = summarize(events) + report = recompute_virtual_time(events) + steps = self._step_report() + cleared = self.belief.channels_by_status(ChannelStatus.CLEARED) + absent = self.belief.channels_by_status(ChannelStatus.ABSENT) + resolved = set(cleared) | set(absent) + unresolved = [channel for channel in sorted(self.belief.channels) + if channel not in resolved] + virtual_time_s = round((info.virtual_time_s if info is not None + else self.client.state.virtual_time_s), 3) + # 清除数达 16 即数量上界证明（其余频道无论状态如何都不可能有源）； + # 否则要求每频道均 CLEARED/ABSENT。 + completed = (self._abort_detail is None + and (len(self.cleared) >= self.config.field.source_count_max + or not unresolved)) + # 完成依据必须显式区分"数量上界"与"逐频道缺席/清除证明"， + # 否则论文与审计会把 16 源截断误读为逐频道证明。 + if self._abort_detail is not None: + completion_basis = "incomplete" + elif len(self.cleared) >= self.config.field.source_count_max: + completion_basis = "count_cap" + elif not unresolved: + completion_basis = "per_channel_proof" + else: + completion_basis = "incomplete" + summary = { + "completed": completed, + "completion_basis": completion_basis, + "stop_reason": self.stop_reason, + "exit_reason": "exit_unreachable" if info is None else info.reason, + "virtual_time_s": virtual_time_s, + "accounted_virtual_time_s": (round(self.accounted_virtual_time_s, 3) + if self.accounted_virtual_time_s is not None + else None), + "persistent_search": self.config.search.persistent_search, + "virtual_reserve_s": round(self._min_virtual_reserve(), 3), + "coverage_plan": self.coverage_plan.name, + "coverage_points": len(self.coverage_plan.points), + "coverage_plan_points": [[p[0], p[1]] for p in self.coverage_plan.points], + "coverage_plan_certificate": ( + self.coverage_plan.certificate.as_dict() + if self.coverage_plan.certificate is not None else None), + "cleared_channels": cleared, + "absent_channels": absent, + "unresolved_channels": unresolved, + "absence_evidence": {str(channel): self.absence_evidence[channel] + for channel in sorted(absent)}, + "redundant_rescan_measures": self.redundant_rescan_measures, + "measures": stats["measures"], + "clears": stats["clears"], + "clear_success": stats["cleared"], + "total_requests": stats["measures"] + stats["clears"], + "move_distance_m": round(stats["distance_m"], 1), + # 题面口径：定位清除总时间（全程虚拟时长）/ 被清除干扰源个数。 + "avg_locate_clear_time_s": (round(virtual_time_s / len(cleared), 3) + if cleared else None), + "step_totals": steps["totals"], + "steps": steps["rows"], + "anomalies": self.anomalies, + "virtual_recompute_mismatches": len(report["mismatches"]), + "channel_status": self._channel_status_snapshot(), + } + if self._abort_detail is not None: + summary["abort_detail"] = _error_brief(self._abort_detail) + return summary + + def _step_report(self) -> dict: + """每步计时汇总 [用户决策 2026-09-11]：实机墙钟 + 比赛虚拟耗时分项。""" + totals = {"count": 0, "real_elapsed_total_s": 0.0, + "real_since_enter_total_s": 0.0, + "virtual_move_s": 0.0, "virtual_switch_s": 0.0, + "virtual_measure_action_s": 0.0, "virtual_clear_action_s": 0.0, + "virtual_total_s": 0.0} + rows = [] + for index, step in enumerate(self.client.log.step_events()): + cost = step["virtual_cost"] + totals["count"] += 1 + totals["real_elapsed_total_s"] += step["real_elapsed_s"] + totals["real_since_enter_total_s"] = step.get( + "real_since_enter_s", totals["real_since_enter_total_s"]) + totals["virtual_move_s"] += cost["move_s"] + totals["virtual_switch_s"] += cost["switch_s"] + if step["path"] == "/measure": + totals["virtual_measure_action_s"] += cost["action_s"] + elif step["path"] == "/clear": + totals["virtual_clear_action_s"] += cost["action_s"] + totals["virtual_total_s"] += cost["total_s"] + rows.append({"index": index, "action": step["path"].lstrip("/"), + "result": step.get("result"), + "channel": step.get("channel"), + "position": step.get("position"), + "real_elapsed_ms": round(step["real_elapsed_s"] * 1000.0, 3), + "real_since_enter_s": step.get("real_since_enter_s"), + "move_s": round(cost["move_s"], 3), + "switch_s": round(cost["switch_s"], 3), + "action_s": round(cost["action_s"], 3), + "step_virtual_s": round(cost["total_s"], 3), + "virtual_time_s": step["virtual_time_s"]}) + for key, value in totals.items(): + if isinstance(value, float): + totals[key] = round(value, 3) + return {"totals": totals, "rows": rows} + + def _channel_status_snapshot(self) -> dict: + """逐频道状态快照：中断收尾时的未完成状态留档（每频道一条）。""" + snapshot = {} + for channel, belief in sorted(self.belief.channels.items()): + entry = {"status": belief.status.value} + if belief.region is not None: + entry["posterior_radius_m"] = round(belief.region.mec()[1], 3) + snapshot[str(channel)] = entry + return snapshot + + +class DirectionalExtension(OmnidirectionalLoop): + """问题4混合源闭环（P5）：全向基线 + 定向观测处理 + 后备清除。 + + 与 P4 的三点差异（协议衔接见 docs/协议规则表与状态机.md §7）： + - 49 点覆盖的发现保证对定向源同样成立，覆盖阶段不区分源类型； + - 保证接收盘内的 no_signal 只能由朝向遮挡解释 [观测推理]：该频道 + 记为"观测到定向"，随后对 MEC 圆心取对跖探点复核；联合约束基线 + 不据此删除空间候选（真源不误删）； + - 定位停滞（候选集有界但未达清除证书）时构造 <=20m 有限圆盘覆盖， + 预算核对后逐格 /clear：清除与朝向无关 [题面]，是定向源不依赖 + 可见性的完备后备。格数超硬顶或现实预算不足则跳过并留痕，绝不盲扫。 + """ + + def __init__(self, client: SimulatorClient, + config: ProblemConfig = ProblemConfig()): + super().__init__(client, config) + # P0-2：第四问切换到同一保证下的最小命中集（默认 q4_mincover_v1）。 + self.coverage_plan = plan_instance(config.search.q4_coverage_plan, + verify=config.search.verify_coverage_plan) + self.ledger = CoverageLedger(config, points=list(self.coverage_plan.points)) + self.directional_observed: list[int] = [] # 观测到定向性的频道 + self.blocked_probes: dict[int, list[Vec2]] = {} + self.fallback_log: list[dict] = [] # 后备清除逐次留痕 + # P0-3：(位置 × 朝向) 联合可行集，仅在频道首次被看见时惰性建立， + # 使其初始化与更新成本只落在"确实存在定向源"的频道上。 + self.joint: dict[int, JointBelief] = {} + self.joint_absent_channels: list[int] = [] + self.visibility_probes = 0 # 由联合信念选出的探点数 + + def _coverage_phase(self) -> None: + """49站的定向覆盖证明不变；每站先串行扫频，再就近服务已发现源。 + + 避免检测一个源后远行清除，再返回同站检测下一个频道。 + no_signal不用于删空间候选，也不使用第三问的七站缺席证明。 + """ + while not self._count_limit_reached() and self.stop_reason is None: + index = self._next_point_index() + if index is None: + return + point = self.ledger.points[index] + pending = self._pending_channels_at(index) + pending.sort(key=lambda c: (c != self.client.state.channel, c)) + for channel in pending: + if self._virtual_cap_reached(): + return + outcome = self.client.measure(point, channel) + self.ledger.mark_measured(channel, index) + self._observe(channel, point, outcome.result, outcome.svd_deg) + if outcome.result == NEAR: + cert = clear_certificate( + self.belief.candidate_set(channel), channel, self.config) + if cert.certified: + self._attempt_clear(channel, point, cert) + if self._count_limit_reached(): + return + queue = self.belief.channels_by_status(ChannelStatus.DETECTED) + while queue and self.stop_reason is None: + channel = min(queue, key=lambda c: ( + math.dist(self.client.state.position, + self.belief.candidate_set(c).mec()[0]), c)) + queue.remove(channel) + self._localize_and_clear(channel) + if self._count_limit_reached(): + return + + # ------------------------------------------------------------ 定位与清除 + def _localize_and_clear(self, channel: int) -> bool: + """定位子循环：选点测量收敛候选集，拿到清除证书后清除。 + + 与 P4 的差异：保证接收盘内的 no_signal 说明探点被朝向遮挡 + [观测推理]，走"对跖复核 -> 环探"升级梯子（不计入定位步数， + 由 max_blocked_probes 限流），之后仍未收敛再转后备清除。 + """ + search = self.config.search + self._may_clear.add(channel) + steps = 0 + while steps < search.max_localize_steps: + if self._virtual_cap_reached(): + return False + region = self.belief.candidate_set(channel) + if region is None: + return False + cert = clear_certificate(region, channel, self.config) + if cert.certified and channel in self._may_clear: + if self._attempt_clear(channel, cert.center, cert): + return True + self._may_clear.discard(channel) # 证书失败：补测后才可重试 + continue + if len(self.blocked_probes.get(channel, [])) >= search.max_blocked_probes: + break # 梯子用尽仍被遮挡：定位停滞，转后备清除 + point = self._next_probe(region, channel) + within_range = (math.dist(point, region.mec()[0]) + <= safe_disk_radius(region, self.config)) + outcome = self.client.measure(point, channel) + self._observe(channel, point, outcome.result, outcome.svd_deg) + self._may_clear.add(channel) + if outcome.result == NO_SIGNAL: + if within_range and channel not in self.directional_observed: + self.directional_observed.append(channel) + self.blocked_probes.setdefault(channel, []).append(point) + continue # 盘外无信号也可能是距离不足，不据此断言定向 + self.blocked_probes.pop(channel, None) + steps += 1 + if self.belief.channels[channel].status is ChannelStatus.CLEARED: + return True + region = self.belief.candidate_set(channel) + if region is None: + return False + cert = clear_certificate(region, channel, self.config) + if cert.certified and channel in self._may_clear: + if self._attempt_clear(channel, cert.center, cert): + return True + self._may_clear.discard(channel) + return self._fallback_clear(channel, region) + + def _observe(self, channel: int, point: Vec2, result: str, + svd_deg: float | None) -> None: + """同步更新凸候选集与 (位置 × 朝向) 联合可行集。 + + 联合集只在频道首次被看见（direction/near）时建立：从未被看见的 + 频道由覆盖证明负责缺席，不需要朝向维度。联合集一旦为空，直接给出 + 该频道的缺席证明（严格，与覆盖证明同一条件），可提前停止对其检测。 + """ + self.belief.update_measure(channel, point, result, svd_deg) + if not self.config.search.directional_joint_belief: + return + joint = self.joint.get(channel) + if joint is None: + if result not in (DIRECTION, NEAR): + return + joint = JointBelief(self.config) + self.joint[channel] = joint + joint.apply(point, result, svd_deg) + if joint.is_absent() and self.belief.channels[channel].status \ + is not ChannelStatus.CLEARED: + self.belief.mark_absent(channel) + self.absence_evidence[channel] = "joint_empty" + if channel not in self.joint_absent_channels: + self.joint_absent_channels.append(channel) + + def _probe_candidates(self, region: CandidateRegion, channel: int) -> list[Vec2]: + """可见性选点的候选点族：保证接收点 + 对跖点 + 环探 + **抵近点**。 + + D1 关键结构性改动：旧点族全部围绕 MEC 圆心固定环采样，远距离不收敛时 + 没有"主动靠近"这一动作，只能退化到 20m 网格盲清。现在补上 + ``center + (*@\ensuremath{\alpha}@*)·(当前位置 − center)``（(*@\ensuremath{\alpha}@*)(*@\ensuremath{\in}@*)approach_fractions，(*@\ensuremath{\alpha}@*)=0 即圆心） + 的抵近序列，使策略可以在保持可见的前提下逐次逼近真源，最终以正常 + 角域证书或 near 收尾。 + """ + center, radius = region.mec() + position = self.client.state.position + candidates = [select_measurement_point( + region, position, self.config).position] + safe = safe_disk_radius(region, self.config) + blocked = self.blocked_probes.get(channel, []) + if blocked and safe >= 0: + dx, dy = center[0] - blocked[0][0], center[1] - blocked[0][1] + norm = math.hypot(dx, dy) + if norm > 1e-9: + scale = min(1.0, safe / norm) + candidates.append((center[0] + dx * scale, center[1] + dy * scale)) + # 抵近点：从 MEC 圆心到当前点的插值序列（含圆心本身）。 + for fraction in self.config.search.approach_fractions: + candidates.append((center[0] + (position[0] - center[0]) * fraction, + center[1] + (position[1] - center[1]) * fraction)) + for factor in (0.5, 1.0, 1.5): + ring = max(radius * factor, 2.0 * self.config.field.near_radius_m) + for step in range(8): + angle = math.pi * step / 4.0 + candidates.append((center[0] + ring * math.cos(angle), + center[1] + ring * math.sin(angle))) + unique: list[Vec2] = [] + seen: set[tuple[int, int]] = set() + blocked_keys = {(int(round(point[0] * 2)), int(round(point[1] * 2))) + for point in blocked} \ + if self.config.search.probe_exclude_blocked else set() + for point in candidates: + key = (int(round(point[0] * 2)), int(round(point[1] * 2))) + if key in seen or key in blocked_keys: + continue # 已测过且被遮挡的点：再测不会有任何新信息 + seen.add(key) + unique.append(point) + return unique + + def _visibility_probe(self, region: CandidateRegion, channel: int) -> Vec2 | None: + """按联合信念选探点；联合信念不可用时返回 None（退回梯子）。 + + 三种口径（只影响选点顺序，不承担任何安全责任）： + + - ``nearest_visible``（默认）：先按可见概率过滤（只保留 + ``prob_detect (*@\ensuremath{\ge}@*) ratio × max`` 的候选，避免选中"实际必然被朝向遮挡"的 + 点），再取 ``当前位置→q→MEC 圆心`` 移动最省者。9 场景 core 实测： + 后备盲清 125.7 → 4.3 次/局、T 9225 → 8602 s、墙钟最低。 + - ``expected_radius``：在同样过滤后最小化 + ``E[后验 MEC 半径](q) + (*@\ensuremath{\lambda}@*)·移动``。(*@\ensuremath{\lambda}@*)=5 时与上面几乎同分（8604 s）， + (*@\ensuremath{\lambda}@*) 很小时（0.05）值函数主导，为信息多绕路（9740 s）——本题 + "看得见且少走路"比"单步信息量最大"更重要。 + - ``visibility``（旧口径）：最大化 ``prob_detect/(移动+6)``，会反复选中 + 同一个近处被遮挡点（实测 9225 s、后备 125.6 次）。 + """ + joint = self.joint.get(channel) + if joint is None or joint.is_absent(): + return None + position = self.client.state.position + service_s = self.config.cost.measure_s + self.config.cost.switch_s + candidates = self._probe_candidates(region, channel) + if not candidates: + return None + mode = self.config.search.probe_score_mode + if mode == "visibility": + best_point, best_score = None, None + for point in candidates: + probability = joint.prob_detect(point) + if probability <= 0.0: + continue + score = -(probability / (move_time(position, point, self.config.cost) + + service_s)) + if best_score is None or score < best_score: + best_point, best_score = point, score + if best_point is not None: + self.visibility_probes += 1 + return best_point + scored = [(joint.prob_detect(point), point) for point in candidates] + peak = max(probability for probability, _ in scored) + ratio = self.config.search.probe_visibility_ratio + keep = [point for probability, point in scored + if probability >= ratio * peak] or [point for _, point in scored] + center = region.mec()[0] + weight = self.config.search.probe_lambda_move_s + + def approach_cost(point: Vec2) -> float: + return (move_time(position, point, self.config.cost) + + move_time(point, center, self.config.cost) + service_s) + + if mode == "nearest_visible": + # (*@\ensuremath{\lambda}@*) 很大时值函数项对 argmin 已无影响：直接取"可见候选中移动最省"， + # 省掉每个候选一次期望后验半径计算（单局墙钟 −3 s）。 + best = min(keep, key=lambda point: (approach_cost(point), point)) + self.visibility_probes += 1 + return best + best = min(keep, key=lambda point: ( + joint.expected_posterior_radius(point) + weight * approach_cost(point), + point)) + self.visibility_probes += 1 + return best + + + + def _next_probe(self, region: CandidateRegion, channel: int) -> Vec2: + """定向遮挡下的探点升级梯子 [工程]。 + + - 未被遮挡过：worst-posterior 选点器（保证接收盘内）； + - 第 1 次被遮挡：对 MEC 圆心取对跖方向，偏移裁进保证接收盘； + - 之后：绕 MEC 圆心、半径 = (*@\ensuremath{\rho}@*) 的环探，方位自首个被遮挡点起 + 每次 +45°。几何边界必须如实陈述：环上可见弧没有下界—— + 源可位于环上（|g-c| = (*@\ensuremath{\rho}@*)）且朝向沿外切线，可见集退化为单个 + 切点，固定步进环探可以全部漏过。梯子只提高提前命中概率， + 不构成接收或命中保证；完备性完全由后备清除兜底。 + """ + visibility = self._visibility_probe(region, channel) + if visibility is not None: + return visibility + blocked = self.blocked_probes.get(channel, []) + center, radius = region.mec() + if not blocked: + return select_measurement_point(region, self.client.state.position, + self.config).position + safe = safe_disk_radius(region, self.config) + first = blocked[0] + if len(blocked) == 1 and safe >= 0: + dx, dy = center[0] - first[0], center[1] - first[1] + norm = math.hypot(dx, dy) + if norm <= 1e-9: + # 首个被遮挡探点恰在圆心：方向信息为零，沿 +x 走满安全盘。 + return (center[0] + safe, center[1]) + scale = min(1.0, safe / norm) + # 对跖方向，偏移模长 = min(norm, safe)：圆心对称点裁进保证接收盘。 + return (center[0] + dx * scale, center[1] + dy * scale) + base = math.atan2(first[1] - center[1], first[0] - center[0]) + azimuth = base + math.radians(45.0 * (len(blocked) - 1)) + return (center[0] + radius * math.cos(azimuth), + center[1] + radius * math.sin(azimuth)) + + def _fallback_clear(self, channel: int, region: CandidateRegion) -> bool: + """定位停滞的后备：候选集有限圆盘覆盖逐格清除（格数即请求上界）。""" + search, session = self.config.search, self.config.session + width = max(p[0] for p in region.polygon) - min(p[0] for p in region.polygon) + height = max(p[1] for p in region.polygon) - min(p[1] for p in region.polygon) + cells = fallback_clear_cells(region.polygon, self.config) + entry = {"channel": channel, "cells": len(cells), + "bound": fallback_cell_bound(width, height, self.config), + "posterior_radius_m": round(region.mec()[1], 3)} + self.fallback_log.append(entry) + if len(cells) > search.fallback_max_cells: + # 宽候选集盲扫违背预算纪律：留待定位收敛，不得硬扫 [计划§4]。 + entry["outcome"] = "skipped_cell_cap" + self._anomaly("fallback_cell_cap_exceeded", channel, + cells=len(cells), cap=search.fallback_max_cells) + return False + # 现实预算核对：N 次请求 × 单请求高分位估计 + 退出余量，不足不启动。 + remaining = self.client.real_remaining_s + if remaining is None or len(cells) * session.real_rtt_p95_s \ + + session.reserve_exit_s > remaining: + entry["outcome"] = "skipped_budget" + return False + attempts = 0 + order = self._fallback_order(cells) + for cell in order: + if self._virtual_cap_reached(): + entry["outcome"] = "skipped_virtual_budget" + entry["attempts"] = attempts + return False + attempts += 1 + outcome = self.client.clear(cell, channel) + if outcome.result == CLEAR_SUCCESS: + self.belief.mark_cleared(channel) + self.cleared.append(channel) + entry["outcome"] = "cleared" + entry["attempts"] = attempts + return True + # 候选集保守包含真源，格心距格内任一点 <= 10*sqrt(2) < 20m：全部 + # 失败说明守恒性被打破，按异常留痕，不得据此删除候选。 + entry["outcome"] = "exhausted" + entry["attempts"] = attempts + self._anomaly("fallback_exhausted_without_success", channel, + cells=len(cells)) + return False + + def _fallback_order(self, cells: list[Vec2]) -> list[Vec2]: + """后备清除的走格顺序：最近邻打底 + 2-opt（可选 Or-opt）改进。 + + 旧实现每步重新 ``min(remaining, key=dist)``，等价于最近邻开放路径 + （典型为最优的 1.2–1.3 倍）且每次重扫 O(k²)。这里一次性求解改进序 + （D3），把格间移动压到接近最优；格数不变，故完备性不变。 + """ + if not cells: + return [] + if not self.config.search.fallback_optimize_tour or len(cells) < 4: + position = self.client.state.position + remaining = list(cells) + order: list[Vec2] = [] + while remaining: + nxt = min(remaining, key=lambda c: (math.dist(position, c), c)) + remaining.remove(nxt) + order.append(nxt) + position = nxt + return order + return improve_open_path([tuple(c) for c in cells], + self.client.state.position) + + # ------------------------------------------------------------ 收尾 + def _summary(self, info) -> dict: + report = super()._summary(info) + report["directional_observed_channels"] = list(self.directional_observed) + report["fallback_clears"] = self.fallback_log + # 后备 /clear 请求计入总请求口径，仅统计检测次数会低估现实耗时。 + report["fallback_clear_attempts"] = sum( + entry.get("attempts", 0) for entry in self.fallback_log) + report["visibility_probes"] = self.visibility_probes + report["joint_absent_channels"] = list(self.joint_absent_channels) + report["joint_final"] = {str(channel): belief.summary() + for channel, belief in sorted(self.joint.items())} + return report + + +def fallback_cell_bound(width_m: float, height_m: float, + config: ProblemConfig = ProblemConfig()) -> int: + """外包框枚举的格数上界 ((*@\ensuremath{\lceil}@*)w/cell(*@\ensuremath{\rceil}@*)+2)((*@\ensuremath{\lceil}@*)h/cell(*@\ensuremath{\rceil}@*)+2)（计划§4 规模检查）。""" + cell = config.search.fallback_clear_grid_m + return (math.ceil(width_m / cell) + 2) * (math.ceil(height_m / cell) + 2) + + +def fallback_clear_cells(polygon: list[Vec2], + config: ProblemConfig = ProblemConfig()) -> list[Vec2]: + """候选外包多边形的 <=20m 有限圆盘覆盖格心列表（P5 后备清除）。 + + 全局半开 20m 网格索引；多边形与格子的相交判定带正容差（宁可多测）， + 多边形边界恰在格线上时两侧格子都保留，因此格内任意点距某格心 + <= 10*sqrt(2) < 20m，逐格 /clear 至少一次命中。