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2026-09-13 18:43:25 +08:00
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@@ -2,7 +2,6 @@
"cells": [
{
"cell_type": "markdown",
"id": "9f704249",
"metadata": {},
"source": [
"# CUMCM 2026 B 题 · 无线电干扰源的快速自动定位与清除\n",
@@ -43,12 +42,16 @@
"\n",
"各代码单元逐字取自 `src/mcm26b/**`，仅做机械化改写（去包内相对导入、去文件 docstring、\n",
"去掉覆盖计划的 JSON 文件读取改为内嵌字面量、去掉未被生产路径调用的函数）。\n",
"本文件可独立运行：只依赖标准库与 `numpy`（可选加速，缺失时自动回退纯 Python）。\n"
"本文件可独立运行：**零第三方依赖**（`numpy` 仅作可选加速，缺失时自动回退纯 Python；\n",
"`requests` 仅在真正发起 HTTP 时才惰性导入）。最后的总自检单元会复算四问的核心结论，\n",
"15 项断言全部通过才算整理成功。\n",
"\n",
"自检覆盖：问1 角域交会有界/直径圆反例、问2 保证接收与后验收缩、问3 七站解析覆盖证书与\n",
"Voronoi 真源保留、问4 定向最小命中集证书与 (位置×朝向) 联合信念保守性。\n"
]
},
{
"cell_type": "markdown",
"id": "dabe0eb2",
"metadata": {},
"source": [
"## 0. 环境与依赖\n"
@@ -56,18 +59,9 @@
},
{
"cell_type": "code",
"execution_count": 1,
"id": "47afaab3",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"numpy 加速后端: 启用\n"
]
}
],
"outputs": [],
"source": [
"import json\n",
"import math\n",
@@ -92,7 +86,6 @@
},
{
"cell_type": "markdown",
"id": "648b9bca",
"metadata": {},
"source": [
"# 第一部分 · 公共层\n",
@@ -105,8 +98,7 @@
},
{
"cell_type": "code",
"execution_count": 2,
"id": "a77d00d5",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -313,8 +305,7 @@
},
{
"cell_type": "code",
"execution_count": 3,
"id": "18c1702d",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -334,7 +325,6 @@
},
{
"cell_type": "markdown",
"id": "eb41e595",
"metadata": {},
"source": [
"## 2. 协议层（`protocol/`）\n",
@@ -347,8 +337,7 @@
},
{
"cell_type": "code",
"execution_count": 4,
"id": "52874146",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -439,7 +428,6 @@
},
{
"cell_type": "markdown",
"id": "624c4b89",
"metadata": {},
"source": [
"### 2.2 纯计时模型（`timing.py`）\n",
@@ -451,8 +439,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"id": "bb132d37",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -505,7 +492,6 @@
},
{
"cell_type": "markdown",
"id": "0382155e",
"metadata": {},
"source": [
"### 2.3 本地状态机（`state.py`）\n",
@@ -516,8 +502,7 @@
},
{
"cell_type": "code",
"execution_count": 6,
"id": "01f62290",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -603,7 +588,6 @@
},
{
"cell_type": "markdown",
"id": "fdea1f06",
"metadata": {},
"source": [
"### 2.4 传输抽象与会话日志（`transport.py` / `log.py`）\n",
@@ -615,8 +599,7 @@
},
{
"cell_type": "code",
"execution_count": 7,
"id": "75e9e40b",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -655,8 +638,7 @@
},
{
"cell_type": "code",
"execution_count": 8,
"id": "ce38cbf0",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -688,7 +670,6 @@
},
{
"cell_type": "markdown",
"id": "00433092",
"metadata": {},
"source": [
"### 2.5 串行幂等客户端（`client.py`）\n",