列表长度即 /clear + 请求预算上界；先核对 fallback_cell_bound，超预算不得逐格盲扫。 + """ + if not polygon: + return [] + cell = config.search.fallback_clear_grid_m + xs = [p[0] for p in polygon] + ys = [p[1] for p in polygon] + i0, i1 = math.floor(min(xs) / cell), math.floor(max(xs) / cell) + j0, j1 = math.floor(min(ys) / cell), math.floor(max(ys) / cell) + eps = 1e-9 + centers: list[Vec2] = [] + for i in range(i0, i1 + 1): + for j in range(j0, j1 + 1): + clipped = list(polygon) + for a, b, c in ((1.0, 0.0, (i + 1) * cell + eps), + (-1.0, 0.0, -(i * cell - eps)), + (0.0, 1.0, (j + 1) * cell + eps), + (0.0, -1.0, -(j * cell - eps))): + clipped = clip_halfplane(clipped, a, b, c, tol=eps) + if not clipped: + break + if clipped: + centers.append(((i + 0.5) * cell, (j + 0.5) * cell)) + return centers diff --git a/docs/paper/data/listing-source/src/mcm26b/planner/bayes_loop.py.tex b/docs/paper/data/listing-source/src/mcm26b/planner/bayes_loop.py.tex new file mode 100644 index 0000000..49b1bc5 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/planner/bayes_loop.py.tex @@ -0,0 +1,816 @@ +"""P4b 贝叶斯网格滤波闭环（问题3新策略 ``bayes``）。 + +在 :class:`OmnidirectionalLoop` 骨架（run/异常收尾/summary/预算/异常留痕） +上的三层重构，对应 docs/algo-3-bayes.md 的架构： + +1. 感知层：每频道一个网格幸存集（particles.ChannelParticles），全部读数 + （含 no_signal 负观测）即时更新；幸存集为空即缺席证明，无需等覆盖账本； +2. 决策层：统一任务循环——站点扫频、定位测量、清除三类任务合成任务表， + 开放路径最近邻 + 2-opt 排序，每执行一个任务滚动重排（动态 TSP）； +3. 选点层：定位测量点在保证接收盘（凸证书）或 PF MEC 探索环（宽候选集） + 内按"期望 log 幸存占比 + (*@\ensuremath{\lambda}@*)·移动时间"评分（信息增益贪心）。 + +与基线 SevenBatch 的差异：负观测跳站/跳测（必 no_signal 的 (站,频道) 对 +不消耗检测与换频）、PF 缺席证明提前证毕、全局任务排序替代"站内最近邻"。 +清除证书仍以凸证书为主（PF 网格证书仅在负观测挖洞使幸存集更紧时提前 +触发），两者均满足 Voronoi/保守裕量，不牺牲全清率。 +""" + +from __future__ import annotations + +import math +from dataclasses import dataclass + +from ..belief import CandidateRegion, ChannelStatus +from ..config import ProblemConfig, Vec2 +from ..coverage import CoverageLedger +from ..particles import ChannelParticles, as_sample_array +from ..protocol.client import SimulatorClient +from ..protocol.rules import DIRECTION, NEAR, NO_SIGNAL +from ..protocol.timing import move_time +from . import (ClearCertificate, OmnidirectionalLoop, clear_certificate, + candidate_points, safe_disk_radius, select_measurement_point) +from .seven import validate_seven_coverage +from ..guarantee import seven_plan + + +@dataclass(frozen=True) +class Task: + """统一任务表的一项。service_s 为不含移动的固有耗时（检测+换频/清除）。""" + + kind: str # "station" | "locate" | "clear" + position: Vec2 + service_s: float + channel: int | None = None + station_index: int | None = None + station_channels: tuple[int, ...] = () + + +def _point_key(point: Vec2) -> tuple[int, int]: + """候选点去重键：0.5m 网格取整（同一物理点不重复测量）。""" + return (int(round(point[0] * 2)), int(round(point[1] * 2))) + + +class BayesLoop(OmnidirectionalLoop): + """问题3贝叶斯闭环：负观测感知 + 信息增益选点 + 滚动任务排序。""" + + def __init__(self, client: SimulatorClient, + config: ProblemConfig = ProblemConfig()): + super().__init__(client, config) + validate_seven_coverage(config.bayes.station_ring_radius_m, config) + self.coverage_plan = seven_plan(config.bayes.station_ring_radius_m) + self.ledger = CoverageLedger( + config, points=list(self.coverage_plan.points)) + self.particles = {channel: ChannelParticles(config) + for channel in self.belief.channels} + self._measured_points: dict[int, set[tuple[int, int]]] = {} + self._clear_failed: set[int] = set() # 证书清除失败后须先补测再重试 + self._stall: dict[int, int] = {} # 连续无收缩计数（异常留痕用） + self._skip_cache: dict[tuple[int, int], tuple[int, bool]] = {} + self.skipped_measures = 0 # 跳测规则省下的检测次数 + self.no_shrink_measures = 0 # 未收缩幸存集的定位检测（诊断用） + self.pf_absent_channels: list[int] = [] # 由幸存集为空证明缺席的频道 + self.opportunistic_measures = 0 + + # ------------------------------------------------------------ 主循环 + def _coverage_phase(self) -> None: + """统一任务循环：发现 + 定位 + 清除滚动调度，直到任务表为空。""" + while self.stop_reason is None: + if self._count_limit_reached() or self._virtual_cap_reached(): + return + if not self._step_once(): + return + + def _step_once(self) -> bool: + """构建任务表、排序并执行首任务；无可执行任务返回 False。""" + if self.config.bayes.opportunistic_measure: + self._measure_at_stop() + tasks = self._build_tasks() + if not tasks: + return False + tasks = self._refine_locate_tasks(tasks) + order = self._order_tasks(tasks) + self._execute_task(order[0]) + return True + + def _measure_at_stop(self) -> None: + """利用已停靠位置补交会方位；评分只作选测，证书仍用完整角域。 + + 只测尚未在此处测过、有望显著收缩且保证距离可接收的已发现频道。 + 逐频道调用measure，换频与5秒检测照常计费；不在移动中检测。 + 此距离保证仅适用于第三问，不能用于未知定向源。 + """ + point = self.client.state.position + channels = self.belief.channels_by_status(ChannelStatus.DETECTED) + channels.sort(key=lambda c: (c != self.client.state.channel, c)) + for channel in channels: + if self._virtual_cap_reached(): + return + if _point_key(point) in self._measured_points.get(channel, set()): + continue + cert = self._best_certificate(channel) + if cert is not None and cert.certified: + continue + region = self.belief.candidate_set(channel) + farthest = max(math.dist(point, v) for v in region.polygon) + if farthest > self.config.field.r_eff_min_m - 1e-3: + continue + radius = region.mec()[1] + vertices = region.polygon + stride = max(1, len(vertices) // self.config.bayes.mc_representatives) + radii = [] + delta = (self.config.field.bearing_error_half_deg + + self.config.search.bearing_rounding_margin_deg) + for target in vertices[::stride]: + theta = math.degrees(math.atan2(target[1]-point[1], target[0]-point[0])) + probe = CandidateRegion(list(vertices), region.slack_m) + probe.clip_wedge(point, theta, delta) + radii.append(probe.mec()[1] if probe.polygon else radius) + if sum(radii) / len(radii) > radius * self.config.bayes.opportunistic_radius_ratio: + continue + outcome = self.client.measure(point, channel) + self._record_measure(channel, point, outcome) + self._may_clear.add(channel) + self.opportunistic_measures += 1 + + # ------------------------------------------------------------ 任务构建 + def _station_pending(self, index: int) -> list[int]: + """站点待测频道：UNKNOWN、未测过、非"必 no_signal"且未证缺席。""" + point = self.ledger.points[index] + pending = [] + for channel, belief in self.belief.channels.items(): + if belief.status is not ChannelStatus.UNKNOWN: + continue + if self.ledger.measured_at(channel, index): + continue + if self._skip_station_channel(channel, index, point): + continue + pending.append(channel) + return pending + + def _fused_channels_at(self, index: int) -> list[int]: + """本站要测的频道 = 未发现(UNKNOWN) + 已发现但尚未定证(DETECTED)。 + + P0-1：把定位并入覆盖巡回。站点三角化可行性（方案 §1.3 F11）： + 99.28% 的源位置有 (*@\ensuremath{\ge}@*)2 个站在 r_eff_max=1500m 内，最佳交会角中位 + 122.9°、5 分位 58.5°，因此"顺路取第二条方位线"对绝大多数源成立。 + 已有证书、已在同一 0.5m 测点测过、或该点必 no_signal 的频道跳过。 + + 实测结论（2026-09-12，`output/suite/q3-fuse-ab*`）：本机制**不划算**。 + 七站环上通常只有 2–3 个站能对该源取得有效方位线，交会角也不足以 + 直接换到 20m 证书，专用信息增益探点仍然必要；仅在站点顺带测量等于 + 平白多花约 11 次检测（+0.8%），若同时抑制专用探点则 +45.6%（20/20 + 场景更慢）。默认关闭，保留代码以便复现与后续研究。 + """ + point = self.ledger.points[index] + channels = self._station_pending(index) + selected = set(channels) + if not self.config.bayes.fuse_localize_into_tour: + return channels + for channel in self.belief.channels_by_status(ChannelStatus.DETECTED): + if channel in selected or self.ledger.measured_at(channel, index): + continue + if _point_key(point) in self._measured_points.get(channel, set()): + continue + cert = self._best_certificate(channel) + if cert is not None and cert.certified: + continue # 已有证书：交给清除任务，不再多测 + if self._skip_station_channel(channel, index, point): + continue # 幸存集都在 1500m 外：该点必 no_signal + channels.append(channel) + selected.add(channel) + return channels + + def _skip_station_channel(self, channel: int, index: int, point: Vec2) -> bool: + """跳测规则（按 pf.version 缓存；幸存集单调收缩，判定单调）。""" + pf = self.particles[channel] + if not pf: + return True + cached = self._skip_cache.get((channel, index)) + if cached is not None and cached[0] == pf.version: + return cached[1] + value = pf.guaranteed_no_signal(point) + self._skip_cache[(channel, index)] = (pf.version, value) + return value + + def _build_tasks(self) -> list[Task]: + tasks: list[Task] = [] + for index, point in enumerate(self.ledger.points): + pending = self._fused_channels_at(index) + if not pending: + continue + switches = len(pending) - (1 if self.client.state.channel in pending else 0) + tasks.append(Task("station", tuple(point), + self.config.cost.measure_s * len(pending) + + self.config.cost.switch_s * max(switches, 0), + station_index=index, station_channels=tuple(pending))) + for channel in self.belief.channels_by_status(ChannelStatus.DETECTED): + cert = self._best_certificate(channel) + if cert is not None and cert.certified \ + and channel not in self._clear_failed: + tasks.append(Task("clear", cert.center, + self.config.cost.clear_success_s, + channel=channel)) + continue + if self._defer_to_station(channel): + continue # 下一条方位线可由"本就要去的站点"顺路提供 + point = self._select_point(channel) + if point is None: + continue + tasks.append(Task("locate", point, + self.config.cost.measure_s + self.config.cost.switch_s, + channel=channel)) + return tasks + + def _defer_to_station(self, channel: int) -> bool: + """该频道能否由"本就要去的站点"提供下一条方位线。 + + P0-1 的关键：仅仅在站点顺带测量是不够的（那只是多做一次检测）， + 必须同时**抑制专用探点任务**，否则滚动排序仍会优先飞向更近的探点。 + 判据要求该站本来就有 UNKNOWN 频道待测（覆盖巡回必须去），因此不会 + 为了等一条方位线而制造新的绕行，也不会出现"无任务可做"的死锁： + 站点扫完后 ``_station_pending`` 为空，探点任务自然恢复。 + """ + if not self.config.bayes.fuse_localize_into_tour: + return False + for index, point in enumerate(self.ledger.points): + if not self._station_pending(index): + continue + if self.ledger.measured_at(channel, index): + continue + if _point_key(point) in self._measured_points.get(channel, set()): + continue + if self._skip_station_channel(channel, index, point): + continue + return True + return False + + # ------------------------------------------------------------ 任务排序 + def _order_tasks(self, tasks: list[Task]) -> list[Task]: + """开放路径排序：小任务表用精确 DP，否则最近邻 + 2-opt。 + + Held-Karp（S5/T1）把"已访问集合 × 结束时测向频道"并入状态，因此换频 + 代价是精确的，而不是 :meth:`_path_cost` 里"按频道排序"的贪心近似。 + """ + if len(tasks) <= 2: + ordered = sorted(tasks, key=lambda t: ( + move_time(self.client.state.position, t.position, self.config.cost), + t.kind, t.channel or 0)) + return min((ordered, ordered[::-1]), key=self._path_cost) + limit = self.config.bayes.exact_order_limit + if 0 < limit and len(tasks) <= limit: + exact = self._exact_order(tasks) + if exact is not None: + return exact + order = self._nearest_order(tasks) + if not self.config.bayes.two_opt_enabled: + return order + return self._two_opt(order) + + def _service_and_exit(self, task: Task, + channel: int) -> tuple[float, int]: + """任务在进入频道 ``channel`` 时的固有耗时与离开后的测向频道。""" + cost = self.config.cost + if task.kind == "locate": + return (cost.measure_s + (cost.switch_s if channel != task.channel else 0.0), + task.channel) + if task.kind == "station" and task.station_channels: + pending = sorted(task.station_channels, + key=lambda c: (c != channel, c)) + switches = len(pending) - (1 if channel in pending else 0) + return (cost.measure_s * len(pending) + cost.switch_s * switches, + pending[-1]) + return task.service_s, channel + + def _exact_order(self, tasks: list[Task]) -> list[Task] | None: + """Held-Karp 精确开放路径（起点固定、终点自由，含换频状态）。 + + 状态 ``(mask, c)`` = 已访问任务集 mask、离开最后一个任务后测向频道为 c； + 频道取值域只需 {当前频道} (*@\ensuremath{\cup}@*) {locate 频道} (*@\ensuremath{\cup}@*) {station 离开频道}。 + 规模 ``2^n·n·|C|``；n 超过 :attr:`BayesConfig.exact_order_limit` 时由 + 调用方回退启发式。返回 ``None`` 表示状态过大（防御性）。 + """ + n = len(tasks) + if n <= 1: + return list(tasks) + start = self.client.state.position + init = self.client.state.channel + channels = {init} + for task in tasks: + if task.kind == "locate": + channels.add(task.channel) + elif task.kind == "station" and task.station_channels: + # 离开频道 = 按"当前频道优先"排序后的最后一个：通常是最大值； + # 进入频道恰为最大值时退化为次大值，故两者都要进状态空间。 + ordered = sorted(task.station_channels) + channels.add(ordered[-1]) + if len(ordered) > 1: + channels.add(ordered[-2]) + channels = sorted(channels) + width = len(channels) + if width * (1 << n) * n > 4_000_000: + return None + index_of = {channel: i for i, channel in enumerate(channels)} + c_init = index_of[init] + service: list[list[float]] = [] + exits: list[list[int]] = [] + for task in tasks: + row_service, row_exit = [], [] + for channel in channels: + value, exit_channel = self._service_and_exit(task, channel) + row_service.append(value) + row_exit.append(index_of[exit_channel]) + service.append(row_service) + exits.append(row_exit) + move = [[move_time(tasks[i].position, tasks[j].position, self.config.cost) + for j in range(n)] for i in range(n)] + from_start = [move_time(start, task.position, self.config.cost) + for task in tasks] + inf = float("inf") + # dp[(mask, ci)] = 最小代价；parent[(mask, ci)] = (上一 mask, 上一 ci) + dp: dict[tuple[int, int], float] = {} + last_task: dict[tuple[int, int], int] = {} + parent: dict[tuple[int, int], tuple[int, int] | None] = {} + for k in range(n): + key = (1 << k, exits[k][c_init]) + value = from_start[k] + service[k][c_init] + if value < dp.get(key, inf): + dp[key] = value + last_task[key] = k + parent[key] = None + for mask in range(1, 1 << n): + for ci in range(width): + state = (mask, ci) + cost = dp.get(state) + if cost is None: + continue + for k in range(n): + if (mask >> k) & 1: + continue + nxt = (mask | (1 << k), exits[k][ci]) + value = cost + move[last_task[state]][k] + service[k][ci] + if value < dp.get(nxt, inf) - 1e-12: + dp[nxt] = value + last_task[nxt] = k + parent[nxt] = state + full = (1 << n) - 1 + best_key, best_cost = None, inf + for ci in range(width): + state = (full, ci) + if state in dp and dp[state] < best_cost: + best_key, best_cost = state, dp[state] + if best_key is None: + return None + order: list[Task] = [] + key: tuple[int, int] | None = best_key + while key is not None: + order.append(tasks[last_task[key]]) + key = parent[key] + order.reverse() + return order + + + + def _nearest_order(self, tasks: list[Task]) -> list[Task]: + remaining = list(tasks) + order = [] + position = self.client.state.position + while remaining: + best = min(remaining, key=lambda t: ( + move_time(position, t.position, self.config.cost), + t.kind, t.channel or 0)) + remaining.remove(best) + order.append(best) + position = best.position + return order + + def _path_cost(self, order: list[Task]) -> float: + total = 0.0 + position = self.client.state.position + channel = self.client.state.channel + for task in order: + total += move_time(position, task.position, self.config.cost) + if task.kind == "locate": + total += self.config.cost.measure_s + total += self.config.cost.switch_s * (channel != task.channel) + channel = task.channel + elif task.kind == "station" and task.station_channels: + pending = sorted( + task.station_channels, + key=lambda c, channel=channel: (c != channel, c)) + total += self.config.cost.measure_s * len(pending) + total += self.config.cost.switch_s * (len(pending) - (channel in pending)) + channel = pending[-1] + else: + total += task.service_s # 清除不改变测向频道 + position = task.position + return total + + def _two_opt(self, order: list[Task]) -> list[Task]: + best = list(order) + best_cost = self._path_cost(best) + for _ in range(self.config.bayes.two_opt_passes): + improved = False + for i in range(len(best) - 1): + for j in range(i + 1, len(best)): + candidate = best[:i] + best[i:j + 1][::-1] + best[j + 1:] + cost = self._path_cost(candidate) + if cost < best_cost - 1e-6: + best, best_cost, improved = candidate, cost, True + if not improved: + break + return best + + # ------------------------------------------------------------ 任务执行 + def _execute_task(self, task: Task) -> None: + if task.kind == "station": + self._execute_station(task.station_index) + elif task.kind == "clear": + cert = self._best_certificate(task.channel) + if cert is not None and cert.certified: + if not self._attempt_clear(task.channel, cert.center, cert): + self._clear_failed.add(task.channel) + self._may_clear.discard(task.channel) + else: + self._clear_failed.discard(task.channel) + elif task.kind == "locate": + self._execute_locate(task.channel, task.position) + + def _execute_station(self, index: int) -> None: + """单站批量扫频：只测待测频道（跳测规则已过滤），扫完即返回重排。 + + P0-1：本站同时测量"已发现未定证"频道，使第二/第三条方位线在巡回 + 途中顺路取得；证书一旦成立即就地清除，不额外绕行。 + """ + point = self.ledger.points[index] + pending = self._fused_channels_at(index) + unknown = [c for c, b in self.belief.channels.items() + if b.status is ChannelStatus.UNKNOWN] + self.skipped_measures += len(unknown) - len( + [c for c in pending if self.belief.channels[c].status + is ChannelStatus.UNKNOWN]) + # 当前频道优先，减少换频；同站 near 直接清除不打断扫频 + pending.sort(key=lambda c: (c != self.client.state.channel, c)) + for channel in pending: + if self.stop_reason is not None or self._count_limit_reached() \ + or self._virtual_cap_reached(): + return + detected_before = (self.belief.channels[channel].status + is ChannelStatus.DETECTED) + outcome = self.client.measure(point, channel) + self.ledger.mark_measured(channel, index) + self._record_measure(channel, point, outcome) + if outcome.result in (DIRECTION, NEAR): + self._may_clear.add(channel) + if outcome.result == NEAR: + region = self.belief.candidate_set(channel) + cert = clear_certificate(region, channel, self.config) + if cert.certified: + if self._attempt_clear(channel, point, cert): + self._clear_failed.discard(channel) + else: + self._clear_failed.add(channel) + self._may_clear.discard(channel) + else: + self._anomaly("near_without_certificate", channel, position=point) + continue + if not detected_before: + continue + if outcome.result == NO_SIGNAL: + # 该频道已被发现：保证接收盘内不可能 no_signal，属守恒性异常 + region = self.belief.candidate_set(channel) + safe = (safe_disk_radius(region, self.config) + if region is not None else -1.0) + if safe >= 0 and math.dist(point, region.mec()[0]) <= safe: + self._anomaly("no_signal_in_safe_disk", channel, + position=point) + continue + cert = self._best_certificate(channel) + if cert is not None and cert.certified: + if self._attempt_clear(channel, cert.center, cert): + self._clear_failed.discard(channel) + else: + self._clear_failed.add(channel) + self._may_clear.discard(channel) + + def _execute_locate(self, channel: int, point: Vec2) -> None: + """单步定位测量：执行后立即重排（滚动时域），收敛则顺路清除。""" + pf = self.particles[channel] + before = len(pf) + outcome = self.client.measure(point, channel) + self._record_measure(channel, point, outcome) + self._may_clear.add(channel) + if outcome.result == NO_SIGNAL: + region = self.belief.candidate_set(channel) + if region is not None and safe_disk_radius(region, self.config) >= 0 \ + and math.dist(point, region.mec()[0]) \ + <= safe_disk_radius(region, self.config): + self._anomaly("no_signal_in_safe_disk", channel, position=point) + after = len(pf) + cert = self._best_certificate(channel) + if cert is not None and cert.certified: + if self._attempt_clear(channel, cert.center, cert): + self._clear_failed.discard(channel) + self._stall.pop(channel, None) + return + self._clear_failed.add(channel) + self._may_clear.discard(channel) + if after == before: + self._stall[channel] = self._stall.get(channel, 0) + 1 + self.no_shrink_measures += 1 # 只是浪费不破坏守恒性，不进异常表 + else: + self._stall[channel] = 0 + + # ------------------------------------------------------------ 感知与证书 + def _record_measure(self, channel: int, position: Vec2, outcome) -> None: + """belief（凸证书）与 PF（幸存集）同步更新；PF 空即证缺席。""" + self.belief.update_measure(channel, position, outcome.result, + outcome.svd_deg) + # 同一 0.5m 测点 × 同一频道的重复检测：历史上一次官方演练有 98.84% + # 的虚拟时间耗在空复扫上，本计数是该问题的回归指标。 + key = _point_key(position) + seen = self._measured_points.setdefault(channel, set()) + if key in seen: + self.redundant_rescan_measures += 1 + seen.add(key) + self._clear_failed.discard(channel) # 新证据落地：允许再次尝试清除 + belief = self.belief.channels[channel] + if belief.status in (ChannelStatus.CLEARED, ChannelStatus.ABSENT): + return # 已证毕：清除/缺席后的 no_signal 与距离无关，不进 PF + pf = self.particles[channel] + pf.apply_measure(position, outcome.result, outcome.svd_deg) + if not pf: + if belief.status is ChannelStatus.UNKNOWN: + self.belief.mark_absent(channel) + self.absence_evidence[channel] = "pf_empty" + if channel not in self.pf_absent_channels: + self.pf_absent_channels.append(channel) + else: + self._anomaly("pf_empty_while_detected", channel, position=position) + self._apply_count_bound() + + def _apply_count_bound(self) -> None: + """存在证据达到题面源数上界时，其余 UNKNOWN 可由计数直接判缺席。 + + 依据 [题面]：每频道至多一个源、全局限定 10..16 个源。一旦 + DETECTED/CLEARED 的不同频道数达到 16，任何尚未出现有效信号的 + 频道都不可能是源，无须等 7 站覆盖账本跑完。该判定与位置无关， + 是严格的计数证明；evidence 与 coverage/pf_empty 分开留痕。 + """ + present = [channel for channel, belief in self.belief.channels.items() + if belief.status in (ChannelStatus.DETECTED, + ChannelStatus.CLEARED)] + if len(present) < self.config.field.source_count_max: + return + for channel, belief in self.belief.channels.items(): + if belief.status is ChannelStatus.UNKNOWN: + belief.status = ChannelStatus.ABSENT + self.absence_evidence[channel] = "count_bound" + + def _best_certificate(self, channel: int) -> ClearCertificate | None: + """凸证书优先；负观测挖洞使 PF 幸存集更紧时用网格证书补位。""" + region = self.belief.candidate_set(channel) + cert = clear_certificate(region, channel, self.config) \ + if region is not None else None + if cert is not None and cert.certified: + return self._near_clear_target(cert) + if self.config.bayes.grid_cert_enabled: + pf = self.particles[channel] + if len(pf): + center, radius = pf.mec() + limit = (self.config.field.clear_radius_m - pf.margin_m + - self.config.search.clear_margin_m) + if radius <= limit: + return self._near_clear_target( + ClearCertificate(channel, center, radius, limit, True)) + return cert + + def _near_clear_target(self, cert: ClearCertificate) -> ClearCertificate: + """沿当前来向利用20m清除容差；三角不等式保留整集覆盖证明。""" + position = self.client.state.position + distance = math.dist(position, cert.center) + shift = min(distance, max(0.0, cert.limit_m - cert.radius_m - 1e-6)) + if distance <= 1e-9 or shift <= 0: + return cert + target = tuple(c + (p-c)*shift/distance for p, c in zip(position, cert.center)) + return ClearCertificate(cert.channel, target, cert.radius_m+shift, cert.limit_m, True) + + # ------------------------------------------------------------ 信息增益选点 + def _probe_context(self, channel: int): + """构造某频道下一次定位测量的候选集与信息增益评分函数。 + + 返回 ``(candidates, info_score, mec_center, current_position)``； + 候选为空返回 ``None``。``_select_point`` 与路线感知精修共用此逻辑， + 保证两者只差“移动代价如何折算”。 + """ + bayes, search = self.config.bayes, self.config.search + pf = self.particles[channel] + if not pf: + return None + region = self.belief.candidate_set(channel) + center, radius = pf.mec() + measured = self._measured_points.get(channel, set()) + position = self.client.state.position + candidates: list[Vec2] = [] + safe = safe_disk_radius(region, self.config) if region is not None else -1.0 + if region is not None and safe >= 0: + # 保证接收盘（凸证书口径）：任意候选必产生 direction/near + candidates = candidate_points(tuple(region.mec()[0]), safe, + search.candidate_rings, + search.candidate_angles) + # 以实际来向生成对称交会候选，避免固定全局角度网格的旋转偏差。 + geometric_center = region.mec()[0] + base_angle = math.atan2(position[1] - geometric_center[1], + position[0] - geometric_center[0]) + for fraction in search.candidate_rings: + if fraction <= 0: + continue + for offset in (-math.pi/3, -math.pi/6, 0, math.pi/6, math.pi/3): + angle = base_angle + offset + candidates.append((geometric_center[0] + safe * fraction * math.cos(angle), + geometric_center[1] + safe * fraction * math.sin(angle))) + # 已停靠位置若本身在安全接收盘内，是零移动的合法测点；显式加入 + # 可避免为了固定角度环而白白横移。 + if math.dist(position, geometric_center) <= safe + 1e-9: + candidates.append(tuple(position)) + else: + # 宽候选集：PF MEC 探索环（负观测挖洞后幸存集的包围圆） + for fraction in bayes.wide_rings: + ring = max(radius * fraction, 2.0 * pf.margin_m) + candidates.extend(candidate_points(center, ring, (1.0,), + search.candidate_angles)) + candidates.append(tuple(center)) + candidates.append(tuple(position)) + candidates = [tuple(c) for c in candidates + if _point_key(c) not in measured] + if not candidates: + return None + # 采样一次转成数组（numpy 可用时），使候选评分走向量路径； + # numpy 缺失时 as_sample_array 原样返回列表，语义不变。 + subsample = as_sample_array(pf.subsample(bayes.score_subsample)) + stride = max(len(subsample) // bayes.mc_representatives, 1) + representatives = subsample[::stride] + + def info_score(q: Vec2) -> float: + if bayes.score_mode == "entropy": + return pf.expected_survival(q, subsample, representatives) + return pf.expected_posterior_radius(q, subsample, representatives) + + return candidates, info_score, center, position + + def _select_point(self, channel: int) -> Vec2 | None: + """定位测量点：期望 log 幸存占比 + (*@\ensuremath{\lambda}@*)·移动时间 最小的候选。""" + context = self._probe_context(channel) + if context is None: + return None + candidates, info_score, center, position = context + bayes = self.config.bayes + + def score(q: Vec2) -> float: + # 一次定位后仍需接近源才能清除；仅计到检测点的移动会偏好绕行。 + move = bayes.lambda_move_s * (move_time(position, q, self.config.cost) + + move_time(q, center, self.config.cost)) + return info_score(q) + move + + return min(candidates, key=lambda q: (score(q), _point_key(q))) + + def _refine_locate_tasks(self, tasks: list[Task]) -> list[Task]: + """路线感知精修定位任务点（P2，2026-09-12）。 + + 旧评分只比较 ``current->q + q->MEC``，是局部代理；滚动 2-opt 的真实 + 代价还包含 ``q->next_task``。这里对每个 locate 任务在候选点上计算 + “替换该任务后整条当前路线代价的增量”，再与信息增益、MEC 接近项合并 + 选点。只改变选点启发式，不改变覆盖/清除证明。 + """ + bayes = self.config.bayes + if not bayes.route_aware_probe: + return tasks + locate_indices = [index for index, task in enumerate(tasks) + if task.kind == "locate"] + if not locate_indices: + return tasks + base_order = self._order_tasks(tasks) + base_cost = self._path_cost(base_order) + refined = list(tasks) + for task_index in locate_indices: + task = tasks[task_index] + context = self._probe_context(task.channel) + if context is None: + continue + candidates, info_score, center, position = context + try: + order_index = next(index for index, item in enumerate(base_order) + if item is task) + except StopIteration: # pragma: no cover - 同对象应始终存在 + order_index = next(index for index, item in enumerate(base_order) + if item.kind == "locate" + and item.channel == task.channel) + best_score: float | None = None + best_point: Vec2 | None = None + for point in candidates: + trial_order = list(base_order) + trial_order[order_index] = Task( + "locate", tuple(point), task.service_s, channel=task.channel) + route_delta = self._path_cost(trial_order) - base_cost + move_proxy = bayes.lambda_move_s * ( + move_time(position, point, self.config.cost) + + move_time(point, center, self.config.cost)) + clear_near = move_time(point, center, self.config.cost) + value = (info_score(point) + + move_proxy + + bayes.route_aware_insert_weight * route_delta + + bayes.route_aware_clear_weight * clear_near) + if best_score is None or value < best_score: + best_score, best_point = value, tuple(point) + if best_point is not None: + refined[task_index] = Task( + "locate", best_point, task.service_s, channel=task.channel) + return refined + + # ------------------------------------------------------------ 安全网与复扫 + def _localize_and_clear(self, channel: int) -> bool: + """阻塞式定位子循环（resolve 阶段安全网）：PF 选点，失败退凸选点。""" + search = self.config.search + self._may_clear.add(channel) + for _ in range(search.max_localize_steps): + if self._virtual_cap_reached(): + return False + cert = self._best_certificate(channel) + if cert is not None and cert.certified and channel in self._may_clear: + if self._attempt_clear(channel, cert.center, cert): + self._clear_failed.discard(channel) + return True + self._clear_failed.add(channel) + self._may_clear.discard(channel) + continue + point = self._select_point(channel) + if point is None: + region = self.belief.candidate_set(channel) + if region is None: + return False + point = select_measurement_point( + region, self.client.state.position, self.config).position + outcome = self.client.measure(point, channel) + self._record_measure(channel, point, outcome) + self._may_clear.add(channel) + if outcome.result == NO_SIGNAL: + region = self.belief.candidate_set(channel) + if region is not None and safe_disk_radius(region, self.config) >= 0 \ + and math.dist(point, region.mec()[0]) \ + <= safe_disk_radius(region, self.config): + self._anomaly("no_signal_in_safe_disk", channel, position=point) + cert = self._best_certificate(channel) + if cert is not None and cert.certified: + if self._attempt_clear(channel, cert.center, cert): + self._clear_failed.discard(channel) + return True + self._clear_failed.add(channel) + self._may_clear.discard(channel) + return self.belief.channels[channel].status is ChannelStatus.CLEARED + + def _persistent_round(self) -> None: + """一轮复扫：与基线一致的全站复测，但读数同步进 PF（防假设偏差）。""" + measured: set[tuple[int, int]] = set() + while self.stop_reason is None: + index = self._next_resweep_point(measured) + if index is None: + return + point = self.ledger.points[index] + for channel in self._resweep_channels_at(index, measured): + if self._virtual_cap_reached(): + return + measured.add((channel, index)) + was_absent = (self.belief.channels[channel].status + is ChannelStatus.ABSENT) + outcome = self.client.measure(point, channel) + self._record_measure(channel, point, outcome) + if was_absent and outcome.result in (DIRECTION, NEAR): + # 复测推翻了缺席证明：守恒性留痕，按新证据定位清除。 + self._anomaly("absent_detected_on_resweep", channel, + position=point, result=outcome.result) + if outcome.result == DIRECTION: + self._localize_and_clear(channel) + elif outcome.result == NEAR: + cert = self._best_certificate(channel) + if cert is not None and cert.certified: + if not self._attempt_clear(channel, cert.center, cert): + self._clear_failed.add(channel) + else: + self._anomaly("near_without_certificate", channel, + position=point) + if self.stop_reason is not None: + return + + # ------------------------------------------------------------ 收尾 + def _summary(self, info) -> dict: + report = super()._summary(info) + report["strategy"] = "bayes" + report["opportunistic_measures"] = self.opportunistic_measures + report["skipped_measures"] = self.skipped_measures + report["no_shrink_measures"] = self.no_shrink_measures + report["pf_absent_channels"] = sorted(self.pf_absent_channels) + report["pf_alive_final"] = { + str(channel): len(self.particles[channel]) + for channel in sorted(self.particles) + if self.belief.channels[channel].status is ChannelStatus.DETECTED} + return report diff --git a/docs/paper/data/listing-source/src/mcm26b/planner/seven.py.tex b/docs/paper/data/listing-source/src/mcm26b/planner/seven.py.tex new file mode 100644 index 0000000..2bd2803 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/planner/seven.py.tex @@ -0,0 +1,113 @@ +"""P4 七点覆盖策略族：解析证明的六边形发现站 + 同站批量扫频。 + +从 scripts/benchmark_q3_search.py 提升为库代码（A2 基线，官方演练 +12/12 全清、虚拟 5232s）。覆盖几何：原点 + 半径 RING_RADIUS_M 环上 +6 等分点；域半径R、环半径r时，最近站距离的解析 +上界 max(r/√3, sqrt(R²+r²−√3Rr)) < 1000m [题面 +r_eff 下界]，故任意合法源必被至少一站检出——缺席证明只需该频道 +7 站全 no_signal（CoverageLedger.coverage_complete）。 + +调度变体： +- SevenImmediate：站内即时进入定位子循环（A1）； +- SevenBatch：站内只扫频，扫完按"距候选集 MEC 圆心最近"服务队列（A2）； +- SevenSweep：全域扫完再统一服务（A3）。 +""" + +from __future__ import annotations + +import math + +from ..belief import ChannelStatus +from ..config import ProblemConfig +from ..coverage import CoverageLedger +from ..guarantee import seven_plan +from ..protocol.rules import NEAR +from . import OmnidirectionalLoop, clear_certificate + +RING_RADIUS_M = 1200.0 # [工程] 解析证明见 docs/algo-3.md §5 与 geometry_check + + +def seven_points(ring_radius_m: float = RING_RADIUS_M) -> list[tuple[float, float]]: + """原点 + 环上 6 等分点的七站覆盖集。""" + return [(0.0, 0.0)] + [(ring_radius_m * math.cos(k * math.pi / 3), + ring_radius_m * math.sin(k * math.pi / 3)) for k in range(6)] + + +def validate_seven_coverage(ring_radius_m: float, config: ProblemConfig) -> float: + """六个60°扇区内的最近站最远距离上界；仅证明全向源覆盖。 + + 原点/环站Voronoi交点给出r/√3，目标圆边界的扇区接缝给出另一项。 + 环半径满足0 config.field.r_eff_min_m - 1e-6: + raise ValueError("七站未覆盖整个目标域，不能据此证明频道缺席") + return bound + + +class SevenImmediate(OmnidirectionalLoop): + """七点覆盖 + 站内即时定位（基类覆盖阶段逻辑不变，仅换站集）。""" + + def __init__(self, client, config: ProblemConfig = ProblemConfig(), + ring_radius_m: float = RING_RADIUS_M): + super().__init__(client, config) + validate_seven_coverage(ring_radius_m, config) + self.coverage_plan = seven_plan(ring_radius_m) + self.ledger = CoverageLedger(config=config, + points=list(self.coverage_plan.points)) + + +class SevenBatch(SevenImmediate): + """站内只扫频，扫完按最近候选集圆心顺序服务检测队列（A2 主策略）。""" + + defer_all = False + + def _serve_queue(self): + # Each detected channel gets at most one localization call in this pass. + queue = self.belief.channels_by_status(ChannelStatus.DETECTED) + while queue: + c = min(queue, key=lambda c: (math.dist(self.client.state.position, + self.belief.candidate_set(c).mec()[0]), c)) + queue.remove(c) + self._localize_and_clear(c) + if self._count_limit_reached(): + break + + def _coverage_phase(self): + while not self._count_limit_reached(): + index = self._next_point_index() + if index is None: + return + point = self.ledger.points[index] + pending = self._pending_channels_at(index) + # Keeping the current measuring channel first saves a switch when possible. + pending.sort(key=lambda c: (c != self.client.state.channel, c)) + for c in pending: + outcome = self.client.measure(point, c) + self.ledger.mark_measured(c, index) + self.belief.update_measure(c, point, outcome.result, outcome.svd_deg) + if outcome.result == NEAR: + cert = clear_certificate(self.belief.candidate_set(c), c, self.config) + # Same-station near clear; do not displace the station scan. + if cert.certified: + self._attempt_clear(c, point, cert) + if self._count_limit_reached(): + return + if not self.defer_all: + self._serve_queue() + + def _resolve_detected(self): + self._serve_queue() + unresolved = [c for c, b in self.belief.channels.items() + if b.status not in (ChannelStatus.CLEARED, ChannelStatus.ABSENT)] + return "all_resolved" if not unresolved else "unresolved_channels" + + +class SevenSweep(SevenBatch): + """Finish discovery at all necessary stations before servicing the queue.""" + + defer_all = True diff --git a/docs/paper/data/listing-source/src/mcm26b/protocol/__init__.py.tex b/docs/paper/data/listing-source/src/mcm26b/protocol/__init__.py.tex new file mode 100644 index 0000000..85bfdf2 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/protocol/__init__.py.tex @@ -0,0 +1,15 @@ +"""P0/P1 协议层：字段表、规则表、计时模型、状态机与客户端。""" + +from .client import (ActionRejected, ClearOutcome, DeadlineExceeded, + ExitInfo, MeasureOutcome, ProtocolError, + ProtocolViolation, SimulatorClient) +from .log import SessionLog +from .state import RobotState, StateError +from .timing import CostBreakdown, clear_cost, measure_cost, move_time +from .transport import RequestsTransport, Transport, TransportError, TransportResponse + +__all__ = ["ActionRejected", "ClearOutcome", "CostBreakdown", "DeadlineExceeded", + "ExitInfo", "MeasureOutcome", "ProtocolError", "ProtocolViolation", + "RequestsTransport", "RobotState", "SessionLog", "SimulatorClient", + "StateError", "Transport", "TransportError", "TransportResponse", + "clear_cost", "measure_cost", "move_time"] diff --git a/docs/paper/data/listing-source/src/mcm26b/protocol/client.py.tex b/docs/paper/data/listing-source/src/mcm26b/protocol/client.py.tex new file mode 100644 index 0000000..373f87a --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/protocol/client.py.tex @@ -0,0 +1,333 @@ +"""P1 协议基线：串行、幂等、带现实预算的模拟器客户端。 + +协议硬规则 [题面] 与实现对应： +- 每个新动作使用新的 request_id；仅在网络失败后重试"完全相同的动作"时， + 复用原 request_id 与原请求体 —— 本类通过一次性序列化出 bytes 并原样重发保证； +- 必须同时检查 HTTP 状态与 accepted；accepted=false 不更新状态， + 其 virtual_time_s=0 不当作当前虚拟时刻； +- 逐次等待响应、不得并发；本类完全同步，一个动作未决不发起下一个； +- 现实截止用 /enter 响应的 remaining_real_duration_s 建立本地单调时钟， + 预留退出余量；/exit 不做预算拦截。 +""" + +from __future__ import annotations + +import json +import math +import uuid +from dataclasses import dataclass +from time import monotonic, sleep + +from ..config import ProblemConfig, Vec2 +from .log import SessionLog +from .rules import (CLEAR_RESULTS, DIRECTION, EXIT_USER, MEASURE_RESULTS, + POSITION_FIELDS, STATUS_OK, STATUS_RETRYABLE) +from .state import RobotState +from .timing import CostBreakdown +from .transport import RequestsTransport, Transport, TransportError + + +class ProtocolError(RuntimeError): + """协议层失败，含 HTTP 状态与响应体；默认不重试（确定性错误）。""" + + def __init__(self, message: str, status: int | None = None, body=None): + super().__init__(message) + self.status = status + self.body = body + + +class ActionRejected(ProtocolError): + """HTTP 200 但 accepted=false：动作未生效，状态不得更新。""" + + def __init__(self, message: str, body=None): + super().__init__(message, status=STATUS_OK, body=body) + + +class ProtocolViolation(ProtocolError): + """响应与协议约定不符（字段缺失、值非法、虚拟时刻回退等）。""" + + +class DeadlineExceeded(RuntimeError): + """现实预算不足：预留退出余量后剩余时间不够执行新动作。""" + + +@dataclass(frozen=True) +class MeasureOutcome: + result: str + svd_deg: float | None + virtual_time_s: float + predicted: CostBreakdown + raw: dict + + +@dataclass(frozen=True) +class ClearOutcome: + result: str + virtual_time_s: float + predicted: CostBreakdown + raw: dict + + +@dataclass(frozen=True) +class ExitInfo: + reason: str + virtual_time_s: float + raw: dict + + +def _validate_identifier(name: str, value: str, max_bytes: int) -> None: + if not isinstance(value, str) or not value: + raise ValueError(f"{name} 必须是非空字符串") + encoded = value.encode("utf-8") + if not 1 <= len(encoded) <= max_bytes: + raise ValueError(f"{name} 的 UTF-8 长度须在 1..{max_bytes} 字节") + if any(code < 0x20 or code == 0x7F for code in encoded): + raise ValueError(f"{name} 不能包含控制字符") + + +def _validate_position(position: dict, limit: float) -> None: + if set(position) != set(POSITION_FIELDS): + raise ValueError("position 字段必须是且只能是 x、y") + for key in ("x", "y"): + value = position[key] + if isinstance(value, bool) or not isinstance(value, (int, float)): + raise ValueError(f"position.