@@ -702,8 +683,7 @@
},
{
"cell_type": "code",
"execution_count": 9,
"id": "9b89cf0b",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -1015,7 +995,6 @@
},
{
"cell_type": "markdown",
"id": "1b378ab3",
"metadata": {},
"source": [
"## 3. 几何内核（`geometry/`）\n",
@@ -1035,8 +1014,7 @@
},
{
"cell_type": "code",
"execution_count": 10,
"id": "3b895426",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -1318,7 +1296,6 @@
},
{
"cell_type": "markdown",
"id": "0e26ba66",
"metadata": {},
"source": [
"### 3.2 问题二的安全候选盘证书（`planning.py`）\n",
@@ -1331,8 +1308,7 @@
},
{
"cell_type": "code",
"execution_count": 11,
"id": "96ea4f0f",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -1366,7 +1342,6 @@
},
{
"cell_type": "markdown",
"id": "15dfa096",
"metadata": {},
"source": [
"## 4. 信念层与保证层\n",
@@ -1385,8 +1360,7 @@
},
{
"cell_type": "code",
"execution_count": 12,
"id": "48977ca8",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -1651,7 +1625,6 @@
},
{
"cell_type": "markdown",
"id": "d5ebeb37",
"metadata": {},
"source": [
"### 4.2 逐频道覆盖账本（`coverage/__init__.py`）\n",
@@ -1662,8 +1635,7 @@
},
{
"cell_type": "code",
"execution_count": 13,
"id": "83ef8c99",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -1707,7 +1679,6 @@
},
{
"cell_type": "markdown",
"id": "2797039e",
"metadata": {},
"source": [
"### 4.3 覆盖计划与证书（`guarantee/cover.py`）\n",
@@ -1727,8 +1698,7 @@
},
{
"cell_type": "code",
"execution_count": 14,
"id": "9fe42d17",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -2092,7 +2062,6 @@
},
{
"cell_type": "markdown",
"id": "b6709645",
"metadata": {},
"source": [
"### 4.4 第四问最小命中集（内嵌计划）\n",
@@ -2106,8 +2075,7 @@
},
{
"cell_type": "code",
"execution_count": 15,
"id": "2892e247",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -2177,8 +2145,7 @@
},
{
"cell_type": "code",
"execution_count": 16,
"id": "51d5ac79",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -2275,7 +2242,6 @@
},
{
"cell_type": "markdown",
"id": "5fdc48f7",
"metadata": {},
"source": [
"### 4.5 第三问解析七站计划（`planner/seven.py` 覆盖部分）\n",
@@ -2287,8 +2253,7 @@
},
{
"cell_type": "code",
"execution_count": 17,
"id": "62b4aec6",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -2319,7 +2284,6 @@
},
{
"cell_type": "markdown",
"id": "d0db208e",
"metadata": {},
"source": [
"### 4.6 网格幸存集粒子滤波（`particles.py`）\n",
@@ -2338,8 +2302,7 @@
},
{
"cell_type": "code",
"execution_count": 18,
"id": "63499de6",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -2769,7 +2732,6 @@
},
{
"cell_type": "markdown",
"id": "7cfa64a2",
"metadata": {},
"source": [
"### 4.7 (位置 × 朝向) 联合可行集（`belief/joint.py`）\n",
@@ -2791,8 +2753,7 @@
},
{
"cell_type": "code",
"execution_count": 19,
"id": "3e8eb944",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -3128,7 +3089,6 @@