{key} 必须是数值") + if not math.isfinite(value): + raise ValueError(f"position.{key} 必须是有限数值") + if abs(value) > limit: + raise ValueError(f"position.{key} 绝对值不得超过 {limit} 米") + + +def _validate_channel(channel) -> int: + # 写成 JSON number 1.0 且恰为整数也接受 [题面]；1.5 拒绝。 + if isinstance(channel, bool) or not isinstance(channel, (int, float)): + raise ValueError("channel 必须是数值") + if isinstance(channel, float) and not channel.is_integer(): + raise ValueError("channel 必须是整数") + channel = int(channel) + if not 1 <= channel <= 20: + raise ValueError("channel 必须在 1..20 范围内") + return channel + + +class SimulatorClient: + """四条指令的同步客户端。状态只在 accepted=true 后推进。""" + + def __init__(self, robot_id: str, *, + config: ProblemConfig = ProblemConfig(), + transport: Transport | None = None, + log: SessionLog | None = None, + clock=monotonic): + _validate_identifier("robot_id", robot_id, config.session.robot_id_max_bytes) + self.robot_id = robot_id + self.config = config + self.session = config.session + self.transport = transport if transport is not None else RequestsTransport() + self.log = log if log is not None else SessionLog() + self.clock = clock + self.state = RobotState() + self._prefix = uuid.uuid4().hex[:12] + self._seq = 0 + self._deadline: float | None = None # 本地单调时钟截止 + self._server_deadline_ms: float | None = None # 服务器时间戳交叉核对 + self._enter_monotonic: float | None = None # 实机计时起点（/enter 成功） + + # ------------------------------------------------------------ 公共动作 API + def enter(self) -> dict: + started = self.clock() + payload = self._payload("/enter") + response = self._call("/enter", payload) + self.state.apply_enter(response) + remaining = response["remaining_real_duration_s"] + if not isinstance(remaining, (int, float)) or remaining < 0: + raise ProtocolViolation("remaining_real_duration_s 缺失或非法", body=response) + self._deadline = self.clock() + remaining + self._server_deadline_ms = (response["real_timestamp_ms"] + + remaining * 1000.0) + self._enter_monotonic = self.clock() + self._log_step("/enter", payload, response, started, + predicted=CostBreakdown(0.0, 0.0, 0.0)) + return response + + def measure(self, position: Vec2, channel: int) -> MeasureOutcome: + started = self.clock() + payload = self._payload("/measure", position=position, channel=channel) + response = self._call("/measure", payload) + predicted = self.state.apply_measure(payload, response, + cost=self.config.cost) + result = response.get("measure_result") + if result not in MEASURE_RESULTS: + raise ProtocolViolation(f"measure_result 非法: {result!r}", body=response) + svd = response.get("svd_deg") + if result == DIRECTION: + if not isinstance(svd, (int, float)) or isinstance(svd, bool): + raise ProtocolViolation("direction 响应缺少数值 svd_deg", body=response) + self._log_step("/measure", payload, response, started, result=result, + predicted=predicted, channel=payload["channel"]) + return MeasureOutcome(result, float(svd) if svd is not None else None, + response["virtual_time_s"], predicted, response) + + def clear(self, position: Vec2, channel: int) -> ClearOutcome: + started = self.clock() + payload = self._payload("/clear", position=position, channel=channel) + response = self._call("/clear", payload) + predicted = self.state.apply_clear(payload, response, + cost=self.config.cost) + result = response.get("clear_result") + if result not in CLEAR_RESULTS: + raise ProtocolViolation(f"clear_result 非法: {result!r}", body=response) + self._log_step("/clear", payload, response, started, result=result, + predicted=predicted, channel=payload["channel"]) + return ClearOutcome(result, response["virtual_time_s"], predicted, response) + + def exit(self) -> ExitInfo: + started = self.clock() + payload = self._payload("/exit") + response = self._call("/exit", payload) + self.state.apply_exit(response) + reason = response.get("exit_reason") + if reason != EXIT_USER: + raise ProtocolViolation(f"exit_reason 非法: {reason!r}", body=response) + self._log_step("/exit", payload, response, started, + predicted=CostBreakdown(0.0, 0.0, 0.0)) + return ExitInfo(reason, response["virtual_time_s"], response) + + # ---------------------------------------------------------------- 预算控制 + @property + def real_remaining_s(self) -> float | None: + """按本地单调时钟估计的剩余现实秒数（未 enter 时为 None）。""" + return None if self._deadline is None else self._deadline - self.clock() + + def _log_step(self, path: str, payload: dict, response: dict, + started: float, *, result: str | None = None, + predicted: CostBreakdown, channel: int | None = None) -> None: + """每步计时留档 [用户决策 2026-09-11]：实机墙钟耗时 + 比赛虚拟耗时分项 + （移动=直线距离/5、切频道 1s、检测 5s、清除成功 5s/未发现 3s）。 + + step 事件不含 response 字段，不会混入 action_events / 虚拟时刻复算。 + """ + now = self.clock() + entry: dict = {"event": "step", "path": path, + "request_id": payload["request_id"], + "real_elapsed_s": round(now - started, 6), + "virtual_time_s": response["virtual_time_s"], + "virtual_cost": {"move_s": round(predicted.move_s, 6), + "switch_s": round(predicted.switch_s, 6), + "action_s": round(predicted.action_s, 6), + "total_s": round(predicted.total_s, 6)}} + if self._enter_monotonic is not None: + entry["real_since_enter_s"] = round(now - self._enter_monotonic, 6) + if "position" in payload: + entry["position"] = {"x": payload["position"]["x"], + "y": payload["position"]["y"]} + if channel is not None: + entry["channel"] = channel + if result is not None: + entry["result"] = result + self.log.append(entry) + + def _check_budget(self, path: str) -> None: + if path == "/exit" or self._deadline is None: + return + margin = self.session.reserve_exit_s + if self.real_remaining_s <= margin: + raise DeadlineExceeded( + f"剩余现实时间 {self.real_remaining_s:.1f}s 不足以预留 {margin:.1f}s 退出余量") + + # ---------------------------------------------------------------- 内部机制 + def _payload(self, _path: str, *, position: Vec2 | None = None, + channel: int | None = None) -> dict: + payload = {"arena_id": self.session.arena_id, + "robot_id": self.robot_id, + "request_id": self._next_request_id()} + if position is not None: + x, y = float(position[0]), float(position[1]) + _validate_position({"x": x, "y": y}, self.config.field.coord_abs_limit_m) + payload["position"] = {"x": x, "y": y} + if channel is not None: + payload["channel"] = _validate_channel(channel) + return payload + + def _next_request_id(self) -> str: + self._seq += 1 + request_id = f"{self._prefix}-{self._seq:04d}" + _validate_identifier("request_id", request_id, + self.session.request_id_max_bytes) + return request_id + + def _call(self, path: str, payload: dict) -> dict: + """串行执行一个动作；网络失败原样重发，HTTP 确定性错误立即抛出。""" + self._check_budget(path) + body = json.dumps(payload, ensure_ascii=False, allow_nan=False).encode("utf-8") + if len(body) > self.session.request_body_max_bytes: + raise ValueError("请求体超过 65536 字节") + headers = {"Content-Type": "application/json"} + url = self.session.base_url + path + attempts, last_error = 0, None + while attempts < self.session.max_attempts: + attempts += 1 + started = self.clock() + self.log.append({"event": "attempt", "path": path, + "request_id": payload["request_id"], + "attempt": attempts, "request": payload}) + try: + result = self.transport.post( + url, body, headers, + timeout=(self.session.connect_timeout_s, + self.session.read_timeout_s)) + except TransportError as exc: + last_error = exc + self.log.append({"event": "transport_error", "path": path, + "request_id": payload["request_id"], + "attempt": attempts, "error": str(exc), + "elapsed_s": self.clock() - started}) + if attempts < self.session.max_attempts: + sleep(self.session.retry_backoff_s * (2 ** (attempts - 1))) + continue + if result.status in STATUS_RETRYABLE: + self.log.append({"event": "retryable_status", "path": path, + "request_id": payload["request_id"], + "attempt": attempts, "status": result.status}) + if attempts < self.session.max_attempts: + sleep(self.session.retry_backoff_s * (2 ** (attempts - 1))) + continue + if result.status != STATUS_OK: + raise ProtocolError( + f"{path} 返回 HTTP {result.status}", status=result.status, + body=self._safe_json(result.body)) + response = self._safe_json(result.body) + if response is None or response.get("accepted") is not True: + raise ActionRejected( + f"{path} 未被接受: {response}", body=response) + self._verify_clock(response) + self.log.append({"event": "accepted", "path": path, + "request_id": payload["request_id"], + "request": payload, "response": response, + "attempts": attempts, + "elapsed_s": self.clock() - started}) + return response + raise TransportError( + f"{path} 重试 {attempts} 次仍失败: {last_error}") from last_error + + def _verify_clock(self, response: dict) -> None: + """accepted=true 的虚拟时刻必须单调不减；现实时间戳用于漂移核对。""" + virtual = response.get("virtual_time_s") + if not isinstance(virtual, (int, float)) or isinstance(virtual, bool): + raise ProtocolViolation("accepted 响应缺少 virtual_time_s", body=response) + if virtual < self.state.virtual_time_s - 1e-9: + raise ProtocolViolation( + f"虚拟时刻回退: {self.state.virtual_time_s} -> {virtual}", + body=response) + if self._server_deadline_ms is not None: + drift = (self._server_deadline_ms - response["real_timestamp_ms"]) / 1000.0 + if drift < self.session.reserve_exit_s / 2: + # 服务器视角余量告急（本地时钟漂移或请求排队）；仅记录，交由上层决策。 + self.log.append({"event": "server_time_warning", + "server_remaining_s": drift}) + + @staticmethod + def _safe_json(body: bytes): + try: + return json.loads(body.decode("utf-8")) + except (UnicodeDecodeError, json.JSONDecodeError): + return None diff --git a/docs/paper/data/listing-source/src/mcm26b/protocol/log.py.tex b/docs/paper/data/listing-source/src/mcm26b/protocol/log.py.tex new file mode 100644 index 0000000..a35109b --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/protocol/log.py.tex @@ -0,0 +1,38 @@ +"""会话日志：机器狗程序必须自行记录指令序列与响应 [题面] 附件2 12节。 + +事件逐条追加写入 JSONL，进程崩溃时已完成的动作不丢； +内存中的 events 同时供回放测试与 evaluation 复算使用。 +""" + +from __future__ import annotations + +import json +from dataclasses import dataclass, field +from pathlib import Path +from time import time + + +@dataclass +class SessionLog: + path: Path | None = None + events: list = field(default_factory=list) + + def __post_init__(self): + if self.path is not None: + self.path.parent.mkdir(parents=True, exist_ok=True) + + def append(self, event: dict) -> None: + event = {**event, "logged_at_unix_s": time()} + self.events.append(event) + if self.path is not None: + with self.path.open("a", encoding="utf-8") as handle: + handle.write(json.dumps(event, ensure_ascii=False, allow_nan=False) + "\n") + + def action_events(self) -> list[dict]: + """仅最终被接受的动作事件（每个 request_id 一条，含重试次数）。""" + return [event for event in self.events if event.get("response") is not None + and event["response"].get("accepted") is True] + + def step_events(self) -> list[dict]: + """每步计时事件（客户端 _log_step 写入，按发生顺序）。""" + return [event for event in self.events if event.get("event") == "step"] diff --git a/docs/paper/data/listing-source/src/mcm26b/protocol/rules.py.tex b/docs/paper/data/listing-source/src/mcm26b/protocol/rules.py.tex new file mode 100644 index 0000000..8e89aea --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/protocol/rules.py.tex @@ -0,0 +1,94 @@ +"""P0 规则固定：四条指令的字段表、结果码与错误语义，全部落成可执行数据。 + +依据 issue/附件/附件2.docx《模拟器通信接口说明及编程指南》第 5-9 节。 +客户端用它构造与预校验请求，自建模拟器用它校验并拒绝未知字段； +表格本身即交付物"字段表/规则表"，人类可读版本见 docs/协议规则与状态机.md。 +""" + +from __future__ import annotations + +from dataclasses import dataclass + +# ---- 结果码 [题面] ---------------------------------------------------------- + +NO_SIGNAL = "no_signal" # 收不到信号：无未清除源 / 超接收半径 / 定向覆盖角外 +NEAR = "near" # 距离 <=5m 且在覆盖角内；不返回 svd_deg +DIRECTION = "direction" # 有信号；附 svd_deg（含 ±1° 误差，保留两位小数） +MEASURE_RESULTS = (NO_SIGNAL, NEAR, DIRECTION) + +CLEAR_SUCCESS = "success" # 20m 内发现并清除；耗时 5s +CLEAR_NO_TARGET = "no_target_in_range" # 未发现（无源/已清除/超20m）；耗时 3s +CLEAR_RESULTS = (CLEAR_SUCCESS, CLEAR_NO_TARGET) + +EXIT_USER = "user_exit" # /exit 成功响应中的固定退出原因 + +# accepted=false 的响应只含这 3 个字段；virtual_time_s 恒为 0，不是当前时刻 [题面] +BASE_RESPONSE_FIELDS = ("accepted", "real_timestamp_ms", "virtual_time_s") + + +# ---- 请求字段表 -------------------------------------------------------------- + + +@dataclass(frozen=True) +class FieldSpec: + """单个请求字段的约束。[题面] 附件2 5.1 节与各指令小节。""" + + kind: type # str / dict；数值字段由 sim 按整型/浮点细则单独校验 + required: bool = True + max_bytes: int | None = None # 字符串字段的 UTF-8 长度上限 + + +COMMON_FIELDS: dict[str, FieldSpec] = { + "arena_id": FieldSpec(str), # 必须为 "default" + "robot_id": FieldSpec(str, max_bytes=64), # 逐字节等于登录参赛队号 + "request_id": FieldSpec(str, max_bytes=128), # 会话内幂等键，新动作用新 ID +} + +POSITION_FIELDS: dict[str, FieldSpec] = { + "x": FieldSpec(float), # 有限 JSON number，|x| <= 2_000_000 + "y": FieldSpec(float), +} + +# 路径 -> 除公共字段外的动作字段；/enter 与 /exit 无附加字段 +ACTION_FIELDS: dict[str, dict[str, FieldSpec]] = { + "/enter": {}, + "/measure": {"position": FieldSpec(dict), "channel": FieldSpec(float)}, + "/clear": {"position": FieldSpec(dict), "channel": FieldSpec(float)}, + "/exit": {}, +} +ACTION_PATHS = tuple(ACTION_FIELDS) + +# channel 写成 JSON number 1.0 且恰为整数也接受；1.5 返回 HTTP 400 [题面] + + +# ---- 响应字段表（accepted=true 时的附加字段） -------------------------------- + +RESPONSE_FIELDS: dict[str, tuple[str, ...]] = { + "/enter": ("max_virtual_duration_s", "max_real_duration_s", "remaining_real_duration_s"), + "/measure": ("measure_result",), # direction 时另有 svd_deg + "/clear": ("clear_result",), + "/exit": ("exit_reason",), +} + + +# ---- 错误语义 [题面] 附件2 5.3 节 -------------------------------------------- + +STATUS_OK = 200 +STATUS_BAD_REQUEST = 400 # JSON 语法/重复键/缺字段/类型/频道或坐标范围 +STATUS_CONFLICT = 409 # 同 request_id 对应不同动作，或并发不同动作 +STATUS_RETRYABLE = (429, 500) # 流量保护/幂等记录上限、服务器内部错误：可原样重试 + + +def http_status_meaning(status: int) -> str: + table = { + 200: "动作已执行，或 JSON 合法但被业务拒绝（看 accepted）", + 400: "请求结构错误；不占用 request_id，修正后可复用该 ID", + 404: "路径未知或不精确（不接受尾随斜线与查询参数）", + 405: "已知路径使用了非 POST 方法", + 409: "request_id 幂等冲突或并发发送不同动作", + 413: "请求体超过 65536 字节", + 415: "Content-Type 或 Content-Encoding 不受支持", + 429: "连接/流量保护触发，或本局幂等记录达到上限", + 500: "模拟器内部错误", + } + return table.get(status, "未知状态码") diff --git a/docs/paper/data/listing-source/src/mcm26b/protocol/state.py.tex b/docs/paper/data/listing-source/src/mcm26b/protocol/state.py.tex new file mode 100644 index 0000000..7788266 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/protocol/state.py.tex @@ -0,0 +1,97 @@ +"""P0/P1 机器狗本地状态机：位置、测向频道、虚拟时刻与进出状态。 + +更新规则 [题面]： +- 只有 accepted=true 的响应才允许调用 apply_*；accepted=false 一律不更新， + 其 virtual_time_s=0 不是当前虚拟时刻； +- 虚拟时刻以最近一次 accepted=true 的响应为准，本地预测值仅作一致性核对； +- /clear 不改变测向机当前频道，也不产生切换耗时； +- 只有合法 /measure 会把测向机频道更新为本次检测频道。 +""" + +from __future__ import annotations + +from dataclasses import dataclass, field + +from ..config import CostConfig, Vec2 +from .rules import CLEAR_SUCCESS +from .timing import CostBreakdown, clear_cost, measure_cost + + +class StateError(RuntimeError): + """状态机被以非法顺序驱动（例如未 enter 就 apply_measure）。""" + + +@dataclass +class RobotState: + position: Vec2 = (0.0, 0.0) # /enter 成功后的初始位置 [题面] + channel: int = 1 # /enter 成功后的初始频道 [题面] + virtual_time_s: float = 0.0 + entered: bool = False + exited: bool = False + action_count: int = 0 + # 预测与实测的偏差记录；strict 模式下出现偏差会直接抛错。 + mismatches: list = field(default_factory=list) + + # -------------------------------------------------------------- enter/exit + def apply_enter(self, response: dict, *, strict: bool = False) -> None: + self._require_accepted(response) + if strict and (self.entered or self.exited): + raise StateError("重复 /enter 或已退出后再 enter") + self.entered = True + self.virtual_time_s = response["virtual_time_s"] + + def apply_exit(self, response: dict) -> None: + self._require_accepted(response) + self.exited = True + self.virtual_time_s = response["virtual_time_s"] + + # ----------------------------------------------------------------- measure + def apply_measure(self, request: dict, response: dict, *, + cost: CostConfig = CostConfig(), + strict: bool = False) -> CostBreakdown: + self._require_accepted(response) + if strict and (not self.entered or self.exited): + raise StateError("/measure 要求已 enter 且未退出") + pos = (request["position"]["x"], request["position"]["y"]) + channel = request["channel"] + predicted = measure_cost(self.position, pos, self.channel, channel, cost) + predicted = self._advance(pos, channel, response, predicted, strict) + return predicted + + # ------------------------------------------------------------------- clear + def apply_clear(self, request: dict, response: dict, *, + cost: CostConfig = CostConfig(), + strict: bool = False) -> CostBreakdown: + self._require_accepted(response) + if strict and (not self.entered or self.exited): + raise StateError("/clear 要求已 enter 且未退出") + pos = (request["position"]["x"], request["position"]["y"]) + success = response["clear_result"] == CLEAR_SUCCESS + predicted = clear_cost(self.position, pos, success, cost) + # 频道保持不变：/clear 不切换测向机频道 [题面] + return self._advance(pos, self.channel, response, predicted, strict) + + # ------------------------------------------------------------------ 共用 + def _advance(self, pos: Vec2, channel: int, response: dict, + predicted: CostBreakdown, strict: bool) -> CostBreakdown: + # 先完成全部校验再落子：strict 模式下失败时不留半更新状态。 + actual_delta = response["virtual_time_s"] - self.virtual_time_s + if abs(actual_delta - predicted.total_s) > 1e-6: + message = (f"耗时预测不一致: 预测 {predicted.total_s:.6f}s, " + f"实测 {actual_delta:.6f}s ({predicted})") + if strict: + raise StateError(message) + # 非严格模式：状态仍以响应为准，偏差记入日志供复盘。 + self.mismatches.append( + {"action": self.action_count + 1, "predicted_s": predicted.total_s, + "actual_s": actual_delta, "message": message}) + self.position = pos + self.channel = channel + self.virtual_time_s = response["virtual_time_s"] + self.action_count += 1 + return predicted + + @staticmethod + def _require_accepted(response: dict) -> None: + if response.get("accepted") is not True: + raise StateError("accepted=false 的响应不允许更新状态") diff --git a/docs/paper/data/listing-source/src/mcm26b/protocol/timing.py.tex b/docs/paper/data/listing-source/src/mcm26b/protocol/timing.py.tex new file mode 100644 index 0000000..baf1be8 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/protocol/timing.py.tex @@ -0,0 +1,61 @@ +"""P0 纯计时模型：/measure 与 /clear 的耗时分解，不涉及网络与状态。 + +附件1表2 与附件2第10节的计时示例是唯一权威锚点： +逐步得到 105、111、194、199 秒（tests/test_protocol_timing.py 固化）。 +客户端用本模块预测动作代价，模拟器用同一函数推进虚拟时钟， +保证"预测-执行-复算"三方一致。 +""" + +from __future__ import annotations + +from dataclasses import dataclass +from math import dist + +from ..config import CostConfig, Vec2 + + +@dataclass(frozen=True) +class CostBreakdown: + """一次合法动作的三段耗时 [题面]：移动 + 换频道（仅检测）+ 动作本身。""" + + move_s: float + switch_s: float + action_s: float + + @property + def total_s(self) -> float: + return self.total_us / 1_000_000 + + @property + def total_us(self) -> int: + """逐段量化后按整数微秒累计，与官方虚拟时钟一致。""" + return sum(round(value * 1_000_000) + for value in (self.move_s, self.switch_s, self.action_s)) + + +def measure_cost(prev_pos: Vec2, pos: Vec2, prev_channel: int, channel: int, + cost: CostConfig = CostConfig()) -> CostBreakdown: + """合法 /measure 的耗时。移动按直线距离；换频道只看前后频道是否不同。""" + return CostBreakdown( + move_s=dist(prev_pos, pos) / cost.speed_mps, + switch_s=0.0 if channel == prev_channel else cost.switch_s, + action_s=cost.measure_s, + ) + + +def clear_cost(prev_pos: Vec2, pos: Vec2, success: bool, + cost: CostConfig = CostConfig()) -> CostBreakdown: + """合法 /clear 的耗时。 + + /clear 的 channel 是目标干扰源频道，不切换测向机频道，也不产生换频道耗时 [题面]。 + """ + return CostBreakdown( + move_s=dist(prev_pos, pos) / cost.speed_mps, + switch_s=0.0, + action_s=cost.clear_success_s if success else cost.clear_fail_s, + ) + + +def move_time(a: Vec2, b: Vec2, cost: CostConfig = CostConfig()) -> float: + """任意两点间的移动耗时（规划用）。""" + return dist(a, b) / cost.speed_mps diff --git a/docs/paper/data/listing-source/src/mcm26b/protocol/transport.py.tex b/docs/paper/data/listing-source/src/mcm26b/protocol/transport.py.tex new file mode 100644 index 0000000..0f0f4b5 --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/protocol/transport.py.tex @@ -0,0 +1,44 @@ +"""传输抽象：HTTP 细节与协议客户端解耦，便于故障注入与本地模拟。 + +真实运行用 :class:`RequestsTransport`；自建模拟器经 :class:`LocalSimTransport` +（sim 模块）挂载；回放用 PlaybackTransport。连接失败与读超时统一抛 +:class:`TransportError` —— 此类失败后重试"同一动作"必须复用原 request_id +与原请求体 [题面]，由 client 层保证。 +""" + +from __future__ import annotations + +from dataclasses import dataclass + +import requests + + +class TransportError(Exception): + """网络层失败：连接不上、读写超时。动作可能未送达，也可能结果未知。""" + + +@dataclass(frozen=True) +class TransportResponse: + status: int + body: bytes + + +class Transport: + """最小 POST 接口。同步阻塞，一次一个请求（协议要求串行）。""" + + def post(self, url: str, body: bytes, headers: dict[str, str], + timeout: tuple[float, float]) -> TransportResponse: + raise NotImplementedError + + +class RequestsTransport(Transport): + """基于 requests 的默认实现。timeout=(连接, 读取)。""" + + def post(self, url, body, headers, timeout): + try: + response = requests.post(url, data=body, headers=headers, timeout=timeout) + except (requests.exceptions.Timeout, requests.exceptions.ConnectionError) as exc: + raise TransportError(str(exc)) from exc + except requests.exceptions.RequestException as exc: # 其它请求级异常同样按网络失败处理 + raise TransportError(str(exc)) from exc + return TransportResponse(response.status_code, response.content) diff --git a/docs/paper/data/listing-source/src/mcm26b/routing.py.tex b/docs/paper/data/listing-source/src/mcm26b/routing.py.tex new file mode 100644 index 0000000..f8c330e --- /dev/null +++ b/docs/paper/data/listing-source/src/mcm26b/routing.py.tex @@ -0,0 +1,254 @@ +"""图论/动态规划工具箱：开放路径排序、下界与路由度量（S1/S5）。 + +设计原则（docs/第三四问图论与动态规划优化方案.md §1、§3.2、§3.4）： + +- **开放路径**（起点固定为原点、终点自由）是本题的真实图问题：一次作业回合 + = 依次停靠若干作业点，代价 = Σ 移动时间 + Σ 动作耗时； +- 小规模（n (*@\ensuremath{\le}@*) ``EXACT_LIMIT``）直接用 Held-Karp 精确 DP，规模更大时用 + 最近邻打底 + 2-opt / Or-opt 改进，并始终给出 **MST 下界**用于在线后悔值审计； +- 所有函数只做"排序与度量"，不承担任何安全责任，也不改变覆盖/清除语义。 + +约定：边权为**欧氏距离**（米）；时间折算由调用方按 ``speed_mps`` 处理。 +2-opt / Or-opt 用 O(1) 增量代价评估，使 n (*@\ensuremath{\approx}@*) 10² 量级仍可在毫秒内完成。 +""" + +from __future__ import annotations + +import math + +from .config import Vec2 + +EXACT_LIMIT = 13 # Held-Karp 状态数 2^n·n：n=13 → 106 496，纯 Python 可接受 +OR_OPT_LIMIT = 60 # 作业点数超过此值时跳过高阶 Or-opt（见 improve_open_path） + + +def path_length(order: list[Vec2], start: Vec2 = (0.0, 0.0)) -> float: + """开放路径长度（起点 start，终点自由）。""" + total = 0.0 + position = start + for point in order: + total += math.dist(position, point) + position = point + return total + + +def nearest_neighbor_order(points: list[Vec2], + start: Vec2 = (0.0, 0.0)) -> list[Vec2]: + """最近邻开放路径（O(n²)，启发式上界）。""" + remaining = list(points) + order: list[Vec2] = [] + position = start + while remaining: + nxt = min(remaining, key=lambda q: math.dist(position, q)) + remaining.remove(nxt) + order.append(nxt) + position = nxt + return order + + +def two_opt_open(order: list[Vec2], start: Vec2 = (0.0, 0.0), + max_passes: int = 8) -> list[Vec2]: + """开放路径 2-opt（终点自由：只反转内部片段，不做首尾相接）。 + + 增量代价 O(1)：反转 [i..j] 只影响 (prev, i) 与 (j, next) 两条边。 + """ + best = list(order) + n = len(best) + if n < 3: + return best + for _ in range(max_passes): + improved = False + for i in range(n - 1): + prev = best[i - 1] if i > 0 else start + pi = best[i] + d_prev_i = math.dist(prev, pi) + for j in range(i + 1, n): + pj = best[j] + nxt = best[j + 1] if j + 1 < n else None + d_prev_j = math.dist(prev, pj) + removed = d_prev_i + added = d_prev_j + if nxt is not None: + removed += math.dist(pj, nxt) + added += math.dist(pi, nxt) + if added < removed - 1e-9: + best[i:j + 1] = best[i:j + 1][::-1] + improved = True + pi = best[i] + d_prev_i = math.dist(prev, pi) + if not improved: + break + return best + + +def or_opt_open(order: list[Vec2], start: Vec2 = (0.0, 0.0), + max_passes: int = 4, max_segment: int = 3) -> list[Vec2]: + """Or-opt：把长度 (*@\ensuremath{\le}@*) max_segment 的片段搬家（开放路径，增量代价 O(1)）。""" + best = list(order) + n = len(best) + if n < 4: + return best + for _ in range(max_passes): + improved = False + for length in range(1, min(max_segment, n - 1) + 1): + for i in range(0, n - length + 1): + segment = best[i:i + length] + rest = best[:i] + best[i + length:] + for j in range(len(rest) + 1): + if j == i: + continue + candidate = rest[:j] + segment + rest[j:] + if _segment_move_gain(best, i, length, j, start) > 1e-9: + best = candidate + improved = True + break + if improved: + break + if improved: + break + if not improved: + break + return best + + +def _segment_move_gain(order: list[Vec2], i: int, length: int, j: int, + start: Vec2) -> float: + """把 order[i:i+length] 插到去掉该段后的第 j 位所省下的长度（正=更省）。""" + rest = order[:i] + order[i + length:] + segment = order[i:i + length] + + def length_of(seq: list[Vec2]) -> float: + return path_length(seq, start) + + return length_of(order) - length_of(rest[:j] + segment + rest[j:]) + + +def improve_open_path(points: list[Vec2], start: Vec2 = (0.0, 0.0), + max_passes: int = 8) -> list[Vec2]: + """最近邻 + 2-opt + Or-opt 的开放路径改进（大规模兜底）。 + + Or-opt 的搬移评估是 O(n³)，作业点数超过 :data:`OR_OPT_LIMIT` 时只做 + O(n²) 的 2-opt（度量口径下 Or-opt 的相对收益远小于其墙钟代价）。 + """ + order = nearest_neighbor_order(points, start) + order = two_opt_open(order, start, max_passes) + if len(order) > OR_OPT_LIMIT: + return order + return or_opt_open(order, start, max_passes) + + +def held_karp_open(points: list[Vec2], start: Vec2 = (0.0, 0.0)) -> list[Vec2]: + """Held-Karp 精确开放路径（起点固定、终点自由）。 + + 状态 ``dp[mask][j]`` = 访问集合 mask、当前停在 j 的最小长度； + 规模 2^n·n，仅用于 n (*@\ensuremath{\le}@*) :data:`EXACT_LIMIT`。返回最优访问顺序。 + """ + n = len(points) + if n == 0: + return [] + if n == 1: + return list(points) + dist = [[math.dist(points[i], points[j]) for j in range(n)] for i in range(n)] + from_start = [math.dist(start, points[j]) for j in range(n)] + full = (1 << n) - 1 + inf = float("inf") + dp: list[list[float]] = [[inf] * n for _ in range(1 << n)] + parent: list[list[int]] = [[-1] * n for _ in range(1 << n)] + for j in range(n): + dp[1 << j][j] = from_start[j] + for mask in range(1 << n): + row = dp[mask] + for j in range(n): + current = row[j] + if current == inf or not (mask >> j) & 1: + continue + rest = full ^ mask + while rest: + bit = rest & -rest + k = bit.bit_length() - 1 + rest ^= bit + candidate = current + dist[j][k] + nxt = mask | bit + if candidate < dp[nxt][k]: + dp[nxt][k] = candidate + parent[nxt][k] = j + best_end = min(range(n), key=lambda j: dp[full][j]) + order: list[Vec2] = [] + mask, j = full, best_end + while j != -1: + order.append(points[j]) + previous = parent[mask][j] + mask ^= 1 << j + j = previous + order.reverse() + return order + + +def optimal_open_path(points: list[Vec2], start: Vec2 = (0.0, 0.0), + exact_limit: int = EXACT_LIMIT) -> list[Vec2]: + """离线最优（或近优）开放路径：小规模精确，大规模 2-opt + Or-opt。""" + unique = _dedupe(points) + if len(unique) <= exact_limit: + return held_karp_open(unique, start) + return improve_open_path(unique, start) + + +def mst_weight(points: list[Vec2], start: Vec2 | None = (0.0, 0.0)) -> float: + """最小生成树权重（Prim，O(n²)）；含 start 时给出开放路径最优值的下界。 + + 开放路径删除其最后一条边即得一条生成树，故 MST 权重 (*@\ensuremath{\le}@*) 最优路径长度。 + """ + nodes = ([start] if start is not None else []) + list(points) + n = len(nodes) + if n <= 1: + return 0.0 + in_tree = [False] * n + best = [float("inf")] * n + best[0] = 0.0 + total = 0.0 + for _ in range(n): + u, u_cost = -1, float("inf") + for i in range(n): + if not in_tree[i] and best[i] < u_cost: + u, u_cost = i, best[i] + if u < 0: + break + in_tree[u] = True + total += u_cost + ux, uy = nodes[u] + for v in range(n): + if in_tree[v]: + continue + distance = math.hypot(nodes[v][0] - ux, nodes[v][1] - uy) + if distance < best[v]: + best[v] = distance + return total + + +def _dedupe(points, cell_m: float = 0.5) -> list[Vec2]: + """按 ``cell_m`` 网格去重（同一物理点只算一次作业）。""" + seen: set[tuple[int, int]] = set() + unique: list[Vec2] = [] + for point in points: + key = (int(round(point[0] / cell_m)), int(round(point[1] / cell_m))) + if key in seen: + continue + seen.add(key) + unique.append((float(point[0]), float(point[1]))) + return unique + + +def route_metrics(service_points, actual_move_m: float, + speed_mps: float = 5.0) -> dict: + """路由度量：离线最优开放回路、MST 下界与相对 gap（S1 必报列）。""" + unique = _dedupe(service_points) + offline = path_length(optimal_open_path(unique)) if unique else 0.0 + lower = mst_weight(unique) + gap = ((actual_move_m - offline) / actual_move_m) if actual_move_m > 0 else 0.0 + return { + "distinct_service_points": len(unique), + "offline_opt_open_path_m": round(offline, 1), + "offline_opt_open_path_s": round(offline / speed_mps, 1), + "route_lower_bound_s": round(lower / speed_mps, 1), + "route_gap_vs_offline": round(gap, 4), + } diff --git a/docs/paper/data/source-listings.tex b/docs/paper/data/source-listings.tex new file mode 100644 index 0000000..4210530 --- /dev/null +++ b/docs/paper/data/source-listings.tex @@ -0,0 +1,70 @@ +\begingroup +\linespread{1.0}\selectfont +\lstset{basicstyle=\ttfamily\fontsize{8}{10}\selectfont,numberstyle=\tiny,aboveskip=6pt,belowskip=8pt,xleftmargin=1.5em,frame=none} +\subsection*{\pathtext{src/mcm26b/__init__.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/__init__.py.tex} +\subsection*{\pathtext{src/mcm26b/belief/__init__.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/belief/__init__.py.tex} +\subsection*{\pathtext{src/mcm26b/belief/joint.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/belief/joint.py.tex} +\subsection*{\pathtext{src/mcm26b/cli.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/cli.py.tex} +\subsection*{\pathtext{src/mcm26b/config.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/config.py.tex} +\subsection*{\pathtext{src/mcm26b/coverage/__init__.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/coverage/__init__.py.tex} +\subsection*{\pathtext{src/mcm26b/evaluation/__init__.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/evaluation/__init__.py.tex} +\subsection*{\pathtext{src/mcm26b/geometry/__init__.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/geometry/__init__.py.tex} +\subsection*{\pathtext{src/mcm26b/geometry/__main__.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/geometry/__main__.py.tex} +\subsection*{\pathtext{src/mcm26b/geometry/localization.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/geometry/localization.py.tex} +\subsection*{\pathtext{src/mcm26b/geometry/planning.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/geometry/planning.py.tex} +\subsection*{\pathtext{src/mcm26b/guarantee/__init__.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/guarantee/__init__.py.tex} +\subsection*{\pathtext{src/mcm26b/guarantee/cover.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/guarantee/cover.py.tex} +\subsection*{\pathtext{src/mcm26b/harness/__init__.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/harness/__init__.py.tex} +\subsection*{\pathtext{src/mcm26b/harness/playback.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/harness/playback.py.tex} +\subsection*{\pathtext{src/mcm26b/harness/scenes.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/harness/scenes.py.tex} +\subsection*{\pathtext{src/mcm26b/harness/simulator.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/harness/simulator.py.tex} +\subsection*{\pathtext{src/mcm26b/harness/suites.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/harness/suites.py.tex} +\subsection*{\pathtext{src/mcm26b/harness/transport.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/harness/transport.py.tex} +\subsection*{\pathtext{src/mcm26b/particles.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/particles.py.tex} +\subsection*{\pathtext{src/mcm26b/planner/__init__.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/planner/__init__.py.tex} +\subsection*{\pathtext{src/mcm26b/planner/bayes_loop.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/planner/bayes_loop.py.tex} +\subsection*{\pathtext{src/mcm26b/planner/seven.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/planner/seven.py.tex} +\subsection*{\pathtext{src/mcm26b/protocol/__init__.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/protocol/__init__.py.tex} +\subsection*{\pathtext{src/mcm26b/protocol/client.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/protocol/client.py.tex} +\subsection*{\pathtext{src/mcm26b/protocol/log.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/protocol/log.py.tex} +\subsection*{\pathtext{src/mcm26b/protocol/rules.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/protocol/rules.py.tex} +\subsection*{\pathtext{src/mcm26b/protocol/state.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/protocol/state.py.tex} +\subsection*{\pathtext{src/mcm26b/protocol/timing.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/protocol/timing.py.tex} +\subsection*{\pathtext{src/mcm26b/protocol/transport.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/protocol/transport.py.tex} +\subsection*{\pathtext{src/mcm26b/routing.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/src/mcm26b/routing.py.tex} +\subsection*{\pathtext{scripts/audit_paper_formal.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/scripts/audit_paper_formal.py.tex} +\subsection*{\pathtext{scripts/build_paper_support.py}} +\lstinputlisting[escapeinside={(*@}{@*)}]{data/listing-source/scripts/build_paper_support.py.tex} +\endgroup diff --git a/docs/paper/figures/formal-time-bars.tex b/docs/paper/figures/formal-time-bars.tex new file mode 100644 index 0000000..6b6ae21 --- /dev/null +++ b/docs/paper/figures/formal-time-bars.tex @@ -0,0 +1,45 @@ +\begin{figure}[htbp]\centering +\begin{tikzpicture}[x=0.00108cm,y=0.85cm,font=\small] +\node[anchor=east] at (-100,3.3) {Q3-1}; +\fill[inkblue] (0,3) rectangle (2408.978068,3.6); +\fill[inkblue!50] (2408.978068,3) rectangle (2933.978068,3.6); +\fill[warmgray!70] (2933.978068,3) rectangle (3029.978068,3.6); +\fill[black!18] (3029.978068,3) rectangle (3094.978068,3.6); +\node[anchor=west,font=\scriptsize] at (3174.978068,3.3) {3095.0}; +\node[anchor=east] at (-100,2.3) {Q3-2}; +\fill[inkblue] (0,2) rectangle (2725.33514,2.6); +\fill[inkblue!50] (2725.33514,2) rectangle (3310.33514,2.6); +\fill[warmgray!70] (3310.33514,2) rectangle (3418.33514,2.6); +\fill[black!18] (3418.33514,2) rectangle (3493.33514,2.6); +\node[anchor=west,font=\scriptsize] at (3573.33514,2.3) {3493.3}; +\node[anchor=east] at (-100,1.3) {Q4-1}; +\fill[inkblue] (0,1) rectangle (7277.225736,1.6); +\fill[inkblue!50] (7277.225736,1) rectangle (9022.225736,1.6); +\fill[warmgray!70] (9022.225736,1) rectangle (9297.225736,1.6); +\fill[black!18] (9297.225736,1) rectangle (9362.225736,1.6); +\node[anchor=west,font=\scriptsize] at (9442.225736,1.3) {9362.2}; +\node[anchor=east] at (-100,0.3) {Q4-2}; +\fill[inkblue] (0,0) rectangle (7101.30208,0.6); +\fill[inkblue!50] (7101.30208,0) rectangle (8906.30208,0.6); +\fill[warmgray!70] (8906.30208,0) rectangle (9221.30208,0.6); +\fill[black!18] (9221.30208,0) rectangle (9271.30208,0.6); +\node[anchor=west,font=\scriptsize] at (9351.30208,0.3) {9271.3}; +\draw[->] (0,-0.25)--(10500,-0.25); +\draw (0,-0.25)--(0,-0.35) node[below,font=\scriptsize] {0}; +\draw (2000,-0.25)--(2000,-0.35) node[below,font=\scriptsize] {2000}; +\draw (4000,-0.25)--(4000,-0.35) node[below,font=\scriptsize] {4000}; +\draw (6000,-0.25)--(6000,-0.35) node[below,font=\scriptsize] {6000}; +\draw (8000,-0.25)--(8000,-0.35) node[below,font=\scriptsize] {8000}; +\draw (10000,-0.25)--(10000,-0.35) node[below,font=\scriptsize] {10000}; +\node[anchor=west,font=\scriptsize] at (10400,-0.65) {s}; +\fill[inkblue] (0,-1.3) rectangle (350,-1.05); +\node[anchor=west] at (450,-1.175) {移动}; +\fill[inkblue!50] (2600,-1.3) rectangle (2950,-1.05); +\node[anchor=west] at (3050,-1.175) {检测}; +\fill[warmgray!70] (5200,-1.3) rectangle (5550,-1.05); +\node[anchor=west] at (5650,-1.175) {换频}; +\fill[black!18] (7600,-1.3) rectangle (7950,-1.05); +\node[anchor=west] at (8050,-1.175) {清除}; +\end{tikzpicture} +\caption{四次正式测试的累计虚拟耗时。移动项由总时间扣除官方动作计数对应耗时反推。} +\label{fig:costbars}\end{figure} diff --git a/docs/paper/figures/q4-plan.tex b/docs/paper/figures/q4-plan.tex new file mode 100644 index 0000000..f9baab6 --- /dev/null +++ b/docs/paper/figures/q4-plan.tex @@ -0,0 +1,50 @@ +\begin{figure}[htbp]\centering +\begin{tikzpicture}[x=0.00145cm,y=0.00145cm,font=\small] +\fill[inkblue!5] (0,0) circle (1800); +\draw[thick] (0,0) circle (1800); +\draw[->,warmgray] (-2900,0)--(2950,0) node[right] {$x$/m}; +\draw[->,warmgray] (0,-2800)--(0,2850) node[above] {$y$/m}; +\draw (-2000,-35)--(-2000,35); +\node[below,font=\scriptsize] at (-2000,-50) {-2000}; +\draw (-1000,-35)--(-1000,35); +\node[below,font=\scriptsize] at (-1000,-50) {-1000}; +\draw (1000,-35)--(1000,35); +\node[below,font=\scriptsize] at (1000,-50) {1000}; +\draw (2000,-35)--(2000,35); +\node[below,font=\scriptsize] at (2000,-50) {2000}; +\fill[inkblue] (-800.0,-200.0) circle (33); +\fill[inkblue] (800.0,200.0) circle (33); +\fill[inkblue] (-200.0,900.0) circle (33); +\fill[inkblue] (200.0,-900.0) circle (33); +\fill[inkblue] (-1200.0,700.0) circle (33); +\fill[inkblue] (1200.0,-700.0) circle (33); +\fill[inkblue] (800.0,1200.0) circle (33); +\fill[inkblue] (-1800.0,-300.0) circle (33); +\fill[inkblue] (1800.0,300.0) circle (33); +\fill[inkblue] (-400.0,1800.0) circle (33); +\fill[inkblue] (0.0,0.0) circle (33); +\fill[inkblue] (1400.0,-1400.0) circle (33); +\fill[inkblue] (-1500.0,-1300.0) circle (33); +\fill[inkblue] (1500.0,1300.0) circle (33); +\fill[inkblue] (-400.0,-1800.0) circle (33); +\fill[inkblue] (400.0,1800.0) circle (33); +\fill[inkblue] (-1800.0,400.0) circle (33); +\fill[inkblue] (1800.0,-400.0) circle (33); +\fill[inkblue] (-500.0,700.0) circle (33); +\fill[inkblue] (-700.0,-700.0) circle (33); +\fill[inkblue] (700.0,700.0) circle (33); +\fill[inkblue] (1300.0,1100.0) circle (33); +\fill[inkblue] (-1300.0,1500.0) circle (33); +\fill[inkblue] (500.0,-1800.0) circle (33); +\fill[inkblue] (-900.0,-2100.0) circle (33); +\fill[inkblue] (600.0,1900.0) circle (33); +\fill[inkblue] (-2500.0,500.0) circle (33); +\fill[inkblue] (1900.0,-900.0) circle (33); +\fill[inkblue] (-1700.0,-500.0) circle (33); +\fill[inkblue] (-700.0,-1200.0) circle (33); +\fill[inkblue] (900.0,-700.0) circle (33); +\node[anchor=west,align=left] at (3250,900) {圆域：源位置先验\\蓝点：31个检测站}; +\node[anchor=west,align=left] at (3250,-700) {部分站点在圆域外\\用于接收向外发射的源}; +\end{tikzpicture} 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zKiIv9d;Jv<8tVFnaf?f(OE$SzA$LD;b+C@arEl3q*r2#(S&90lZkRM#L09eK-7F(W z&SXz$cm@qh*)&x(kXu?GlzF^ z>Yb%BenB!dhgP$0>Tt`@n;=<->CzyG}^m8J$1om*$>+~>YorQ=jriH zwhO^+k*}dmOzT-nbyMsLkE)%R@v0$)WBaIfp!pHmc1?Ms=daS2nRy6_eR z{h~(E$of$fFj8e#OlM;6UJK9*Doxe|%71^fJ;3JfV2HbwH3ly)mk=Stealth, + box/.style={draw=inkblue,rounded corners=2pt,align=center,text width=3.6cm, + minimum height=1.05cm,fill=inkblue!4}] + \node[box] (obs) {接口观测\\示向度／近距离／无信号}; + \node[box,right=1cm of obs] (belief) {候选集更新\\几何外包／网格／朝向}; + \node[box,below=0.85cm of belief] (decision) {选择下一任务\\覆盖／定位／清除}; + \node[box,left=1cm of decision] (act) {执行一个动作\\移动、计时与状态更新}; + \draw[->] (obs)--(belief); \draw[->] (belief)--(decision); + \draw[->] (decision)--(act); \draw[->] (act)--(obs); + \node[align=center,right=0.5cm of decision,text width=2.5cm] (stop) + {完成证据成立\\或预算到限\\$\Downarrow$\\退出并报告}; + \draw[->] (decision)--(stop); +\end{tikzpicture} +\caption{四问共用的观测与决策闭环。