},
{
"cell_type": "markdown",
"id": "63720d6b",
"metadata": {},
"source": [
"## 5. 调度层：开放路径排序（`routing.py`）\n",
@@ -3140,8 +3100,7 @@
},
{
"cell_type": "code",
"execution_count": 20,
"id": "f2e043c8",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -3218,7 +3177,6 @@
},
{
"cell_type": "markdown",
"id": "9325502c",
"metadata": {},
"source": [
"# 第二部分 · 策略层（`planner/`）\n",
@@ -3234,8 +3192,7 @@
},
{
"cell_type": "code",
"execution_count": 21,
"id": "f4e91fbc",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -3388,7 +3345,6 @@
},
{
"cell_type": "markdown",
"id": "76749d32",
"metadata": {},
"source": [
"### 6.1 全向闭环骨架（`OmnidirectionalLoop`）\n",
@@ -3403,8 +3359,7 @@
},
{
"cell_type": "code",
"execution_count": 22,
"id": "22efcd41",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -3841,7 +3796,6 @@
},
{
"cell_type": "markdown",
"id": "1515ae48",
"metadata": {},
"source": [
"### 6.2 第四问定向扩展（`DirectionalExtension`）\n",
@@ -3857,8 +3811,7 @@
},
{
"cell_type": "code",
"execution_count": 23,
"id": "c2acad85",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -4269,7 +4222,6 @@
},
{
"cell_type": "markdown",
"id": "dfc8e5b3",
"metadata": {},
"source": [
"### 6.3 第三问默认策略：贝叶斯网格滤波闭环（`planner/bayes_loop.py`）\n",
@@ -4289,8 +4241,7 @@
},
{
"cell_type": "code",
"execution_count": 24,
"id": "5934cb40",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -5083,7 +5034,6 @@
},
{
"cell_type": "markdown",
"id": "52d71ea9",
"metadata": {},
"source": [
"### 6.4 第三问对照策略：七站批量扫频（`planner/seven.py`）\n",
@@ -5094,8 +5044,7 @@
},
{
"cell_type": "code",
"execution_count": 25,
"id": "0c911581",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@@ -5145,7 +5094,6 @@
},
{
"cell_type": "markdown",
"id": "d9df020d",
"metadata": {},
"source": [
"# 第三部分 · 逐问算例与自检\n",
@@ -5161,23 +5109,9 @@
},
{
"cell_type": "code",
"execution_count": 26,
"id": "4075e650",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"== 三点交会 ==\n",
"状态 : polygon 顶点数 5\n",
"直径 : 26.986 m\n",
"直径圆覆盖区域 : False 最大超出 3.964 m\n",
"最小包围圆 : 圆心 (81.874, 98.042) 半径 13.943 m\n",
"可原地清除 : True\n"
]
}
],
"outputs": [],
"source": [
"Q1_EXAMPLES = {\n",
" \"normal\": { # 三点交会：区域有界、MEC 远小于 20 m\n",
@@ -5221,29 +5155,9 @@
},
{
"cell_type": "code",
"execution_count": 27,
"id": "efa9f69a",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"== 直径圆反例（等边三角形） ==\n",
"定位区域顶点： [[-0.0, 0.0], [40.0, 0.0], [20.0, 34.64]]\n",
"直径 40.000 m（最远顶点对 [[-0.0, 0.0], [40.0, 0.0]]）\n",
"直径圆：圆心 [20.0, 0.0] 半径 20.000 m\n",
"圆外顶点下标 [2]（见证顶点 [20.0, 34.64]），最大超出 14.641 m\n",
"直径圆覆盖整个定位区域： False\n",
"最小包围圆半径 23.094 m（>= 直径/2 = 20.0 m，才是真正的最小覆盖半径）\n",
"\n",
"== 近共线细长区域 ==\n",
"状态 polygon，直径 3085.3 m，最小包围圆半径 1542.6 m，可原地清除 False\n",
"\n",