覆盖证据和清除证据分别承担不同职责。} +\label{fig:framework} +\end{figure} -\textbf{问题~4 的分析}。定向源的发射半平面使得“无信号”不能单独否定位置假设： -源可能恰在检测点背后发射。把观测视为对“位置—半径—朝向”联合假设的约束即可保持 -不漏源的保守性；同时证明覆盖基线对定向源依然成立，失去信号后的已定位源可用有限 -圆盘覆盖逐点清除作为后备。 - -\section{模型假设} - -\begin{enumerate}[label=\arabic*.,leftmargin=2.5em] - \item 示向度误差满足 $|\varepsilon|\le 1^{\circ}$，且同一检测点重复检测误差不变； - 仅在不同地点误差才呈现统计规律（题设）。本文取有界误差模型，不假设误差的 - 分布形式。 - \item 每个频道至多存在一个干扰源，源总数为 $10$--$16$，频道编号 $1$--$20$； - 不同源信号互不影响（题设）。 - \item 各源有效接收半径未知但属于 $[1000,1500]$ 米；信号场强仅随距离衰减， - 与角度无关（题设）。 - \item 定向源有效覆盖角度为定向方向两侧各 $90^{\circ}$（含边界）；光学精确定位与 - 清除只依赖距离、不受覆盖角度限制（题设）。 - \item 策略仅依赖接口返回的三值观测（\texttt{no\_signal}、\texttt{near}、 - \texttt{direction} 及示向度读数），不引入场强、距离等接口未提供的观测量 - （工程约定）。 - \item 机器狗沿直线匀速行进、停机检测，虚拟时间按题设动作耗时累计；程序运行时间 - 与虚拟时间相互独立（题设）。 +\section{模型假设与信息边界} +\begin{enumerate}[label=假设\arabic*：,leftmargin=4.5em,itemsep=4pt] + \item 源的位置、频道、发射朝向和有效接收半径在一次测试中保持不变， + 不同频道互不干扰。这与静态测试案例及题设的频道独立性一致。 + \item 采用二维欧氏距离，忽略高度差；机器人匀速直线移动， + 检测、换频、光学定位与清除按给定时间串行执行。 + \item 几何保证只使用有界误差和接收半径上下界。 + 为覆盖接口两位小数的表示误差，在线角域取 + $\delta_{\mathrm{eff}}=1^\circ+0.005^\circ$。 + 该附加量为舍入余量，不改变题设的物理误差。 + \item 策略只读取合法响应，不读取源真值、场强、精确距离或隐藏案例。 + 正式实验仅采用选定正式包匹配的官方计数与计时字段。 + \item 信息增益与可见性评分采用均匀候选权重及均匀接收半径作为 + 决策启发式；题目未给出这些概率分布，故不以它们证明接收、缺席或清除。 \end{enumerate} +前三项中的物理约束取自题目和附件，数值余量与评分先验属于实现选择。 +正式日志只提供公开包头和可匹配统计，本文不假设已经获得其中的测点轨迹与真源坐标。 \section{符号说明} - \begin{table}[htbp] - \centering - \caption{主要符号说明} - \label{tab:symbols} - \begin{tabular}{cl} - \toprule - 符号 & 说明 \\ - \midrule - $\Omega$ & 目标区域 $\{(x,y):x^2+y^2\le 1800^2\}$（米） \\ - $R_c$ & 干扰源 $c$ 的有效接收半径，$R_c\in[1000,1500]$ 米 \\ - $\delta$ & 示向度误差界，$\delta=1^{\circ}$ \\ - $s_i,\ \theta_i$ & 第 $i$ 个检测点坐标及其测得的示向度读数 \\ - $W_i$ & 检测点 $s_i$ 处的前向角域 $[\theta_i-\delta,\theta_i+\delta]$ \\ - $P$ & 交会定位区域（诸角域的半平面交） \\ - $D(P)$ & 定位区域 $P$ 的直径 \\ - $K$ & 某频道源的可能位置候选集合 \\ - $\rho(K)$ & $K$ 的最小包围圆半径 \\ - $\mathcal{Q}$ & 第二检测点的安全候选区域 \\ - $B(c,r)$ & 以 $c$ 为圆心、$r$ 为半径的闭圆盘（米） \\ - $R_-,\ R_+$ & 有效接收半径的下、上限，$1000$、$1500$ 米 \\ - $J(q)$ & 第二检测点 $q$ 的最坏保守后验包围半径（米） \\ - $C(q)$ & 在 $q$ 处完成一次检测的虚拟时间增量（秒） \\ - $L$ & 机器狗移动总路程（米） \\ - $N_{\mathrm{switch}},N_{\mathrm{measure}},N_{\mathrm{clear}}$ & 频道切换、检测、清除动作次数 \\ - $T$ & 完成任务的虚拟总时间（秒） \\ - \bottomrule - \end{tabular} +\centering\small +\caption{主要符号及单位} +\begin{tabularx}{\linewidth}{>{$}l<{$} X l} +\toprule +\text{符号} & 含义 & 单位\\ +\midrule +\Omega,\ R & 源位置圆域及其半径，$R=1800$ & m\\ +g,\ s_i,\ q & 真源位置、已有检测点、待选检测点 & m\\ +\theta_i,\ \delta & 示向度及误差半角 & 度或弧度\\ +u(\alpha) & 单位方向向量 $(\cos\alpha,\sin\alpha)$ & --\\ +W_i,\ P & 第 $i$ 个前向角域及纯角域交集 & --\\ +K_c,\ P_c^{\mathrm{out}} & 频道 $c$ 的可行位置集及保守凸外包 & --\\ +D(P),\ m,\ \rho & 区域直径、最小包围圆圆心及半径 & m\\ +R_-,R_+ & 接收半径下、上界，分别为 $1000$、$1500$ & m\\ +\mathcal Q(K) & 对集合 $K$ 保证接收的检测点区域 & --\\ +\ell,\ \epsilon_g & 网格边长及格心位置裕量 $\ell/\sqrt2$ & m\\ +\psi,\ H & 源朝向及朝向离散档数 & 度，个\\ +L,\ T & 移动总距离及总虚拟耗时 & m，s\\ +N_m,N_s,N_c^+,N_c^- & 检测、换频、成功清除、失败清除次数 & 次\\ +\bar T,\ T_{\mathrm{real}} & 平均定位清除时间及程序运行时间 & s/个，s\\ +\bottomrule +\end{tabularx} \end{table} - -\section{问题~1：有界误差交会定位模型} - -\subsection{建模思路来源} - -本问每种方法的取舍都由题面描述直接确定，对应关系如下。 - -\textbf{由误差描述确定集合模型。}题面附录~2 第（1）项指出：示向度与真实方位角之间 -的误差“在一段时间内，同一地点的电磁环境干扰是固定的，所以重复检测不会改变检测 -误差”，且“从目标区域全局来看，所有这些误差在 $[-1^{\circ},1^{\circ}]$ 范围内”。 -因此单次观测不能确定一条精确射线，却可以确定一个必含真实方向的角域；题面没有 -给出误差的分布形式，原地重复测量又不产生新信息，故采用有界误差下的集合相交， -而非直线最小二乘或多次读数平均——后两者既不能保证真源不被排除，也与“同点误差 -不变”的题设相悖。 - -\textbf{由交会定位的规定确定半平面交。}问题~1 要求“采用交会定位法（见附录~2） -计算多边形定位区域直径”，附录~2 第（3）项的图~2 把定位区域画成两个检测点示向度 -实线两侧各 $1^{\circ}$ 虚线所夹的四边形。角域边界是直线，故定位区域是二维线性 -不等式组的可行域，可用半平面交显式构造，问题随之成为凸几何问题\cite{boyd}。 - -\textbf{由直径的定义确定顶点枚举。}题目规定直径是“区域内任意两点之间距离的最大 -值”。两点距离关于其变元是凸函数，在紧凸集上的最大值必在极点处取得，故只需在 -顶点对上枚举，无需任何近似。 - -\textbf{由覆盖之问确定“先判定、后反例”。}题目追问“以定位区域直径为直径的圆能否 -覆盖此定位区域”。“直径”是最长弦概念，与“外接”并非同一对象，因此先给出存在 -覆盖圆的充要判定，再构造符合题设测向条件的反例，据此回答“不一定”。 - -\textbf{由清除条件确定最小包围圆。}附录~2 第（8）项规定光学精确定位与清除“在距离 -干扰源不超过 $20$ 米”时进行，且成功与否仅与清除点到干扰源的距离有关。定位精度的 -最终判据因而是“存在一点到所有可能源位置都不超过 $20$ 米”，即最小包围圆半径 -$\rho\le 20$，而非直径不超过 $40$ 米。 - -\subsection{测向观测的前向角域与半平面约束} - -设第 $i$ 个检测点 $s_i=(s_{ix},s_{iy})$ 处测得示向度 $\theta_i$（题面附录~2 -第（1）项：示向度自 $x$ 轴正向逆时针计量，范围 $[0^{\circ},360^{\circ})$）。 -由假设~1，真实方位角位于 $[\theta_i-\delta,\theta_i+\delta]$ 内，故源必然落在 -以 $s_i$ 为顶点、以该方向区间为边界的前向角域 -\begin{equation} - W_i=\bigl\{s_i+t\,u(\varphi):t\ge 0,\ \varphi\in[\theta_i-\delta,\theta_i+\delta]\bigr\}, - \qquad u(\varphi)=(\cos\varphi,\sin\varphi) - \label{eq:wedge} -\end{equation} -内。记二维叉积 $[a,b]=a_xb_y-a_yb_x$ 与 $u_i^{\pm}=u(\theta_i\pm\delta)$。当 -$0<\delta<90^{\circ}$ 时，“位于两条边界射线之间”等价于 -\begin{equation} - [\,u_i^-,\,g-s_i\,]\ge 0,\qquad [\,u_i^+,\,g-s_i\,]\le 0, - \label{eq:cross} -\end{equation} -即 $g-s_i$ 位于下边界射线的左侧、上边界射线的右侧。展开即标准线性约束 -\begin{align} - \sin(\theta_i-\delta)\,x-\cos(\theta_i-\delta)\,y - &\le \sin(\theta_i-\delta)\,s_{ix}-\cos(\theta_i-\delta)\,s_{iy},\\ - -\sin(\theta_i+\delta)\,x+\cos(\theta_i+\delta)\,y - &\le -\sin(\theta_i+\delta)\,s_{ix}+\cos(\theta_i+\delta)\,s_{iy}. -\end{align} -另保留前向约束 $u(\theta_i)\cdot(g-s_i)\ge0$：它在 $0<\delta<90^{\circ}$ 时冗余， -但 $\delta=0$ 时前两条约束只限定一条直线，加入它才得到正确的射线。角域顶点本身 -包含在闭集合内，这是保守处理，并不表示在该点仍能获得示向度。采用向量不等式后， -$359^{\circ}$ 与 $0^{\circ}$ 跨界无需分段比较角度。示向度读数保留两位小数时，可 -取 $\delta=1.005^{\circ}$ 作显式声明的保守裕量；本节推导对任意 -$\delta\in(0,90^{\circ})$ 成立，本题算例始终取 $\delta=1^{\circ}$。 - -\subsection{定位区域的构造与分类} - -交会定位区域为诸角域之交 -\begin{equation} - P=\bigcap_i W_i=\{g:Ag\le b\}. - \label{eq:polygon} -\end{equation} -每个 $W_i$ 都是闭凸集，故 $P$ 也是闭凸集；它可能为空、为单点、为线段、为有界凸 -多边形，也可能无界，算法必须显式区分这五种情形，不得混同处理。 - -\textbf{边界交点枚举。}把约束统一写成 $a_jx+b_jy\le c_j$，两条边界的行列式 -$\Delta_{jk}=a_jb_k-a_kb_j\ne0$ 时，交点为 $x=(c_jb_k-c_kb_j)/\Delta_{jk}$、 -$y=(a_jc_k-a_kc_j)/\Delta_{jk}$。保留满足全部约束的交点，去重后构造凸包即得 -$P$ 的顶点集。 - -\textbf{命题~1}（极点存在保证判空）\quad 至少有一次观测时，非空的角域交集一定存在 -极点，因此可通过可行边界交点枚举判空。 - -\textbf{证明}\quad 取第一个角域的轴向 $u_1$，其中任意 $g$ 满足 -$u_1\cdot(g-s_1)\ge\cos\delta_1\,\|g-s_1\|$，且 $\cos\delta_1>0$。在非空 $P$ 上 -最小化线性函数 $u_1\cdot(g-s_1)$：由该不等式，以任一可行点的函数值截得的下水平 -集有界，从而是非空紧集，最小值可达；最小化点集位于一条支撑直线上且有界，因而是 -点或线段，取其点或端点即得 $P$ 的极点。二维线性约束的极点至少有两条法向量线性 -无关的有效边界（否则沿所有有效边界的公共切向可作双向小扰动，与极点定义矛盾）， -故必出现在上述交点枚举中。\hfill$\square$ - -无观测时 $P=\R^2$，应直接判为无界，不能用“没有交点”判为空集。 - -\textbf{有界性判定。}对非空 $P$ 定义衰退锥 $\mathcal{R}=\{d:Ad\le0\}$。若存在 -$d\ne0$，则任取 $g_0\in P$ 都有 $g_0+td\in P$（$t\ge0$），$P$ 无界；反之若 $P$ -无界，取 $g_k\in P$ 使 $\|g_k-g_0\|\to\infty$，将 $Ag_k\le b$ 减去 $Ag_0\le b$、 -除以 $\|g_k-g_0\|$ 并取极限，知单位向量 $(g_k-g_0)/\|g_k-g_0\|$ 的任一聚点 $d$ -满足 $Ad\le0$。故 $P$ 有界当且仅当 $\mathcal{R}=\{0\}$。本模型的衰退锥被一个小于 -$180^{\circ}$ 的闭角域约束，若含非零向量必含一条极射线，该射线平行于某条有效 -约束边界，故只需检查每个法向量 $(a_j,b_j)$ 的两个切向方向 $(b_j,-a_j)$、 -$(-b_j,a_j)$ 是否满足全部齐次不等式。 - -\textbf{分类约定。}可行交点为空时返回空集；存在非零衰退方向时返回无界；否则对 -可行交点去重求凸包，按顶点数与仿射维数区分单点、线段和二维多边形。空集的直径 -约定为无定义，无界区域的直径为 $+\infty$。显示窗口只用于绘图裁剪：任何大矩形都 -不能取代衰退锥判定，更不能把截断图形的直径称为原无界区域的直径。 - -\subsection{定位区域直径的顶点定理} - -\textbf{定理~1}（直径在顶点上取得）\quad 若 $P=\mathrm{conv}\{v_1,\dots,v_m\}$ 非空 -且有界，则 -\begin{equation} - D(P)=\max_{1\le i0$ 即覆盖失败，取达到最大值的顶点即得可独立复核的失败证据。 - -\textbf{结论：直径圆不一定覆盖定位区域。}反例如表~\ref{tab:counterexample} 所示 -（误差半角均取 $1^{\circ}$，符合题设测向条件）。 - -\begin{table}[htbp] - \centering - \caption{符合题设测向条件的反例：三点观测} - \label{tab:counterexample} - \begin{tabular}{ccc} - \toprule - 检测点 & 坐标（米） & 示向度 \\ - \midrule - $s_1$ & $(-1000,0)$ & $1^{\circ}$ \\ - $s_2$ & $(540,-500\sqrt{3})$ & $121^{\circ}$ \\ - $s_3$ & $(520,520\sqrt{3})$ & $241^{\circ}$ \\ - \bottomrule - \end{tabular} -\end{table} - -三个角域的下边界方向分别为 $0^{\circ},120^{\circ},240^{\circ}$，对应左半平面 -$y\ge0$、$\sqrt{3}\,x+y\le40\sqrt{3}$、$y\le\sqrt{3}\,x$，其交为顶点 $A=(0,0)$、 -$B=(40,0)$、$C=(20,20\sqrt{3})$ 的等边三角形。以 $s_1$ 为例，它到三顶点的方向分别 -为 $0^{\circ},0^{\circ},\arctan(20\sqrt{3}/1020)\approx1.945^{\circ}$，均在 -$[0^{\circ},2^{\circ}]$ 内，故上边界不切去该三角形；其余两站由绕三角形中心旋转 -$120^{\circ}$ 的对称性同理成立，三个完整前向角域之交恰为该三角形。取真实源为 -三角形中心 $g_*=(20,20\sqrt{3}/3)$：以 $s_1$ 为例，真实方位约 $0.649^{\circ}$，与 -读数 $1^{\circ}$ 的偏差不超过 $1^{\circ}$，检测距离约 $1020$ 米，不超过 $1500$ 米， -另两站同理，故该反例符合题设的误差界与有效接收半径范围。此时 $D=40$ 米，以 $AB$ -为直径的圆中心为 $(20,0)$，到 $C$ 的距离为 $20\sqrt{3}>20$ 米，不能覆盖；换任何 -最远顶点对亦然。该三角形的最小包围圆即其外接圆，半径 -$40/\sqrt{3}\approx23.094011$ 米。这同时说明“直径不超过 $40$ 米”不足以保证一次 -清除。 - -\subsection{最小包围圆与可保证清除} - -定位的最终目的是清除（附录~2 第（8）项的 $20$ 米距离判据），故正确工具是最小 -包围圆 -\begin{equation} - \rho(K)=\min_{z}\max_{g\in K}\|g-z\|. - \label{eq:mec} -\end{equation} -对有限顶点集 $V$，$f(z)=\max_{v\in V}\|v-z\|$ 连续且随 $\|z\|\to\infty$ 趋于无穷， -最小值存在；若两个不同中心 $c_1,c_2$ 都以半径 $r$ 覆盖 $V$，则中点 $c=(c_1+c_2)/2$ -对每个顶点满足 -$\|v-c\|^2=(\|v-c_1\|^2+\|v-c_2\|^2)/2-\|c_1-c_2\|^2/40$），但最小 -包围圆半径均小于 $20$ 米，即存在一点可保证清除，与可视化结果一致。该演练未公开 -源坐标且未执行清除，故仅用于观测交会与计算一致性复核，不能据此声称实测定位误差 -或清除成功率。\todonote{此处可补充定位区域图（figures/）} - -\begin{table}[htbp] - \centering - \caption{官方演练三点观测的离线复算结果} - \label{tab:q1practice} - \begin{tabular}{cccc} - \toprule - 误差半角 & 直径 $D$ / 米 & 最小包围半径 $\rho$ / 米 & 直径圆最大超出 $E$ / 米 \\ - \midrule - $1^{\circ}$ & 23.996723 & 12.068583 & 0.604002 \\ - $1.005^{\circ}$ & 24.119088 & 12.130377 & 0.608486 \\ - \bottomrule - \end{tabular} -\end{table} - -\section{问题~2：第二检测点的主动选点模型} - -\subsection{建模思路来源} - -问题~2 给定“某全向干扰源在一个检测点处测得的示向度”，要求“给出第二个检测点的 -选择策略，以获得关于该干扰源较好的定位效果，并给出第二个检测点的候选区域”。 -注意源类型明确为全向，不能混入问题~4 的朝向可见性条件。本问方法的取舍同样由 -题面描述逐项确定。 - -\textbf{先接收、后优化。}附录~2 第（2）项规定各源有效接收半径在 $1000$ 至 $1500$ -米之间且具体值未知。真实源位置未知时，若第二检测点距真源超过其实际接收半径， -第二次检测将返回 \texttt{no\_signal}，任何定位收益都无从谈起。因此把本问拆成 -先后两个问题：先构造“无论真源在候选集合内何处都能收到信号”的安全候选区域， -再在其中优化定位效果。若只追求较大交会角而不控制到真实源的距离，预期几何收益 -可能根本无法实现。 - -\textbf{由误差描述确定最坏情形指标。}题面只给出有界误差（附录~2 第（1）项），没有 -给出源位置的概率分布，也不存在可独立重抽样的测向噪声模型（同一地点误差固定， -重复检测不产生新信息）。因此不能把卡尔曼滤波、协方差传播或费舍尔信息直接用作 -严格保证，本文以最坏情形的后验包围半径作为选点主目标\cite{boyd}；交会角仍有 -明确的几何意义，但只作局部解释与候选筛选依据。 - -\textbf{由区域描述确定活动范围。}题面第~1 页的 $1800$ 米圆域限制的是干扰源位置； -附录~3 说明机器狗位置通常不构成约束（接口坐标分量绝对值上限仅为数值防护）。 -故第二检测点允许位于 $\Omega$ 之外，安全候选区域不受源位置圆域限制。 - -\textbf{由 near 机制确定分支处理。}附录~2 第（9）项规定检测点距源不超过 $5$ 米时 -“无法获得示向度信息，此时可直接进行光学精确定位并清除干扰源”。返回 -\texttt{near} 不是策略失败，而是定位效果更好的分支（不确定半径不超过 $5$ 米）， -应单独建模并就地清除。 - -\textbf{由动作耗时确定成本项。}附录~2 第（5）、（6）项规定检测耗时 $5$ 秒、移动 -速度 $5$ 米/秒，故第二点的成本取移动与检测耗时之和，作为后验半径择优之后的次 -目标，避免任意混合米与秒。 - -\subsection{首次观测后的候选集合} - -设在 $s_1$ 处首次测得 \texttt{direction}，示向度 $\theta_1$，记 $u=u(\theta_1)$。 -由角域模型、题面第~1 页的源位置圆域与附录~2 第（2）项的接收半径上界，真实源 -$g$ 满足 -\begin{equation} - g\in K_1=\Omega\cap W(s_1,\theta_1,\delta)\cap B(s_1,R_+), - \qquad R_+=1500, - \label{eq:k1} -\end{equation} -即保守位置候选集合 $K_1$ 为闭凸紧集；观测一致时它必含真源，从而非空。首次返回 -\texttt{direction} 还意味着 $\|g-s_1\|>5$（附录~2 第（9）项），但排除这个开圆盘 -会破坏凸性，本文暂不使用该信息，保留包含真源的凸外包集合：由此得到的保证可能 -更保守，但绝不误删真实位置。若计算得到 $K_1=\varnothing$，说明输入、频道、误差 -界或数值处理与题设不一致，应返回不一致状态，不能继续给空集计算圆心。 - -\subsection{安全候选区域的定义与非空判据} - -第二个检测点 $q$ 必须保证：无论真源位于 $K_1$ 内何处，都有 $\|q-g\|\le R_-$ -（$R_-=1000$），从而对任何 $R_c\ge R_-$ 都能收到信号。定义 -\begin{equation} - F_K(q)=\max_{g\in K}\|q-g\|,\qquad - \mathcal{Q}(K)=\{q:F_K(q)\le R_-\}=\bigcap_{g\in K}B(g,R_-). - \label{eq:Q} -\end{equation} -保证接收不等于保证返回示向度：距离不超过 $5$ 米时可能返回 \texttt{near}，该分支 -定位效果更好（见 6.6 节），不能视为策略失败。 - -\textbf{命题~1}（$F_K$ 的凸性与稳定性）\quad 对任意非空紧集 $K$，$F_K$ 为凸函数， -且 $|F_K(q_1)-F_K(q_2)|\le\|q_1-q_2\|$。 - -\textbf{证明}\quad 对每个固定的 $g$，距离函数关于 $q$ 凸，逐点取最大值保持凸性； -由三角不等式 $\|q_1-g\|\le\|q_2-g\|+\|q_1-q_2\|$，对 $g$ 取最大得到一个方向的 -不等式，再交换两点即得 Lipschitz 性。\hfill$\square$ - -故 $\mathcal{Q}(K)$ 为闭凸集；非空时它含于任一 $B(g_0,R_-)$ 内，因而有界。 - -\textbf{定理~1}（非空判据）\quad $\mathcal{Q}(K)\ne\varnothing$ 当且仅当 -$\rho(K)\le R_-$。 - -\textbf{证明}\quad 由定义 $\rho(K)=\min_q F_K(q)$；$F_K$ 连续且随 $\|q\|\to\infty$ -趋于无穷，最小值可达，故“存在 $q$ 使 $F_K(q)\le R_-$”与“该最小值不超过 $R_-$” -完全等价。\hfill$\square$ - -当 $\rho(K)=R_-$ 时，安全区域仅含最小包围圆中心这个单点（唯一性见 5.6 节），因此 -判据必须使用不严格不等式，不能把等号情形误判为空。 - -\textbf{外包圆给出的充分区域。}若已知 $K\subseteq B(c,r)$ 且 $r\le R_-$，则对任意 -$\|q-c\|\le R_--r$ 的点都有 $\|q-g\|\le\|q-c\|+\|c-g\|\le R_-$，故 -\begin{equation} - B(c,R_--r)\subseteq\mathcal{Q}(K). - \label{eq:sufficient} -\end{equation} -这给出容易计算的充分候选区域；但一个满足 $r>R_-$ 的宽松外包圆只能说明该外包圆 -不能提供证书，不能据此判定真实的 $\mathcal{Q}(K)$ 为空。 - -\subsection{截断角域的解析最小包围圆} - -首次角域狭窄（$\delta=1^{\circ}$）这一题设特征，使 \eqref{eq:sufficient} 所需的 -外包圆可以解析地算到最小。暂时去掉只会缩小集合的 $\Omega$ 约束，考虑完整截断 -角域 $S=W(s_1,\theta_1,\delta)\cap B(s_1,R_+)$，其点可写成 -$g=s_1+t\,u(\theta_1+\varphi)$（$0\le t\le R_+$，$|\varphi|\le\delta$）。令 -\begin{equation} - a=\frac{R_+}{2\cos\delta},\qquad c=s_1+a\,u. - \label{eq:ac} -\end{equation} - -\textbf{定理~2}（截断角域的最小包围圆）\quad 对 $0\le\delta\le45^{\circ}$，$S$ 的 -最小包围圆恰为 $B(c,a)$。 - -\textbf{证明}\quad 先证包含。对 $g=s_1+t\,u(\theta_1+\varphi)\in S$， -\begin{equation} - \|g-c\|^2=t^2+a^2-2at\cos\varphi. - \label{eq:dist} -\end{equation} -固定 $\varphi$ 时右端关于 $t$ 为凸二次函数，区间最大值在端点取得：$t=0$ 时等于 -$a^2$；$t=R_+$ 时由 $\cos\varphi\ge\cos\delta$ 得 -$\|g-c\|^2\le R_+^2+a^2-2aR_+\cos\delta=a^2$，最后一步代入了 -$a=R_+/(2\cos\delta)$。故 $S\subseteq B(c,a)$。 - -再证最小。取 $p_0=s_1$、$p_{\pm}=s_1+R_+u(\theta_1\pm\delta)$，三点都在 $B(c,a)$ -的圆周上。令 $\lambda_+=\lambda_-=1/(4\cos^2\delta)$、 -$\lambda_0=1-1/(2\cos^2\delta)$；$\delta\le45^{\circ}$ 时三权重非负且和为 $1$， -直接代入得 $c=\lambda_0p_0+\lambda_+p_++\lambda_-p_-$。于是对任意中心 $z$，由加权 -距离恒等式 -\begin{equation} - \sum_j\lambda_j\|p_j-z\|^2=a^2+\|c-z\|^2\ge a^2, -\end{equation} -故任何覆盖这三点的圆半径不小于 $a$；而覆盖 $S$ 的圆必须覆盖这三点，结合包含性 -知最小半径恰为 $a$。$\delta=0$ 时两个远端点重合，结论退化为长度 $R_+$ 的线段 -直径圆，仍成立。\hfill$\square$ - -该推导不依赖源位置先验与任何概率分布；它给出完整截断角域的精确最小圆，与 -$\Omega$ 相交后，真实 $K_1$ 的最小圆可能更小。 - -\subsection{本题可直接采用的安全候选圆盘} - -由 $K_1\subseteq S\subseteq B(c,a)$ 与 \eqref{eq:sufficient}，取 -\begin{equation} - \mathcal{Q}_0=B(c,b),\qquad b=R_--a=1000-\frac{1500}{2\cos\delta}, - \label{eq:Q0} -\end{equation} -数值见表~\ref{tab:q2disk}。 - -\begin{table}[htbp] - \centering - \caption{安全候选圆盘的解析参数} - \label{tab:q2disk} - \begin{tabular}{ccc} - \toprule - 误差半角 $\delta$ & 轴向中心距离 $a$ / 米 & 安全候选半径 $b$ / 米 \\ - \midrule - $1^{\circ}$ & 750.114246 & 249.885754 \\ - $1.005^{\circ}$ & 750.115391 & 249.884609 \\ - \bottomrule - \end{tabular} -\end{table} - -两种口径下 $b>0$，故本题首次有效测向后的安全候选区域由解析证明严格非空，无需把 -“若安全区域为空就去最小包围圆圆心”作为保底步骤（对一般候选集合，$\rho(K)>R_-$ -时根本不存在保证接收的点）。几何上 $\mathcal{Q}_0$ 位于首测示向方向前方约 $750$ -米处、半径约 $250$ 米，与首测点相距至少约 $500$ 米，还天然避免了同点重复测量不 -产生新信息的问题（附录~2 第（1）项）。机器狗不受源位置圆域限制，即使 $c$ 位于 -$\Omega$ 外，选点也合法。为抵消坐标计算与动作提交中的工程舍入，可取缩小区域 -$\mathcal{Q}_\eta=B(c,b-\eta)$（$0<\eta5$ 的候选位置记真实方位 $h_q(g)=\operatorname{atan2}(g_y-q_y,g_x-q_x)$， -则可能读数集合为 -$\mathcal{B}(q)=\{\beta:\exists\, g\in K_1,\ \|g-q\|>5,\ d_{\mathbb{S}^1}(\beta,h_q(g)) -\le\delta\}$。这里用所有允许误差描述可能读数，而不是假设误差可以随机独立重抽样。 - -\textbf{最坏后验半径指标。}定义 $J(q)$ 为所有可能 \texttt{direction} 分支 -$\rho(K_d(q,\beta))$ 与非空 \texttt{near} 分支 $\rho(K_n(q))$ 的上确界，即未来所有 -允许观测下最坏的保守包围半径；不存在的观测分支不参与取最大。选点主目标即在安全 -候选区域内降低 $J(q)$。该指标直接服务一次清除要求：$J(q)\le20$ 时每个可能分支都 -有半径不超过 $20$ 米的保守定位圆；它比面积更贴合任务——面积较小的集合仍可能 -十分狭长。注意后验总是 $K_1$ 的子集，故 $J(q)\le\rho(K_1)$，但不一定严格小于： -不能仅由“增加一次观测”推断精度必然严格改善，更不能保证两次测向即达 $20$ 米 -阈值。 - -\textbf{移动成本与字典序。}连续测量同一频道时，本次动作的虚拟时间增量为 -\begin{equation} - C(q)=\|q-s_1\|/5+5\ \text{秒}. - \label{eq:cost} -\end{equation} -以 $\widehat{J}(q)$ 表示实际计算的评估量（6.8 节取保守上界 $\overline{J}(q)$）， -推荐先按后验半径择优，再保留满足 $\widehat{J}(q)\le J_{\min}+\tau$ 的近优点并取 -其中 $C(q)$ 最小者，其中 $\tau\ge0$ 是显式声明的定位容忍量（米），$\tau=0$ 对应 -严格字典序；本文不预设未经实验支持的最优 $\tau$。 - -\subsection{交会角的局部几何解释} - -在假定真实位置 $g$ 附近，记两站距离为 $r_1,r_2$，真实视线单位向量为 $u_1,u_2$， -对应法向量为 $n_1,n_2$。角误差很小且位置扰动相对站距很小时，方位函数的一阶展开 -给出 $n_i\cdot\Delta g\approx r_ie_i$（$|e_i|\le\delta_{\mathrm{rad}}$，弧度），即 -局部不确定区域近似由两条带状约束 $|n_i\cdot\Delta g|\le r_i\delta_{\mathrm{rad}}$ -限定。若视线交会角为 $\phi$，法向量矩阵的行列式绝对值为 $|\sin\phi|$，对法向坐标 -中的矩形作线性逆变换，得近似面积 -\begin{equation} - A_{\mathrm{loc}}\approx\frac{4\,r_1r_2\,\delta_{\mathrm{rad}}^{2}}{|\sin\phi|}. - \label{eq:anglearea} -\end{equation} -这解释了两点：视线近于平行或反向时误差被显著放大；在距离不变的局部比较下，接近 -直角的交会较有利。但真实源位置未知，$r_2$ 与 $\phi$ 随 $g$ 改变，且有限角域并非 -无限带状区域，故不能由此推出“总应横移固定距离”或“对某个假定源位置成 -$90^{\circ}$ 即全局最优”。本文仅用它优先考虑轴线两侧的候选点，最终仍以后验集合 -指标评价，交会角只作同分筛选指标。 - -\subsection{圆弧先验的保守离散与读数区间评估} - -\textbf{外包切线多边形。}直接连接圆周采样点得到的是内接多边形，会错误排除圆盘 -边缘的真实位置。为复用问题~1 的半平面工具，取 $M\ge3$ 个均匀法向量 -$v_j=u(2\pi j/M)$，定义 -\begin{equation} - P_M(o,R)=\{x:v_j\cdot(x-o)\le R,\ j=0,\dots,M-1\}. -\end{equation} -由柯西不等式，$B(o,R)\subseteq P_M(o,R)$；相邻切线交点到圆心的距离为 -$R\sec(\pi/M)$，故单个圆盘外包的最大径向超出不超过 $R[\sec(\pi/M)-1]$。令 -$\widetilde{K}_1=P_M(0,1800)\cap W(s_1,\theta_1,\delta)\cap P_M(s_1,1500)$，则 -$K_1\subseteq\widetilde{K}_1$，对任何第二读数再求半平面交仍保留真源。靠近切触或 -退化情形须加密检查，不能把单圆径向误差未经论证直接当成最终定位半径的误差界。 -安全选点仍使用解析的 $\mathcal{Q}_\eta$：即使粗糙外包多边形的最小圆偏大，也不能 -据此推翻解析安全区域的非空结论。若改用任意有界凸外包多边形 -$\widetilde{K}=\mathrm{conv}\{v_j\}$，则 -$\max_{g\in\widetilde{K}}\|q-g\|=\max_j\|q-v_j\|$（与 5.4 节相同的凸组合论证）， -其保证接收区域由有限个圆盘约束 $\|q-v_j\|\le1000$ 给出；离散区域为空时优先加密 -或回到解析候选盘，不把离散失败误报为问题无解。 - -\textbf{读数区间的保守评估。}仅枚举少量假定源位置与误差端点，只得到被枚举情形的 -最大值，可能漏掉真正最坏的读数。将整周按圆周意义划分为若干区间 $I_j$（中心 -$\beta_j$、宽度 $h_j$，要求 $\delta+h_j/2<90^{\circ}$，跨 $0^{\circ}$ 的区间按 -圆周距离处理）。 - -\textbf{命题~2}\quad 对任意 $\beta\in I_j$，有 -$W(q,\beta,\delta)\subseteq W(q,\beta_j,\delta+h_j/2)$。 - -\textbf{证明}\quad 左侧角域内任意非顶点位置，其方向到 $\beta$ 的圆周距离不超过 -$\delta$，而 $\beta$ 到区间中心的距离不超过 $h_j/2$，由圆周距离的三角不等式，其 -方向到中心的距离不超过两者之和；顶点在两个闭角域中均被保留。\hfill$\square$ - -定义 $U_j(q)=\widetilde{K}_1\cap W(q,\beta_j,\delta+h_j/2)$，则落在该区间的任何 -真实读数对应的保守后验都含于 $U_j(q)$，从而 -$\rho(K_d(q,\beta))\le\rho(U_j(q))$；\texttt{near} 分支取统一上界 -$\min\{5,\rho(\widetilde{K}_1)\}$。令 $\overline{J}(q)$ 为所有非空 $U_j(q)$ 的最小 -包围半径与该上界的最大值，则 $J(q)\le\overline{J}(q)$（精确几何计算下成立；浮点 -实现还须另行给出包含性与数值误差处理）。二分角区间或增加外包切线都使相应上界 -单调不增，给出稳定的自适应加密方向。实际可先以少量读数采样粗筛，再对入围点使用 -完整区间上界：粗筛只决定计算资源分配，最终报告的保守上界必须来自完整覆盖的 -区间，不能来自粗筛样本最大值。 - -\subsection{选点算法与边界情形} - -\textbf{算法~2}（安全区域内的有限候选主动测向） -\begin{enumerate}[label=\arabic*.,leftmargin=2.5em] - \item 核验首次观测为同一全向源的有效示向度，构造 $K_1$ 或其保守表示； - \item 按 \eqref{eq:ac} 计算 $a$、$c$ 与 $b=1000-a$，选取满足误差预算的缩小半径 - $b-\eta$； - \item 构造有限候选集：圆心 $c$ 及 - $q=c+r_\ell(\cos\psi_j\,u+\sin\psi_j\,u_\perp)$（$01000$：不存在对该集合全部位置保证接收的点，圆心仅是最小化最坏 -距离的探索选择，改善交会角若要求偏离该中心还会牺牲最坏距离最优性，两项冲突的 -要求不能同时称为已保证；（v）外包圆半径大于 $1000$：只能说明该证书不足，不能 -判真实安全区域为空；（vi）测量轴接近 $0^{\circ}/360^{\circ}$：使用向量约束与 -圆周区间，避免角度断点错误；（vii）两次测向交会较差：保留完整后验并继续测量， -不把小面积当成小直径；（viii）源类型为定向：距离证书仍成立，但接收还受朝向 -限制，不能直接沿用本问的接收保证（见问题~4）。 -\todonote{候选区域示意图与选点对比实验待补} - -\section{问题~3：全向干扰源的搜索定位与清除调度} - -\subsection{虚拟时间与动作成本模型} - -依据题设动作耗时，完成任务所需虚拟时间 -\begin{equation} - T=\frac{L}{5}+N_{\mathrm{switch}}+5N_{\mathrm{measure}} - +5N_{\mathrm{clear}}^{\mathrm{s}}+3N_{\mathrm{clear}}^{\mathrm{f}}, - \label{eq:time} -\end{equation} -其中 $L$ 为移动总路程（含检测与清除引发的移动），频道切换次数只计被接受的检测 -动作。优化顺序为：先保证全部清除，再减小 $T$；不能通过少清除源来改善平均时间。 -虚拟活动时长上限为 $100$ 小时；程序运行时间另受 $20$ 分钟窗口约束，二者独立。 - -\subsection{全域覆盖发现基线} - -在 $s$ 处对某频道测得 \texttt{no\_signal}，只能排除以 $s$ 为中心、半径 $1000$ 米 -圆盘内存在该频道源（有效接收半径可能只有 $1000$ 米），不能一律排除到 $1500$ 米。 -据此构造覆盖点集 -\begin{equation} - S=\{(700i,700j):i,j=-3,-2,\dots,3\},\qquad |S|=49, -\end{equation} -其覆盖范围 $[-2100,2100]^2$ 包含 $\Omega$。对任一单元内的源 $g$，其所在单元的 -$4$ 个格点到 $g$ 的距离均不超过 $700\sqrt{2}\approx 989.95<1000$ 米，故必存在 -合格检测点；又 $g$ 位于 $4$ 个格点的凸包内部，经过 $g$ 的任意发射半平面必包含 -至少一个格点（否则全部格点落入相反开半平面，与 $g$ 在凸包内矛盾）。因此 $49$ 点 -逐一检测可保证发现该频道的源；源恰在网格线上时按半开区间归入相邻单元处理。 -$49$ 点 $\times\,20$ 频道至多 $980$ 次检测，虚拟耗时上界约 $1.32\times 10^4$ 秒， -在 $100$ 小时上限内有充分设计空间；实际执行中已清除频道跳过、同点共享多频道测量、 -已发现频道转入定位队列。 - -\subsection{发现—定位—清除闭环} - -机器狗维护逐频道状态：未知／已发现待定位／可清除／已清除／已证明不存在，以及候选 -集合 $K_c$。闭环流程为：覆盖扫描发现源 $\to$ 用问题~2 的主动选点缩小 $K_c$ 直至 -$\rho(K_c)\le 20$ $\to$ 移动到 $C_{20}(K_c)$ 内距当前点最近的点清除 $\to$ 更新覆盖 -记录与队列。多个已发现源按“预期信息改善／增量虚拟耗时”排序处理；候选采样点恰 -返回 \texttt{near} 时立即就地清除。 - -\subsection{停止条件与结果统计} - -\textbf{停止成功的依据为以下之一}：（i）已成功清除 $16$ 个不同频道的源（数量 -上界）；（ii）每个频道都已有清除成功记录或经完整覆盖证明不存在。发现 $10$ 个源、 -连续若干次无信号、候选采样为空均不是充分停止条件；程序运行时间或窗口不足而退出 -记为未证明完成，不与成功混记。结果统计按题设给出 -\begin{align} - \text{被清除干扰源个数的比例} &= \frac{\text{被清除干扰源的个数}}{\text{干扰源总数}} ,\\ - \text{平均定位清除时间} &= \frac{\text{定位清除总时间}}{\text{被清除干扰源的个数}} . -\end{align} - -\begin{table}[htbp] - \centering - \caption{问题~3 正式测试结果（按题目表~1 格式）} - \label{tab:q3formal} - \begin{tabular}{lcccc} - \toprule - & 测试案例编码 & 清除干扰源个数 & 平均定位清除时间 & 程序运行时间 \\ - \midrule - 测试~1 & \todonote{待填} & \todonote{待填} & \todonote{待填} & \todonote{待填} \\ - 测试~2 & \todonote{待填} & \todonote{待填} & \todonote{待填} & \todonote{待填} \\ - 测试~3 & \todonote{待填} & \todonote{待填} & \todonote{待填} & \todonote{待填} \\ - \bottomrule - \end{tabular} -\end{table} - -\todonote{演练测试统计值（清除比例、平均定位清除时间）待演练后填入} - -\section{问题~4：含定向干扰源的检测与清除} - -\subsection{定向源观测模型} - -定向源的接收条件是“距离 $\le R_c$ 且检测点位于发射半平面内”。因此 -\texttt{no\_signal} 约束的是位置—半径—朝向的\textbf{联合假设}：若不联合维护朝向 -可行集合，就不能用它单独删除空间候选点。可靠基线是对 \texttt{no\_signal} 只记录 -“该点覆盖检测已完成”，不做空间删除；加速版本再维护朝向可行集合，且必须验证 -不误删真源。 - -\subsection{覆盖发现基线对定向源仍然有效} - -由 7.2 节的凸包论证：源 $g$ 位于所在单元 $4$ 格点的凸包内部，故经过 $g$ 的任意 -发射半平面必含至少一个格点；该格点同时满足距离不超过 $989.95<1000$ 米。因此 -$49$ 点逐频道检测对全向与定向源统一保证发现，包括贴近 $\Omega$ 边界朝外发射的源 -（格点允许越出 $\Omega$ 访问）。 - -\subsection{失去信号后的后备清除} - -已发现的定向源在定位过程中可能再次失去信号。对已知有界候选集合 $K$，构造边长 -$20$ 米的全局网格：格中心到格内任意点距离不超过 $10\sqrt{2}\approx 14.14<20$ 米， -保留与 $K$ 的外包框相交的格子即得无空洞的有限圆盘覆盖，逐点调用清除动作。请求 -次数上界 -\begin{equation} - N\le\Bigl(\lceil w/20\rceil+2\Bigr)\Bigl(\lceil h/20\rceil+2\Bigr), -\end{equation} -其中 $w,h$ 为候选集合外包框的宽与高；单源全失败清除耗时为 $L/5+3N$。若 $K$ 外包 -尺寸较大（如半径 $1500$ 米圆盘的外包框达上万格点），盲扫不满足现实预算，应先继续 -定位缩小候选集合。现实时间预算按“剩余请求数 $\times$ 实测单请求高分位耗时”估计， -不满足预算时转入其他任务或按预算退出。 - -\begin{table}[htbp] - \centering - \caption{问题~4 正式测试结果（按题目表~1 格式）} - \label{tab:q4formal} - \begin{tabular}{lcccc} - \toprule - & 测试案例编码 & 清除干扰源个数 & 平均定位清除时间 & 程序运行时间 \\ - \midrule - 测试~1 & \todonote{待填} & \todonote{待填} & \todonote{待填} & \todonote{待填} \\ - 测试~2 & \todonote{待填} & \todonote{待填} & \todonote{待填} & \todonote{待填} \\ - 测试~3 & \todonote{待填} & \todonote{待填} & \todonote{待填} & \todonote{待填} \\ - \bottomrule - \end{tabular} -\end{table} - -\section{模型评价与推广} - -\textbf{优点}：（1）四个问题复用同一几何内核（角域半平面交—直径—最小包围圆）， -模型一致、实现可复用；（2）全程坚持保守几何：有界误差不取平均、无信号只排除 -$1000$ 米、\texttt{no\_signal} 对定向源不删位置、停止条件需覆盖证明，所有“清除 -完毕”的结论都可验证；（3）虚拟时间公式把调度目标显式化，且区分了虚拟时间与程序 -运行时间两类约束。 - -\textbf{缺点与改进}：（1）主动选点采用最坏情形采样，是启发式而非全局最优，可研究 -对候选集合的更精细离散化；（2）$49$ 点覆盖基线存在冗余，自适应跳点须以保留逐频道 -覆盖证据为前提；（3）后备清除请求数较大，宜结合朝向可行集合减小候选集合；（4） -当前演练验证限于问题~1 的几何内核，问题~3、4 的闭环策略与统计结果有待演练填充。 - -\begin{thebibliography}{9} - \zihao{5} - \bibitem{preparata} Preparata F P, Shamos M I. Computational Geometry: An - Introduction[M]. New York: Springer-Verlag, 1985. - \bibitem{welzl} Welzl E. Smallest enclosing disks (balls and ellipsoids)[C]// - Maurer H. New Results and New Trends in Computer Science. Lecture Notes in - Computer Science, vol 555. Berlin: Springer, 1991: 359--370. - \bibitem{toussaint} Toussaint G T. Solving geometric problems with the rotating - calipers[C]//Proceedings of IEEE MELECON. Athens: IEEE, 1983. - \bibitem{mcgill} CGAL Project. Bounding Volumes: Min\_circle\_2[EB/OL]. - \url{https://doc.cgal.org/latest/Bounding_volumes/}, 2026. - \bibitem{cgrl} McGill School of Computer Science. Rotating Calipers[EB/OL]. - \url{https://www-cgrl.cs.mcgill.ca/~godfried/research/calipers.html}, 2026. - \bibitem{boyd} Boyd S, Vandenberghe L. Convex Optimization[M]. Cambridge: - Cambridge University Press, 2004. -\end{thebibliography} - +数学推导中三角函数的自变量采用弧度；带 $^\circ$ 的量先换算为弧度。 +记 $[a,b]=a_xb_y-a_yb_x$ 为二维叉积，$\B(c,r)$ 为闭圆盘。 + +\input{sections/q1} +\input{sections/q2} +\input{sections/q3} +\input{sections/q4} +\input{sections/results} +\input{sections/evaluation} +\clearpage +\begin{thebibliography}{99} +\small +\bibitem{problem} 全国大学生数学建模竞赛组委会. +2026年高教社杯全国大学生数学建模竞赛B题：无线电干扰源的快速自动定位与清除[Z]. 2026. +\bibitem{protocol} 赛题配套材料. 模拟器使用说明；模拟器通信接口说明及编程指南[Z]. 2026. +\bibitem{format} 全国大学生数学建模竞赛组委会. 全国大学生数学建模竞赛论文格式规范（2026年修订稿）[Z]. 2026. +\bibitem{welzl} WELZL E. Smallest enclosing disks (balls and ellipsoids)[C]// +New Results and New Trends in Computer Science. LNCS 555. Berlin: Springer, 1991: 359--370. +\url{https://doi.org/10.1007/BFb0038202}. +\bibitem{boyd} BOYD S, VANDENBERGHE L. Convex Optimization[M]. +Cambridge: Cambridge University Press, 2004. \url{https://web.stanford.edu/~boyd/cvxbook/}. +\bibitem{chvatal} CHV\'ATAL V. A greedy heuristic for the set-covering problem[J]. +Mathematics of Operations Research, 1979, 4(3): 233--235. +\url{https://doi.org/10.1287/moor.4.3.233}. +\bibitem{formal} 官方无线电干扰源环境模拟器. +问题三、四正式行为日志与配套统计（客户端1.1.0，四个案例）[DS]. 2026-09-12. +案例编码及文件校验值见附录~\ref{app:data}。 +\end{thebibliography} \clearpage -% ============================================================ -% 附录（页数不限；电子版与纸质版均须包含） -% ============================================================ \appendix - -\section{支撑材料文件列表} - -\todonote{提交前更新为实际支撑材料压缩包内容，须与附录~B 源码一致} -\begin{table}[htbp] - \centering - \caption{支撑材料文件列表} - \begin{tabular}{lll} - \toprule - 文件/目录 & 内容 & 说明 \\ - \midrule - \texttt{geometry/} & 几何内核源代码 & 角域交、直径、最小包围圆 \\ - \texttt{planning.py} & 问题~2 安全候选盘计算 & \texttt{first\_bearing\_candidate\_disk} \\ - \texttt{examples/q1/} & 问题~1 输入样例 & 含等边三角形反例 \\ - \texttt{output/q1/} & 问题~1 输出与演练记录 & 优化报告、可视化 \\ - \bottomrule - \end{tabular} -\end{table} - -\section{程序源代码} - -以下为支撑模型计算的核心源代码，完整可运行代码以支撑材料压缩包为准。 - -\subsection{\texttt{src/mcm26b/geometry/localization.py}：交会定位几何内核} - -\lstinputlisting[language=Python]{../../src/mcm26b/geometry/localization.py} - -\subsection{\texttt{src/mcm26b/geometry/planning.py}：问题~2 安全候选区域} - -\lstinputlisting[language=Python]{../../src/mcm26b/geometry/planning.py} - +\ctexset{section={number=\Alph{section},aftername={\quad}}} +\input{sections/appendix} \end{document} diff --git a/docs/paper/sections/appendix.tex b/docs/paper/sections/appendix.tex new file mode 100644 index 0000000..39dfefe --- /dev/null +++ b/docs/paper/sections/appendix.tex @@ -0,0 +1,57 @@ +\section{正式数据清单与复算说明}\label{app:data} +论文按参考材料中的“逐问建模、证明、结果、评价、源码附录”方式组织， +排版遵守2026年格式规范\cite{format}：A4、四边距 $2.5$ cm， +电子版从摘要页开始连续编号，无目录。所给往届论文仅用于结构与排版参考， +不作为本题算法或数据来源。 + +\input{data/formal-file-list} +原始正式日志以题目要求的文件名保留，包内官方字段不作修改。 +可读统计快照已经去掉账号与设备字段，原始加密包未解密。 +包哈希用于核对同一导出文件，不等同于对官方数字签名的独立验证。 + +复算脚本 \pathtext{scripts/audit_paper_formal.py} 读取所选文件的公开头部， +与官方数据库及同名侧文件匹配，生成 JSON、CSV 与 LaTeX 表格。 +已有匿名快照时也可以离线重新生成表格： +\begin{lstlisting}[language={},numbers=none] +python scripts/audit_paper_formal.py +python scripts/audit_paper_formal.py --snapshot docs/paper/data/formal-results.json +\end{lstlisting} +第二条命令只重算快照中的算术量；如果原始包仍在目录中，还会核对包哈希。 +它不表示脱离官方数据库后又独立验证了一次统计来源。 + +\section{支撑材料与运行方法} +\begin{table}[H] +\centering\small +\caption{支撑材料目录及用途} +\begin{tabularx}{\linewidth}{p{5.8cm}X} +\toprule +文件或目录 & 用途\\ +\midrule +\pathtext{src/mcm26b/} & 四问几何、信念、覆盖、调度与串行通信实现\\ +\pathtext{src/mcm26b/guarantee/plans/} & 第四问已实现的覆盖计划及验证参数\\ +\pathtext{scripts/audit_paper_formal.py} & 正式文件对应核对、匿名快照及表格复算\\ +\pathtext{scripts/build_paper_support.py} & 矢量图、源码附录与支撑包生成\\ +\pathtext{docs/paper/data/} & 仅四个所选正式案例的可读统计、表格及哈希\\ +\pathtext{docs/paper/sections/} & 分章论文源文件\\ +\pathtext{docs/paper/figures/} & 参数构造图和正式累计耗时图的矢量源文件\\ +\pathtext{Jammers-simulator-full/test/} & 四份原名官方加密正式日志\\ +\pathtext{support-manifest.json} & 支撑包文件清单及逐文件 SHA-256\\ +\bottomrule +\end{tabularx} +\end{table} +Python 运行时需要 \texttt{requests}；\texttt{numpy} 为可选加速依赖。 +将 \texttt{src} 加入 Python 模块路径后，可使用 +\texttt{python -m mcm26b.geometry} 进行问题一几何分析， +或调用 \texttt{mcm26b.cli} 的入口运行在线策略。 +正式程序由用户先在模拟器界面开启相应测试； +本次论文重写和数据核对没有启动新的正式或演练测试。 +运行指令、编译步骤及数据缺项说明另见支撑包的 \texttt{README.md}。 + +\section{完整程序源码} +以下按当前仓库列出策略程序、其配套模块及论文数据处理程序的完整源码。 +源码中的历史注释与可选自检功能保留原样；其中旧仿真数值不构成本论文实验结果。 +附录显示副本仅将数学符号转换为 LaTeX 转义命令，支撑包内可执行源码保持原样。 +正式指标仅由附录A列出的四个案例形成。 +部分自检功能依赖独立本地评测机，它不参与本文正式统计的读取或计算。 +长代码使用连续页排版，附录页数不计入正文的30页限制。 +\input{data/source-listings} diff --git a/docs/paper/sections/evaluation.tex b/docs/paper/sections/evaluation.tex new file mode 100644 index 0000000..f49f739 --- /dev/null +++ b/docs/paper/sections/evaluation.tex @@ -0,0 +1,74 @@ +\section{模型评价与推广} +\subsection{模型的有效性与优点} +本文把未知位置始终表示为集合，使测向误差的处理与题设一致。 +问题一的直径定理与直径圆判据给出可复核的几何答案， +最小包围圆又把位置不确定性直接转换为能否清除的距离条件。 +问题二的安全候选盘将可接收性与定位收益分开， +避免通过扩大交会角而牺牲接收的基本条件。 + +对多源搜索，七站构造用少量站点建立了全向连续覆盖证明， +逐频道账本与网格排除使停止判断有明确依据。 +滚动任务排序将移动、检测、换频和清除放在统一时间目标下处理， +能够在新观测到来后调整任务次序。 +对定向遮挡，位置与朝向联合候选为选点提供信息； +后备清除则使用朝向无关的距离规则，避免无限重复无线电探测。 + +实验部分保留正式原始单位与案例对应关系， +将测试包、官方摘要字段及论文表格连接到同一可复算链条。 +数学构造、算法参数和正式实测分别标注，便于独立检查结论的证据范围。 + +\subsection{局限性与改进方向} +\textbf{第一，启发式选点与调度不具有全局最优性。} +算法2的见证点和读数端点枚举只给出采样比较， +信息增益评分的先验又不是题目公布的概率模型。 +2-opt 只优化当前有限任务表，未来观测仍会改变任务位置。 +后续可用区间分支定界为后验评分建立误差界， +并在同一组可重复场景上比较任务调度，不能把局部较优写成全局最优。 + +\textbf{第二，31点计划只有离散覆盖证据。} +其验证距离和最终角度余量没有给出统一连续延拓保证。 +可采用本文证明的 $49$ 点计划，或按式~\eqref{eq:continuous} +同时控制位置、距离与朝向裕量，再开展新的正式或演练验证。 +现有包没有可公开解读的逐动作轨迹，不能为更换后的方案追认成绩。 + +\textbf{第三，混合类型下联合候选为空的含义需要收紧。} +仅维护定向假设无法涵盖全向源从多侧被接收的情况。 +例如源周围三个相隔 $120^\circ$ 的检测点可同时接收全向信号， +却不能同时位于一个固定前向半平面内。 +严格方案应并列维护源类型，或仅将朝向候选用于探点排序； +已有正观测的频道不得仅因定向候选为空而忽略。 + +\textbf{第四，有限预算影响闭环的完成性。} +即使发现覆盖充分且单次清除证书正确， +仍可能因几何退化、持续遮挡、候选区域过大或网络异常而不能在预算内结束。 +定位步数及 $400$ 格上限属于资源约束，不是无条件完备性的组成部分。 +失败状态必须保留具体未解决频道，不能由程序正常退出代替任务完成。 + +\textbf{第五，正式样本尚不完整。} +两问各两次测试不足以覆盖所有源分布与朝向组合； +源真值总数缺失使全清率无法核算，第三次正式记录也尚未提供。 +因此本文报告逐局原始结果及可复算时间分解，不外推总体平均性能。 + +\subsection{参数影响的解析讨论} +在不引入额外仿真数据的前提下，主要参数的影响可从公式分析。 +由 $a(\delta)=1500/(2\cos\delta)$ 得 +$a'(\delta)=750\sec\delta\tan\delta$（$\delta$ 以弧度计）。 +误差增大会使源包围圆变大、安全候选盘缩小； +表~\ref{tab:safeanalytic} 说明两位小数舍入余量对首次安全盘的改变很小， +但在紧贴角域边界时仍必须计入。 + +由式~\eqref{eq:coveragebound}， +环半径减小会缩短简单覆盖路线，却在接近可行下界时消耗覆盖余量。 +默认半径留下约 $15.461$ m 的解析余量，不能只为降低路长无限向圆心收缩。 +网格边长缩小能够减少 $\epsilon_g$、加强位置证书， +但二维格数大致与 $\ell^{-2}$ 成正比，计算与内存开销增加。 +这些是参数变化的数学关系，不是新增正式实测。 + +\subsection{推广} +该框架可用于满足有界方向误差的静态信号源排查、 +室内设备巡检及移动传感器主动定位。 +迁移时应重新校准接收半径、方向误差与动作成本； +若源移动、频道冲突或观测包含额外遮挡， +就需要扩展状态和观测集合，重新证明保留真源与覆盖发现的条件。 +几何证书、候选维护和行动排序的职责可以保留， +具体覆盖点集与参数不能不经校核直接复用。 diff --git a/docs/paper/sections/q1.tex b/docs/paper/sections/q1.tex new file mode 100644 index 0000000..80de03b --- /dev/null +++ b/docs/paper/sections/q1.tex @@ -0,0 +1,170 @@ +\section{问题一：有界误差交会定位与覆盖圆} +\subsection{前向角域的半平面模型} +给定检测点 $s_i=(s_{ix},s_{iy})$ 与读数 $\theta_i$， +误差约束意味着真实方位位于 +$[\theta_i-\delta,\theta_i+\delta]$ 内。因此可行位置属于前向角域 +\begin{equation} +W_i=\left\{g: +\begin{aligned}\relax +[u(\theta_i-\delta),g-s_i]&\ge0,\\ +[u(\theta_i+\delta),g-s_i]&\le0,\\ +u(\theta_i)\cdot(g-s_i)&\ge0 +\end{aligned}\right\}. +\label{eq:wedge} +\end{equation} +三条不等式均可写为 $a x+b y\le c$，其法向依次为 +\begin{equation} +\begin{aligned} +&(\sin(\theta_i-\delta),-\cos(\theta_i-\delta)),\\ +&(-\sin(\theta_i+\delta),\cos(\theta_i+\delta)),\\ +&(-\cos\theta_i,-\sin\theta_i), +\end{aligned} +\end{equation} +右端为相应法向与 $s_i$ 的内积。在 $0<\delta<90^\circ$ 时， +前两条已限定前向窄角域；第三条显式保留方向性， +并使零误差退化情形对应射线而非整条直线。 +采用正弦、余弦表示可自动处理 $0^\circ/360^\circ$ 跨界。 + +问题一的多边形定位区域定义为 +\begin{equation} +P=\bigcap_{i=1}^{n}W_i=\{g:Ag\le b\}. +\label{eq:q1set} +\end{equation} +这是纯角域交会模型。后续问题加入 $\Omega$ 与接收距离先验后会形成更紧的集合， +但不能将这些附加约束混入问题一的直径结果。 +半平面交是闭凸集，可能为空、单点、线段、有界多边形或无界集。 + +\subsection{区域构造、空集及无界情形} +令约束数 $k=3n$。对任意两条不平行边界 +$a x+b y=c$、$d x+e y=f$，候选交点为 +\begin{equation} +x=\frac{ce-bf}{ae-bd},\qquad y=\frac{af-cd}{ae-bd}. +\end{equation} +仅保留满足全部不等式的交点，再经去重和单调链凸包构造得到顶点集合。 +实现先平移与缩放坐标，以降低千米尺度坐标造成的数值误差； +近平行边界仍参与求交，因为其远端交点可能决定细长区域的直径。 + +不能以任意大矩形裁剪后得到的有限直径代替无界性判断。 +对非空集合定义衰退锥 +\begin{equation} +\mathcal R=\{d:Ad\le0\}. +\end{equation} +若 $\mathcal R$ 含非零向量，则 $g+td\in P$ 对所有 $t\ge0$ 成立， +区域无界，直径为 $+\infty$。二维多面锥只需检查约束边界的两个切向 +$(b,-a)$ 与 $(-b,a)$ 是否满足全部齐次不等式。 +本题至少一个前向窄角域会排除直线性，故非空交集存在极点； +在此特定输入族中，没有可行边界交点可以判为空集。 +无观测输入单独返回整个平面，不按空集处理。 + +有界非空区域中，一个顶点对应单点，两个顶点对应线段，其余为凸多边形。 +空集没有本文定义的有效直径与覆盖圆，程序以显式状态报告观测不相容， +便于检查频道、误差界或输入数据。 + +\subsection{直径与直径圆的判定} +\begin{proposition}[顶点直径] +设 $P=\operatorname{conv}\{v_1,\ldots,v_m\}$ 非空有界，则 +\begin{equation} +D(P)=\max_{i,j}\norm{v_i-v_j}. +\label{eq:diameter} +\end{equation} +\end{proposition} +\begin{proof} +任意 $x,y\in P$ 可表示为凸组合 +$x=\sum_i\lambda_i v_i$、$y=\sum_j\mu_jv_j$。 +由于系数非负且各自和为 $1$， +\[ +\norm{x-y} +=\left\|\sum_{i,j}\lambda_i\mu_j(v_i-v_j)\right\| +\le\sum_{i,j}\lambda_i\mu_j\norm{v_i-v_j} +\le\max_{i,j}\norm{v_i-v_j}. +\] +最远顶点对本身属于 $P$，故上界可达。 +\end{proof} +因此无需在整个区域内部搜索，只需枚举顶点对，计算量为 $O(m^2)$。 + +\begin{proposition}[直径圆覆盖的充要条件] +取最远顶点对 $a,b$，令 $D=\norm{a-b}$、$o=(a+b)/2$。 +存在直径等于 $D$ 的圆盘覆盖 $P$，当且仅当 +\begin{equation} +\max_{v\in V(P)}\norm{v-o}\le D/2. +\label{eq:diametercircle} +\end{equation} +\end{proposition} +\begin{proof} +若半径 $D/2$ 的圆盘中心为 $z$ 且包含 $a,b$，则 +$D\le\norm{a-z}+\norm{z-b}\le D$。 +等号迫使 $z=o$。反之，圆盘为凸集，包含全部顶点即包含它们的凸包。 +\end{proof} +若条件不成立，输出圆外顶点及超出量 +$e=\max_v\norm{v-o}-D/2$，即得到可独立检查的否定证据。 +不能仅以直径端点在圆周上判断整个区域被覆盖。 + +\subsection{反例与可清除半径} +构造等边三角形 +\begin{equation} +A=(0,0),\qquad B=(40,0),\qquad C=(20,20\sqrt3). +\end{equation} +其直径为 $40$ m。以 $AB$ 为直径的圆心为 $(20,0)$，半径为 $20$ m， +但 $C$ 到圆心的距离为 $20\sqrt3$ m，位于圆外。 +其最小包围圆圆心为 $(20,20/\sqrt3)$，半径 +$40/\sqrt3\approx23.094$ m，同样大于清除半径。 +图~\ref{fig:triangle} 展示两类圆的差别。 + +\begin{figure}[htbp] +\centering +\begin{tikzpicture}[x=0.095cm,y=0.095cm,font=\small] + \fill[inkblue!10] (0,0)--(40,0)--(20,34.641)--cycle; + \draw[thick] (0,0)--(40,0)--(20,34.641)--cycle; + \draw[warmgray,dashed,thick] (20,0) circle (20); + \draw[inkblue,thick] (20,11.547) circle (23.094); + \fill (0,0) circle (0.6) node[below left] {$A$}; + \fill (40,0) circle (0.6) node[below right] {$B$}; + \fill (20,34.641) circle (0.6) node[above] {$C$}; + \fill[warmgray] (20,0) circle (0.6) node[below] {$o$}; + \fill[inkblue] (20,11.547) circle (0.6) node[right] {$m$}; + \draw[->,warmgray] (49,-14)--(35,-13); + \node[anchor=west,warmgray] at (49,-14) {直径圆：$r=20$}; + \draw[->,inkblue] (49,24)--(41,22); + \node[anchor=west,inkblue] at (49,24) {最小包围圆：$\rho=40/\sqrt3$}; + \node at (20,-26) {$AB=BC=CA=40$ m}; +\end{tikzpicture} +\caption{直径圆不能覆盖等边三角形。此图为解析反例，不是模拟器观测。} +\label{fig:triangle} +\end{figure} + +该形状可由题设的 $\pm1^\circ$ 角域构造出来。例如检测点 +$(-1000,0)$、$(540,-500\sqrt3)$、$(520,520\sqrt3)$， +对应示向度为 $1^\circ$、$121^\circ$、$241^\circ$。 +各角域的一侧边界给出三角形的三条支撑线，另一侧边界包含整个三角形， +故交集恰为上述三角形。这一构造只用于证明一般性命题，并不作为实验成绩。 + +对一般候选区域，定义最小包围圆 +\begin{equation} +\rho(P)=\min_{z\in\mathbb R^2}\max_{g\in P}\norm{g-z},\qquad +m\in\arg\min_z\max_{g\in P}\norm{g-z}. +\label{eq:mec} +\end{equation} +其边界由至多三个支撑点确定，可用 Welzl 随机增量算法计算\cite{welzl}。 +实现采用固定随机种子及显式栈，并在输出前检查全部顶点的包含关系。 +在精确模型中，若 $\rho(P)\le20$，于 $m$ 清除即可覆盖所有可能真源； +考虑浮点计算后采用 $\rho(P)+\eta_{\mathrm{num}}\le20$ 的充分判据。 +$D(P)\le40$ 是必要条件，但并非充分条件。 + +\subsection{算法一及复杂度} +\begin{algorithmblock}{算法1：有界测向角域交会与覆盖圆判定（对应 algo-1）} +\textbf{输入：}同一频道的检测点、示向度和误差半角。\\ +\textbf{输出：}区域状态、顶点、直径、直径圆判定与最小包围圆。 +\begin{enumerate}[leftmargin=2em,itemsep=1pt,topsep=4pt] + \item 若观测为空，返回无界；否则归一化坐标，生成 $3n$ 条半平面。 + \item 枚举非平行边界交点，仅保留满足全部约束的点。 + \item 无可行点时返回空集；存在非零衰退切向时返回无界及无穷直径。 + \item 对可行交点去重、求凸包，并区分单点、线段和二维多边形。 + \item 枚举最远顶点对，计算 $D$、中点 $o$，检查全部顶点距 $o$ 是否不超过 $D/2$。 + \item 求最小包围圆，复核包含性和数值余量，输出清除证书。 +\end{enumerate} +\end{algorithmblock} +边界交点枚举需 $O(k^2)$ 次，每点校验 $k$ 条约束，主计算量为 $O(k^3)$； +凸包最坏需 $O(k^2\log k)$，直径枚举需 $O(m^2)$。 +Welzl 算法在随机排列下具有期望线性时间， +固定种子实现不宣称最坏时间线性。该可审计方案适合少量观测， +当前入口限制最多 $100$ 个检测点；更大规模可替换半平面交算法。 diff --git a/docs/paper/sections/q2.tex b/docs/paper/sections/q2.tex new file mode 100644 index 0000000..60a3119 --- /dev/null +++ b/docs/paper/sections/q2.tex @@ -0,0 +1,174 @@ +\section{问题二：保证接收的第二检测点选择} +\subsection{候选位置集合与安全区域} +设首次有效示向度为 $(s,\theta)$。有效读数除限定角域外， +还说明源距检测点不超过接收半径上界，故 +\begin{equation} +K_1=\Omega\cap W(s,\theta,\delta_{\mathrm{eff}})\cap\B(s,R_+). +\label{eq:k1} +\end{equation} +其中使用 $R_+=1500$ 而非 $R_-=1000$：收到信号并不能推出距离小于 $1000$ m。 +$\direction$ 还隐含距离大于 $5$ m；为了保持凸表示，在线不扣除这个小圆盘， +只会多保留可能位置，不会排除真源。 + +对非空紧集 $K$ 定义 +\begin{equation} +F_K(q)=\max_{g\in K}\norm{q-g},\qquad +\mathcal Q(K)=\{q:F_K(q)\le R_-\} +=\bigcap_{g\in K}\B(g,R_-). +\label{eq:exact-safe} +\end{equation} +该区域内的任何点均在所有可能真源的最小接收范围内。 +$F_K$ 是凸函数且为 $1$-Lipschitz，因而 $\mathcal Q(K)$ 是闭凸集。 +由式~\eqref{eq:mec} 可知 +\begin{equation} +\mathcal Q(K)\ne\varnothing\quad\Longleftrightarrow\quad\rho(K)\le R_-. +\end{equation} +这一表述将第二点的鲁棒可行性转化为最小包围圆判据\cite{boyd}。 + +在线用外切正多边形表示圆盘，再逐半平面裁剪。 +若边数为 $M$、圆半径为 $r$，外切多边形顶点的半径为 +$r\sec(\pi/M)$，其最大径向超出量准确写为 +\begin{equation} +e_M(r)=r\bigl(\sec(\pi/M)-1\bigr). +\label{eq:outer-error} +\end{equation} +默认 $M=192$。由于整个圆盘已包含在多边形中， +裁剪后得到 $K_1\subseteq P^{\mathrm{out}}$。 +算法求 $P^{\mathrm{out}}$ 的实际最小包围圆 $\B(m,\rho_{\mathrm{out}})$， +不将内接多边形误用作保守候选集。 + +由三角不等式，充分安全盘为 +\begin{equation} +\mathcal Q_{\mathrm{in}} +=\B\!\left(m,R_- -\rho_{\mathrm{out}}-\eta\right),\qquad +\eta=10^{-3}\ {\rm m}. +\label{eq:safe-disk} +\end{equation} +任意 $q\in\mathcal Q_{\mathrm{in}}$ 与真源 $g$ 满足 +$\norm{q-g}\le\norm{q-m}+\norm{m-g}\le R_- -\eta$。 +因此第二次检测一定为 $\direction$ 或 $\near$。 +若盘半径为负，只能说明这个充分构造失效， +不能据此断言真实安全区域为空；程序退回圆心探索，并明确无接收保证。 + +\subsection{首次截断角域的解析候选盘} +为给出不依赖离散多边形的显式答案，暂去掉 $\Omega$，考虑 +$S=W(s,\theta,\delta)\cap\B(s,R_+)$。 +当 $0\le\delta\le45^\circ$，令 +\begin{equation} +a=\frac{R_+}{2\cos\delta},\qquad c=s+a\,u(\theta). +\end{equation} +\begin{proposition}[截断角域最小包围圆] +上述 $S$ 的最小包围圆为 $\B(c,a)$。 +\end{proposition} +\begin{proof} +任取 $g=s+t u(\theta+\varphi)$，其中 $0\le t\le R_+$、 +$|\varphi|\le\delta$。有 +$\norm{g-c}^2=t^2+a^2-2at\cos\varphi$。 +该式关于 $t$ 为凸二次式，最大值在区间端点取得。 +$t=0$ 时为 $a^2$；$t=R_+$ 时不超过 +$R_+^2+a^2-2aR_+\cos\delta=a^2$，故全域被包含。 + +再取边界三点 $s,p_\pm=s+R_+u(\theta\pm\delta)$。 +权重 +$\lambda_\pm=1/(4\cos^2\delta)$、 +$\lambda_0=1-1/(2\cos^2\delta)$ 非负且和为 $1$， +其加权中心为 $c$。三点均距 $c$ 为 $a$， +对任意圆心 $z$，加权平方距离等于 $a^2+\norm{z-c}^2$， +故至少一点距 $z$ 不小于 $a$。任何包含三点的圆半径均不小于 $a$。 +\end{proof} +由于 $K_1\subseteq S$，于是 +\begin{equation} +\boxed{ +q\in\B\!\left(s+\frac{1500}{2\cos\delta}u(\theta), +1000-\frac{1500}{2\cos\delta}\right)} +\label{eq:q2-answer} +\end{equation} +即为题目所求的一种明确候选区域，实际使用时再内缩 $1$ mm。 +它是充分子区域，不等于全部可行区域 $\mathcal Q(K_1)$。 + +\begin{table}[htbp] +\centering\small +\caption{解析安全盘参数，由式~\eqref{eq:q2-answer} 直接计算} +\begin{tabular}{lrr} +\toprule +误差半角 & 中心沿首次方向偏移 $a$/m & 候选盘半径/m\\ +\midrule +$1^\circ$ & 750.114246 & 249.885754\\ +$1.005^\circ$ & 750.115391 & 249.884609\\ +\bottomrule +\end{tabular} +\label{tab:safeanalytic} +\end{table} +在线算法继续使用 $\Omega$ 裁剪后的完整候选形状， +通常能够获得更紧的源包围圆与更大的充分安全盘。 +解析公式负责解释保证为何存在，多边形流程负责利用已有的全部几何约束。 + +\begin{figure}[htbp] +\centering +\begin{tikzpicture}[x=0.006cm,y=0.006cm,font=\small,>=Stealth] + \fill[inkblue!8] (0,0)--(1499.77,-26.18) arc[start angle=-1,end angle=1,radius=1500]--cycle; + \draw[inkblue!45] (750.114,0) circle (750.114); + \filldraw[fill=inkblue!12,draw=inkblue,thick] (750.114,0) circle (249.885); + \draw[thick] (0,0)--(1499.77,26.18); + \draw[thick] (0,0)--(1499.77,-26.18); + \draw[->,dashed] (0,0)--(1650,0) node[right] {$u(\theta)$}; + \fill (0,0) circle (8) node[below left] {$s$}; + \fill[inkblue] (750.114,0) circle (8) node[below] {$c$}; + \draw[->,inkblue] (1010,345)--(890,155); + \node[anchor=west,inkblue] at (990,390) {保证接收候选盘}; + \node at (750,-850) {圆域先验 $\Omega$ 可进一步收紧候选集}; + \node[anchor=east] at (1570,-125) {首次截断角域 $S$}; + \node[inkblue!70] at (750,830) {截断角域的最小包围圆}; +\end{tikzpicture} +\caption{第二点解析候选区域的几何关系，采用 $1^\circ$ 半角、同一坐标比例绘制。} +\label{fig:q2disk} +\end{figure} + +\subsection{定位效果指标与有限候选求解} +理想的鲁棒选点模型为 +\begin{equation} +\min_{q\in\mathcal Q_{\mathrm{in}}} +\left(\sup_{y\in\mathcal Y(q,K_1)}\rho(K_1\cap O(q,y)), +\frac{\norm{q-p}}{5}\right)_{\mathrm{lex}}, +\label{eq:q2minimax} +\end{equation} +其中 $p$ 是当前机器人位置，$y$ 表示可能观测， +$O(q,y)$ 为相应观测可行集，下标表示按字典序比较： +先最小化最坏后验半径，再减少移动耗时。 +方向分支取相应角域，近距离分支取 $\B(q,5)$。 +这比仅优化交会角更直接地对应最终清除需求。 + +连续极小极大问题求解成本较高，当前算法采用有限候选近似。 +在式~\eqref{eq:safe-disk} 的盘心及半径比例 +$0.4,0.75,1.0$ 的三个环上各取 $12$ 个方向， +角度为 $(k+\tfrac12)2\pi/12$，共 $37$ 点。 +对每个候选 $q$，在 $P^{\mathrm{out}}$ 边界以不大于 $60$ m 的间距采样， +包含全部顶点。对见证点 $g$ 枚举读数 +$\operatorname{bearing}(q,g)\pm\delta_{\mathrm{eff}}$， +计算新角域交后的最小包围半径，并另外计算 $\near$ 分支； +取所得最大值作为 $\widehat J(q)$。 + +选取使 $(\widehat J(q),\norm{q-p}/5)$ 最小的点， +然后将边界采样间距加密至 $15$ m 复核其评分。 +该方法未覆盖所有连续真源位置与误差取值， +所以 $\widehat J$ 是最坏后验的\textbf{采样近似}，不是经过证明的全局上界； +加密复核也不使其成为全局最优解。接收保证则由安全盘独立成立。 + +\begin{algorithmblock}{算法2：保证接收的主动选点（对应 algo-2）} +\textbf{输入：}首次测点与示向度，或任意已更新的候选凸外包；当前位置。\\ +\textbf{输出：}下一检测点、采样后验评分及接收保证状态。 +\begin{enumerate}[leftmargin=2em,itemsep=1pt,topsep=4pt] + \item 初次调用时构造式~\eqref{eq:k1} 的外包多边形；后续调用使用已有外包。 + \item 计算最小包围圆和安全盘半径 $b=1000-\rho_{\mathrm{out}}-10^{-3}$。 + \item 若 $b<0$，返回圆心探索并注明无保证；否则生成 $37$ 个安全候选点。 + \item 对每点枚举边界见证与方向端点读数，补入近距离分支，得到 $\widehat J$。 + \item 按后验评分优先、移动时间次优选点，并以 $15$ m 见证间距复核。 + \item 获得新观测后更新候选集；$\near$ 可就地清除， + $\direction$ 则继续检查清除证书，不满足时追加测量。 +\end{enumerate} +\end{algorithmblock} +若候选数为 $N_q$、见证数为 $N_g$、多边形顶点数为 $m$， +一次裁剪为 $O(m)$，总计算量主要为 +$O(N_qN_g(m+C_{\mathrm{MEC}}(m)))$。 +该算法复用问题一的角域语义和最小圆函数， +但在线候选集采用多边形裁剪，不直接调用问题一的纯角域直径求解器。 diff --git a/docs/paper/sections/q3.tex b/docs/paper/sections/q3.tex new file mode 100644 index 0000000..3ec59f2 --- /dev/null +++ b/docs/paper/sections/q3.tex @@ -0,0 +1,205 @@ +\section{问题三：全向多源的覆盖搜索与滚动调度} +\subsection{统一时间目标与任务状态} +设整个会话移动距离为 $L$，检测、换频、成功和失败清除次数分别为 +$N_m,N_s,N_c^+,N_c^-$。忽略每段移动时间的微秒量化时，总虚拟耗时为 +\begin{equation} +T=\frac{L}{5}+5N_m+N_s+5N_c^++3N_c^-. +\label{eq:time} +\end{equation} +优化目标是在全部源清除的约束下最小化 $T$。 +题目统计的平均定位清除时间是 $\bar T=T/N_c^+$； +不能用每次清除动作的固定 $5$ s 代替。 +清除请求中的频道是目标频道，不改变测向机频道； +进入与退出均不增加虚拟时间，因此路径终点自由，无需返回原点。 + +各频道的状态按“未知、已发现、可清除、已清除、已证无源”管理。 +首次获得 $\direction$ 或 $\near$ 即确立该频道存在源。 +几何证书仅决定能否清除，成功响应才将状态改为已清除。 +无源频道必须有覆盖或候选集排空的证据，不能由连续几次无信号直接推断。 + +\subsection{七点覆盖的解析证明} +取站点集合 +\begin{equation} +S(a)=\{(0,0)\}\cup +\left\{a\left(\cos\frac{k\pi}{3},\sin\frac{k\pi}{3}\right):k=0,\ldots,5\right\}. +\label{eq:seven} +\end{equation} +\begin{proposition}[七点全向覆盖] +当 $0] (0,0)--(1159.7,0) node[midway,above] {$a$}; + \draw[->,warmgray] (0,0)--(30:1800) node[midway,above left] {$R$}; + \node[anchor=west,align=left] at (2100,750) + {实线：源位置边界\\虚线：六站所在圆\\浅色圆盘：$1000$ m 接收保证}; + \node[anchor=west,align=left] at (2100,-650) + {$a=1159.7$ m\\$R=1800$ m\\最坏距离 $\le984.539$ m}; +\end{tikzpicture} +\caption{七点全向覆盖构造。图示站点来自配置参数，不表示正式测试的实际轨迹。} +\label{fig:seven} +\end{figure} + +顺次从原点访问六个环站的简单开放路线长为 $6a$， +但实际路线还包含定位与清除偏移，不能将 $6a/5$ 当作任务总耗时。 +历史 $49$ 点方格与半径 $1200$ m 的七点批量策略仍保留在代码中作为对照； +本文不引用它们在自建场景中的性能数字，以保持实验数据来源一致。 + +\subsection{正负观测的双重候选表示} +每个已发现频道维护凸外包 $P_c^{\mathrm{out}}$。 +$\direction$ 将候选集与 $\B(s,1500)$ 外切多边形及测向角域相交； +$\near$ 与 $\B(s,5)$ 外切多边形相交。 +全向源的 $\sgnless$ 意味着 +\begin{equation} +\norm{g-s}>r_{\mathrm{eff}}\ge1000, +\end{equation} +其排除圆盘会使候选集非凸，因此凸表示不直接扣除负观测圆盘， +而由另一套网格幸存集 $\mathcal G_c$ 处理。 + +网格边长为 $\ell=14.65$ m，每格中心与格内点的最大距离为 +$\epsilon_g=\ell/\sqrt2$。初始保留所有可能与 $\Omega$ 相交的格， +按以下充分排除条件更新格心 $z$： +\begin{equation} +\begin{array}{ll} +\sgnless: & \norm{z-s}\le1000-\epsilon_g\ \Rightarrow\ \text{删除};\\ +\near: & \norm{z-s}>5+\epsilon_g\ \Rightarrow\ \text{删除};\\ +\direction: & \norm{z-s}>1500+\epsilon_g\ \Rightarrow\ \text{删除}. +\end{array} +\label{eq:gridupdate} +\end{equation} +方向观测另外检查角差。若 $d=\norm{z-s}>\epsilon_g$， +源所在格引起的方位偏差可由 +$\arcsin(\epsilon_g/d)$ 上界； +实现使用更保守的距离内缩版本，并在测点附近不作方位删格。 +只有角差超过 $\delta_{\mathrm{eff}}$ 加格内角裕量时才删除。 + +在上述整格排除条件下，真源所在格不会被合法观测删除。 +因此幸存集为空可证明该频道不存在源。 +若全部幸存格心均满足 $\norm{z-s}>1500+\epsilon_g$， +则在 $s$ 测量必无信号，且所有幸存格已在最小接收圆盘外， +该观测不能带来进一步排除，可跳过并在账本中记录推断依据。 +这避免了为已知无信息的“站点、频道”对重复支付检测与换频时间。 + +\subsection{信息增益选点与清除证书} +问题二的算法2用于基线定位和安全后备； +默认 \texttt{BayesLoop} 采用幸存网格上的信息评分。 +有安全盘时在其中生成环形候选，并增加与当前接近方向相关的候选； +无安全盘时在网格最小圆附近生成探索环。 +当前位置也可参与评分，因而并非所有候选均具有算法2的接收保证。 +对候选 $q$ 计算 +\begin{equation} +J_{\mathrm{IG}}(q)= +\widehat{\mathbb E}\!\left[ +\log\frac{|\mathcal G_c^{\,\mathrm{post}}(q,Y)|}{|\mathcal G_c|} +\right] +\lambda\left(\frac{\norm{p-q}}5+\frac{\norm{q-m_c}}5\right), +\label{eq:ig} +\end{equation} +其中 $\lambda=0.05$，空分支用正的小值截断。 +较小的对数幸存比例意味着较大信息收益，移动项则限制为测量而产生的绕行。 +评分最多取 $800$ 个子样本及 $7$ 个代表假设， +并以均匀 $r_{\mathrm{eff}}\in[1000,1500]$ 估计接收概率。 +这里的“贝叶斯”体现对假设分支的加权决策，不等同于已知官方先验下的精确后验推断。 + +安全判断使用完整候选集合，而非上述评分样本。 +凸候选集的清除判据为 +\begin{equation} +\rho_c+b_c+0.5\le20, +\label{eq:clearpoly} +\end{equation} +其中 $b_c\ge0$ 为代码的累计附加余量。 +凸多边形本身已外包真源，$\rho_c$ 是该实际多边形的包围半径； +$b_c$ 的具体记账近似不作为外包正确性的必要依据。 +若负观测使网格更紧，也可使用 +\begin{equation} +\rho_{\mathrm{grid}}+\epsilon_g+0.5\le20 +\label{eq:cleargrid} +\end{equation} +的网格证书，其中 $\rho_{\mathrm{grid}}$ 为幸存格心的最小包围半径。 +满足任一证书即可选择清除点。 +若证书尚有余量，可将圆心向当前位置平移 $\Delta$， +只要 $\rho+\Delta$ 不超过证书允许半径，包含关系仍由三角不等式成立。 + +\subsection{开放路径上的滚动任务排序} +统一任务表包含三类任务：覆盖站的批量扫频、已发现源的定位测量、 +已有证书的清除。站内检测优先使用测向机当前频道，减少不必要的第一次换频。 +对任务序列 $\pi$，排序代价为 +\begin{equation} +C(\pi)=\frac{\norm{p-q_{\pi_1}}}{5} ++\sum_{j=1}^{k-1}\frac{\norm{q_{\pi_j}-q_{\pi_{j+1}}}}5 ++\sum_{j=1}^{k}t_{\pi_j}(c_{j-1}), +\label{eq:route} +\end{equation} +其中服务时间 $t_{\pi_j}$ 依赖进入任务时的频道，清除不改变该频道。 +从最近邻初序开始，默认最多进行 $4$ 轮开放路径 2-opt 改进； +每次只执行当前序列的首任务，得到新观测后重新生成和排序。 +这样新发现的源、收缩后的清除点和已证无源的频道都能及时改变路线。 +当前未启用精确任务序动态规划及路线感知探点开关， +因此不将这些可选功能写为默认策略的既有性能来源。 + +已停靠位置可以顺带补测：要求此前未在该位置测过、距离保证成立、 +尚无清除证书，且预测半径有足够收缩。一次机会测量仍支付检测和换频费用， +收益来自避免额外移动。同地测向误差固定，反复原地测量不能当作独立样本平均。 + +\subsection{算法三与完成条件} +\begin{algorithmblock}{算法3：七点覆盖、网格更新与滚动调度（对应 algo-3）} +\textbf{输入：}题设参数、七站计划、合法观测接口。\quad +\textbf{输出：}逐频道处理状态与会话统计。 +\begin{enumerate}[leftmargin=2em,itemsep=1pt,topsep=4pt] + \item 检验七点解析覆盖界，初始化频道状态、覆盖账本和网格幸存集。 + \item 进入后同步记录位置、频道及剩余现实预算，必要时执行有信息的机会测量。 + \item 构建覆盖、定位和清除任务；跳过能够证明无信息的检测。 + \item 按最近邻与开放路径 2-opt 排序，执行首任务，更新候选集和频道状态。 + \item 若出现清除证书，安排清除；清除失败后先补充观测，不直接宣称完成。 + \item 若已清除 $16$ 个源，或每个频道均已清除或有严格无源证据，则退出。 + 否则返回步骤2；预算不足或异常时退出并报告未解决频道。 +\end{enumerate} +\end{algorithmblock} +“清除数达到 $16$”利用题设数量上界； +“发现并清除 $10$ 个”只达到数量下界，不能作为完成证明。 +对任意已存在的 $16$ 个不同频道，也可提前排除其余未知频道， +但已发现而未清除的源仍必须继续处理。 + +覆盖证明保障发现，清除证书保障单次动作的正确性， +两者均不自动保证在有限预算内完成全部定位。 +当前每轮追加有效定位测量上限为 $8$； +停滞、协议异常或预算耗尽时应如实报告未完成。 +程序以接口返回的现实预算为准，并预留退出时间， +实际计时在整数微秒状态上累计，避免用实机运行秒数代替虚拟动作耗时。 diff --git a/docs/paper/sections/q4.tex b/docs/paper/sections/q4.tex new file mode 100644 index 0000000..ce07587 --- /dev/null +++ b/docs/paper/sections/q4.tex @@ -0,0 +1,204 @@ +\section{问题四：混合源的定向覆盖与后备清除} +\subsection{定向观测模型与无信号歧义} +设定向源位于 $g$，朝向为 $\psi$。在检测点 $q$ 可见的充要条件为 +\begin{equation} +\norm{q-g}\le r_{\mathrm{eff}},\qquad +(q-g)\cdot u(\psi)\ge0. +\label{eq:visibility} +\end{equation} +边界属于可见半平面。可见且距离不超过 $5$ m 时返回 $\near$， +否则返回 $\direction$；任何一个条件失败均为 $\sgnless$。 +因此在问题二安全盘内，也只能保证距离足够近，不能保证定向源可见。 +若已知该频道存在源且测点位于严格距离安全盘内，此时的无信号可以判定朝向遮挡。 +离开安全盘后则必须同时保留距离不足的解释。 + +问题三七站全部位于源圆域内部，对于位于边界且向外发射的源， +所有站点可能处于其背向半平面。即使七点圆盘覆盖了位置， +也不满足定向发现要求。适用于混合源的站点集合 $S$ 必须满足 +\begin{equation} +\forall g\in\Omega,\ \forall\psi\in[0,2\pi),\ +\exists s\in S:\quad +\norm{s-g}\le1000,\quad (s-g)\cdot u(\psi)\ge0. +\label{eq:halfcover} +\end{equation} +这是一项针对“位置、朝向”二元状态的全覆盖要求。 + +\subsection{严格连续备选：四角凸组合证明} +取 $S_{49}=\{(700i,700j):i,j=-3,\ldots,3\}$。 +其网格方域包含 $\Omega$，每个源落在某个边长为 $700$ m 的闭方格内。 +\begin{proposition}[方格四角的定向覆盖] +$S_{49}$ 满足式~\eqref{eq:halfcover}，对全向与任意朝向的定向源均保证发现。 +\end{proposition} +\begin{proof} +设包含 $g$ 的方格四角为 $v_1,\ldots,v_4$。 +四角距 $g$ 均不超过对角线长 $700\sqrt2<1000$。 +由于 $g$ 是四角的凸组合，存在 $\lambda_i\ge0$、 +$\sum_i\lambda_i=1$ 使 $\sum_i\lambda_i(v_i-g)=0$。 +对任意朝向 $u$ 取内积，得 +$\sum_i\lambda_i(v_i-g)\cdot u=0$， +故不可能四个角均满足 $(v_i-g)\cdot u<0$； +至少一角处于前向闭半平面，且同时满足距离条件。 +\end{proof} +证明必须同时使用四角的距离界与凸组合性质， +仅说明“最近网格点足够近”不能推出定向覆盖。 +这一方案给出连续空间的严格发现保证，代价是站点较多。 + +\subsection{31点离散集合覆盖计划及其适用范围} +当前 \texttt{directional} 实现采用 \texttt{q4\_mincover\_v2} 计划。 +在离线候选站点 $s_j$ 和离散目标状态 $(g_i,\psi_i)$ 上定义命中矩阵 +\begin{equation} +A_{ij}=\mathbf1\{ +\norm{s_j-g_i}\le r_{\mathrm{design}}, +\ (s_j-g_i)\cdot u(\psi_i)\ge +\norm{s_j-g_i}\sin\gamma_{\mathrm{design}}\}. +\end{equation} +站点筛选可写为集合覆盖模型 +\begin{equation} +\min\sum_j z_j,\qquad +\sum_jA_{ij}z_j\ge1\ \ (\forall i),\qquad z_j\in\{0,1\}. +\label{eq:setcover} +\end{equation} +当前生成器用贪心覆盖及逐点删除求近似解，采用集合覆盖的经典思想\cite{chvatal}， +并没有给出 $31$ 点是全局最少点数的证明。 +设计阶段使用 $965$ m 距离与 $5^\circ$ 前向角余量， +最终按 $15$ m 位置间距、$72$ 个朝向采样复核。 +计划文件记录 $3\,256\,200$ 个离散目标、零未覆盖目标， +最坏命中距离约 $990.051$ m。上述量描述\textbf{离线覆盖校验}， +不属于模拟器实测成绩。 + +\input{figures/q4-plan} + +离散零缺口不能直接提升为式~\eqref{eq:halfcover} 的连续定理。 +例如设任意实际位置距某验证位置不超过 $\varepsilon$， +实际朝向距其采样朝向不超过 $\alpha$，某验证见证站距采样位置为 $d$。 +由三角不等式及单位向量差的界，一组充分条件为 +\begin{equation} +d+\varepsilon\le1000,\qquad +(s-g_i)\cdot u(\psi_i)\ge +\varepsilon+2d\sin(\alpha/2). +\label{eq:continuous} +\end{equation} +还需先保证验证位置网覆盖全部 $\Omega$，包括边界。 +对于 $15$ m 方格的通常位置裕量 $15/\sqrt2$， +$990.051+15/\sqrt2\approx1000.658$ m，已超过距离界； +最终证书的前向角余量又为 $0^\circ$，也未满足统一朝向扰动条件。 +因此本文将 $31$ 点方案表述为经过细网格验证的工程方案， +不赋予无条件连续覆盖保证。需要严格发现保证时可选已实现的 $49$ 点方案； +切换后的时间表现需要独立测试，不能沿用既有正式统计。 + +\subsection{位置与朝向联合候选的保守更新} +对定向假设，在位置网格的每个幸存格中心 $z$ 附加 $H=24$ 个朝向档， +档宽为 $15^\circ$。令 $M_z$ 为仍可能的朝向掩码。 +方向与近距离观测先更新位置约束，再保留可能覆盖检测点的朝向； +无信号时只有在整格处于 $1000$ m 保证接收盘内，才可删除必然可见的朝向。 + +记 $\beta=\operatorname{bearing}(z\to s)$、 +$\Delta_\psi=7.5^\circ$，格内方位余量为 $\alpha_z$， +查表舍入余量为 $\eta_\psi=1.5^\circ$。 +以 $d_\circ$ 表示圆周最小角差，保守保留条件为 +\begin{equation} +\begin{aligned} +\text{正观测：}\quad& +d_\circ(\psi_k,\beta)\le90^\circ+\Delta_\psi+\eta_\psi+\alpha_z,\\ +\text{盘内负观测：}\quad& +d_\circ(\psi_k,\beta)>90^\circ-\Delta_\psi-\eta_\psi-\alpha_z. +\end{aligned} +\label{eq:heading} +\end{equation} +第二行的含义是保留\textbf{可能不可见}的档，排除整档必然可见者， +并不要求保留档内所有方向都不可见。 +若格心距测点过近、格内方位可能任意变化，则不进行此类方向裁剪。 +在定向模型与有效裕量条件下，这一保守更新不删除真源的位置与朝向格。 + +\textbf{混合源的类型边界。} +类型未知时，严格可行集应是 +\begin{equation} +\mathcal H_c=\mathcal H_c^{\mathrm{omni}} +\ \cup\ \mathcal H_c^{\mathrm{dir}}, +\label{eq:typeunion} +\end{equation} +分别表示全向与定向解释。 +全向源可能从其周围多个方向均被接收，而不存在一个固定发射半平面包含全部测点； +定向假设为空不意味着全向假设为空。 +当前代码在首次正观测后即建立定向联合集，并包含以 +\texttt{joint\_empty} 标记无源的分支，没有单独维护式~\eqref{eq:typeunion} 的全向分支。 +因此，类型未知时不能把该分支当作严格缺席证明。 +已获正观测的静止源若尚无清除成功响应，候选矛盾应进入异常处理。 +这一点是实现的待完善边界，不由已有四次正式统计消除。 + +\subsection{可见性筛选与探点选择} +联合候选的用途首先是排序探点。对候选 $q$， +以均匀接收半径假设给出距离权重 +\begin{equation} +w_r(d)= +\begin{cases} +1,&d\le1000,\\ +(1500-d)/500,&1000X#O9KQH000080000jT^_>pe`=or0HB}&07C!(07_wPZDn$EEpusYb!=gD zZ*nbWb!==ebY*jNFL5(3W^ZzBVQejMGc7SKIY?DEEmc=aQY}JIR8lQgSwU1TYHV+3 zl(q#_l+o8digbgN2!hf`!_bn$(9F;SGl0a*5W@^H3>^{@3aEsDgmgDZhorQE5=ux) zC=${kT>O3Ccklmy*S&YGJ8QkO-gC~5XFq%IvtK3vC}(>g7k8X3#@&fqgd64NgTlCbplp3mI4>7>H*Q5qksD2a zjJrM3)(hc`!rK2|N8JCTEc)LPqCS#0Ht;BWtgV~-&AF6>l&pljgcLwRQugM+1Ly95 zLH*YmK;(ZAxVRxve*fhMXOF%tRClQ#ZRYjKH{{-0=SkFi9~BNU`>&`2YY zk`92IKY)X@ql7F<8i4perLp#IE{-TKysekBy_AgXKc`5PEW!~5uvd^nqNET~(sB}# 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`9cf9428` 的程序；最后一次官方第三问演练为 `3BW5-9R54-NZNA-MYB9`， -13/13源成功清除、虚拟总时间4058.709750秒。本轮改进验证使用本地模拟器，没有启动或消耗官方测试。 - -## 1. 题设约束及审查结论 - -附录2(3)中的交会是有宽度的角域交集。不能把两条示向线的交点当作精确真值， -也不能利用同地重测求平均缩小±1°误差。程序已保留完整角域及0.005°舍入裕量， -本轮继续使用该证据颁发清除证书。统计评分仅用于选点，不能替代保守几何证书。 - -附录2(4)要求逐频道检测，换频1秒；结合(5)，每次停靠检测5秒且不能在移动中检测。 -已有HTTP客户端是串行的，没有把20频道视为一次免费测量。缺陷在于规划成本和站点利用： - -| 审核发现 | 影响 | 当前改进 | -| --- | --- | --- | -| 已停靠点只测UNKNOWN频道，已发现频道容易错失交会机会 | 之后为第二条方位线另走一段路 | 对DETECTED频道预测收缩；当前位置到整个候选集均小于1000m、未在此处测过且预测半径减少35%时，逐频道补测；每次仍支付5秒和实际换频成本 | -| 定位选点只计到测点的移动 | 测完后到清除区域的路程没有进入选点目标 | 加入候选检测点→候选源中心的接近代价，保留后续根据真实响应重新规划 | -| 候选方向固定在全局角度网格 | 与当前交会几何不对齐，可能产生多余绕行 | 增加以当前位置到候选中心为轴的对称候选；均仍位于距离保证盘内 | -| 路线代价中的service_s按初始频道一次估计 | 2-opt比较不同顺序时没有正确传递频道状态 | 路径成本逐任务传递频道，站内当前频道优先，clear保持频道；两个任务也比较完整开放路径成本 | -| 清除默认走到候选集包围圆心 | 未利用20米光学定位/清除范围 | 在证书允许范围内向当前位置平移目标；平移距离+原包围半径不超过阈值，保留三角不等式证明 | -| 七站环半径可调但没有执行覆盖校验 | 不合法调参可能把“都没测到”误作不存在 | 构造时检查解析覆盖界；不满足条件直接拒绝运行 | -| 第四问盘外探点无信号也可能记为定向遮挡 | 把接收距离不足误诊为已确认定向 | 仅当实际探点位于距离保证盘内才据无信号确认定向；盘外无信号保留不确定性 | -| 第四问发现一个源就离站定位，后续频道再返回原站 | 同站频道间产生长距离往返 | 保留49站定向覆盖，先逐频道扫完本站，再按当前位置就近处理已发现源 | -| 后备清除按初始位置距离静态排序 | 狭长候选集可能反复折返，且循环内无虚拟预算检查 | 每一步从当前位置选最近未处理格，并逐次检查虚拟预算 | - -第三问所有源均为全向，才能用no_signal排除1000米圆盘。第四问源类型与朝向未知， -no_signal还可能是半平面遮挡，不能用上述排除规则，也不能直接沿用七站缺席证明。 -本轮没有把BayesLoop套到第四问；第四问继续采用49站覆盖和独立的定向定位/后备清除。 -回归用例包含(1800,0)向外发射的源：七站全无信号，49站中有站可检出。 - -七站覆盖界为 `max(r/√3, sqrt(R²+r²−√3Rr))`，前提是`020\,\text{米}. -$$ - -![等边三角形定位区域反例](../output/q1/figures/counterexample-736-light.png) - -图中蓝色为定位区域，红色虚线为直径圆，绿色实线为最小包围圆。黑色加号只在合成场景中表示已知真源。 - -## 七、官方演练数据验证 - -2026年9月10日，界面明确为“问题3 演练 测试”后，通过公开HTTP接口采集。案例编码为 `U5ZW-P9KN-TCAG-R7ST`，选取频道9。 - -| 检测点 | x（米） | y（米） | 示向度 | -| --- | ---: | ---: | ---: | -| $S_1$ | $0$ | $0$ | $131.52^\circ$ | -| $S_2$ | $-613.761885$ | $391.530775$ | $34.92^\circ$ | -| $S_3$ | $-314.272134$ | $656.683353$ | $227.19^\circ$ | - -重复在 $S_1$ 测量一次仍返回 $131.52^\circ$。这次重复观测只用于核查原地误差固定，没有作为新的独立测点加入模型。 - -使用 $\pm 1^\circ$ 得到四边形，其顶点按逆时针顺序为： - -| 顶点 | x（米） | y（米） | -| --- | ---: | ---: | -| V1 | −460.698306 | 502.411776 | -| V2 | −456.424236 | 497.750714 | -| V3 | −440.569893 | 515.476604 | -| V4 | −441.370356 | 516.413163 | - -计算结果：D=23.996723米，最远点对为V1和V3；直径圆中心为(−450.634100,508.944190)，半径11.998362米，但最远顶点到这个圆心的距离为12.602364米，所以该圆不能覆盖区域。最小包围圆中心为(−449.976955,507.952835)，半径12.068583米。 - -![官方演练测向所得定位区域](../output/q1/figures/practice-736-light.png) - -共发送14个被接受的请求：1次进入、12次检测、1次退出，最终虚拟时间293.602198秒。日志末尾为 `/exit`、`accepted=true`、`exit_reason=user_exit`；界面显示测试正常结束。没有调用 `/clear`，所以这里不能将演练结束解读为“清除了所有源”。官方没有公开该源的坐标真值，本例验证的是观测交会计算、接口适配和几何自洽性，不声称验证了真实位置误差。 - -原始请求响应保存在 `output/q1/practice/*_actions.json`，保留了复算所需的请求ID、位置、频道与时间；三点观测及其计算结果保存在 `*_observations.json`。没有读取或解密模拟器隐藏场景数据。 - -## 八、运行方式和代码入口 - -核心算法仅用Python标准库，支持Python3.10及以上；工程依赖仅 `requests`（测试另需 `pytest`）。在项目根目录运行： - -```powershell -uv run python -m mcm26b.geometry examples/q1/triangle.json -o output/q1/triangle_recomputed.json -uv run mcm26b q1 examples/q1/normal.json -uv run python -m mcm26b.geometry examples/q1/normal.json --rounding-margin-deg 0.005 -uv run pytest -uv run python scripts/build_q1_demo.py -uv run python scripts/benchmark_q1.py -``` - -输入JSON的最小格式： - -```json -{ - "measurements": [ - {"x": 0, "y": 0, "bearing_deg": 131.52, "half_angle_deg": 1}, - {"x": -613.7618853216438, "y": 391.53077545248124, "bearing_deg": 34.92}, - {"x": -314.2721344680094, "y": 656.6833525352392, "bearing_deg": 227.19} - ] -} -``` - -省略 `half_angle_deg` 时默认为1。输出包含区域状态、顶点、直径、最远点对、直径圆覆盖判断、反例证据、最小包围圆和清除余量。CLI的 `error_policy` 记录追加裕量与每条观测最终半角；默认追加0，不改变输入口径。`tolerance_m` 是归一化容差换算回米的尺度；核心算法不接收真源坐标，样例中的 `target` 只用于合成数据的可视化与测试。空集和无界区域不输出有限圆及清除证书。 - -| 文件 | 职责 | -| --- | --- | -| `src/mcm26b/geometry/localization.py` | 测向角域、半平面、区域分类、直径和包围圆 | -| `src/mcm26b/geometry/planning.py` | 问题二首次测向的距离保证候选圆盘；独立于问题一模型 | -| `src/mcm26b/geometry/__main__.py`、`src/mcm26b/cli.py` | JSON命令行输入输出 | -| `tests/test_geometry.py` | 解析反例、随机几何、独立裁剪对照与退化测试 | -| `tests/test_practice_replay.py` | 离线复算演练计时与观测结果，不连接模拟器 | -| `tests/test_geometry_certificates.py` | 增量圆与穷举法对照、覆盖证据、清除阈值、舍入选项及首次选点证书 | -| `scripts/benchmark_q1.py` | 局部性能对比与官方演练误差界敏感性复算 | -| `scripts/capture_practice.py` | 在已经启动且已核验的演练中采集少量测向 | -| `scripts/build_q1_demo.py` | 用Python算法生成案例、结果和交互图数据 | -| `scripts/assets/q1.template.html` | 可视化源模板；不另写一套求解算法 | -| `output/q1/question1.html` | 可直接打开的离线交互式模拟，所有数据已内嵌 | - -如需再次采集，先在模拟器明确启动“问题3演练测试”，等待接口就绪，读取案例编码，然后运行： - -```powershell -uv run python scripts/capture_practice.py --robot-id 你的参赛队号 --practice-confirmed --case-code 界面中的演练案例编码 -``` - -接口协议没有返回演练／正式模式的字段，`--practice-confirmed` 是操作者确认已核验界面的显式参数，不能替代界面核查。采集脚本没有启动测试的功能，没有正式模式选项，只会调用 `/enter`、`/measure`、`/exit`。禁止在正式测试会话中运行。 - -## 九、验证范围和数值限制 - -20项自动化测试通过，包括100组随机有界案例、60组与独立矩形裁剪实现的对照、250组增量圆与穷举圆对照、1500个共圆点及重复点/共线点、平移旋转缩放不变性，以及已保存演练日志的逐动作计时复算。新增测试还覆盖清除距离20米临界值、显式舍入选项、首次安全候选圆盘边界和零半径情形。已测试一组有限但直径超过10亿米的近乎平行测向，确认不会因为显示范围而被截断成小区域。 - -本次离线优化报告保存在 `output/q1/optimization_report.json`。同一演练观测的敏感性结果如下，原始记录不改写： - -| 误差半角 | 直径 / 米 | MEC半径 / 米 | 直径圆最大超出 / 米 | 含数值裕量的清除余量 / 米 | -| --- | ---: | ---: | ---: | ---: | -| $1^\circ$（默认题设） | 23.996723 | 12.068583 | 0.604002 | 7.931415 | -| $1.005^\circ$（额外舍入） | 24.119088 | 12.130377 | 0.608486 | 7.869621 | - -在本机60个共圆点的局部基准中，旧MEC枚举中位约306.5毫秒，新算法约0.096毫秒；4点时旧法约0.022毫秒、新法约0.029毫秒，小规模没有提速优势。这些是特定输入的局部实测，不是普遍倍率保证，也不代表网络、全清闭环或官方成绩。三点演练的完整问题一求解中位约0.099毫秒。运行基准脚本可以重新生成当前机器的报告。 - -浮点计算不是精确算术。实现使用归一化位置容差 $10^{-9}$、平行行列式阈值 $10^{-12}$ 和较严格的衰退方向角度容差。极端近乎平行、差异接近机器精度或接近退化的输入可能需要高精度几何谓词；结果接近临界阈值时应做容差敏感性检查，而不把最后若干小数位当作严格证明。正常题设坐标和测向精度下，本次案例远离这些数值极限。 - -交互图数据全部由同一Python求解器生成。已在最小DOM测试环境中检查32个“案例／测点数量／视图”组合，未发现缺失控件或NaN等非法图形坐标；并对360与736像素、明暗两种配色的SVG作静态图形检查。浏览器工具对本地文件URL的访问被策略拦截，因此没有声称完成真实浏览器的HTML/CSS布局验证。离线页面和对话内可视化均已生成；静态PNG可作为直接查看的补充。 - -几何算法参考：[CGAL最小包围圆定义与Welzl增量方法](https://doc.cgal.org/latest/Bounding_volumes/classCGAL_1_1Min__circle__2.html)；[McGill旋转卡壳说明](https://www-cgrl.cs.mcgill.ca/~godfried/research/calipers.html)。本次代码仅用Python标准库，不依赖CGAL。 diff --git a/issue/论文格式/附件3. 全国大学生数学建模竞赛论文格式规范.pdf 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