"无观测 -> unbounded | 单条示向度 -> unbounded （衰退方向 [0.8971423583981722, 0.44174154068614097]）\n"
]
}
],
"outputs": [],
"source": [
"# 反例：直径圆的圆心是\"最远顶点对\"的中点，第二个最远顶点可能落在圆外。\n",
"tri = solve_q1(\"triangle\")\n",
@@ -5283,20 +5197,9 @@
},
{
"cell_type": "code",
"execution_count": 28,
"id": "6145af53",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"舍入裕量 0.000°：直径 26.986 m，MEC 半径 13.943 m\n",
"舍入裕量 0.005°：直径 27.143 m，MEC 半径 14.019 m\n",
"放宽 0.005° 使 MEC 半径增加 0.076 m —— 因此库默认带该裕量，否则合法真源可能被角域裁掉\n"
]
}
],
"outputs": [],
"source": [
"# 示向度二位小数的舍入敏感性：误差半角 1.0° vs 1.005°（含 0.005° 舍入裕量）\n",
"tight = solve_q1(\"normal\", 0.0)\n",
@@ -5314,7 +5217,6 @@
},
{
"cell_type": "markdown",
"id": "442dbb20",
"metadata": {},
"source": [
"## 8. 问题二：第二检测点的选择\n",
@@ -5329,24 +5231,9 @@
},
{
"cell_type": "code",
"execution_count": 29,
"id": "abebb69d",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"首次角域扇形的包围圆：圆心 (450.1, 600.1) 半径 750.1 m\n",
"保证接收盘 ：圆心 (450.1, 600.1) 半径 249.9 m\n",
"\n",
"第二检测点 ( 691.65, 535.27)\n",
"最坏后验包围半径 91.42 m（当前候选集 MEC 半径 750.1 m，必须更小才叫有信息）\n",
"移动耗时 174.9 s（次指标：同样精度下取更近的点）\n",
"依据： 安全盘 B(centre,250m) 内 37 候选；粗采样最坏后验 91.4m，1/4 间距加密复核 91.4m\n"
]
}
],
"outputs": [],
"source": [
"class _StateStub:\n",
" \"\"\"最小状态替身：只提供选点器需要的当前位置与当前测向频道。\"\"\"\n",
@@ -5399,24 +5286,9 @@
},
{
"cell_type": "code",
"execution_count": 30,
"id": "226d7cca",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"候选集边界采样点 3056 个\n",
"真源到第二点的最远距离 874.58 m（<= 1000 m 才保证收到信号）\n",
"对候选集最坏点、最不利读数的后验包围半径 91.42 m\n",
"第二点相对候选集包围圆的保证接收余量：0.0 m\n",
"追加第 2 个测点 ( 400.97, 23.81)：最坏后验半径 10.37 m\n",
"\n",
"结论：第二点负责\"保证接收 + 最大化交会角\"，后验精度由后续测点继续压缩；20 m 清除圈通常在第三点后达成。\n"
]
}
],
"outputs": [],
"source": [
"# 用同一套观测语义复核这个点：无论真源落在候选集何处，第二点都必收到信号。\n",
"# 候选集边界按 1 m 加密采样做最坏情形检验。\n",
@@ -5454,26 +5326,9 @@
},
{
"cell_type": "code",
"execution_count": 31,
"id": "504f0aa8",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"首次示向度 第二点位置 最坏后验半径 移动耗时\n",
" 0.0° ( 814.85, 241.29) 93.20 m 465.5 s\n",
" 45.0° ( 465.82, 771.76) 90.96 m 422.4 s\n",
" 90.0° ( -241.29, 814.85) 93.20 m 299.9 s\n",
" 135.0° ( -771.76, 465.82) 90.96 m 172.9 s\n",
" 180.0° ( -814.85, 241.29) 93.20 m 145.3 s\n",
" 225.0° ( -771.76, -465.82) 90.96 m 172.9 s\n",
" 270.0° ( -241.29, -814.85) 93.20 m 299.9 s\n",
" 315.0° ( 465.82, -771.76) 90.96 m 422.4 s\n"
]
}
],
"outputs": [],
"source": [
"# 对照：候选集在不同首次示向度下的选择结果（目标函数与移动代价的权衡）\n",
"print(\"首次示向度 第二点位置 最坏后验半径 移动耗时\")\n",
@@ -5486,7 +5341,6 @@
},
{
"cell_type": "markdown",
"id": "b7a898d2",
"metadata": {},
"source": [
"## 9. 问题三：全向源闭环\n",
@@ -5505,20 +5359,9 @@
},
{
"cell_type": "code",
"execution_count": 32,
"id": "8d78f6b8",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"七站环半径 1200.0 m，最近站最远距离解析上界 968.9 m（阈值 1000 m）\n",
"站点： [(0.0, 0.0), (1200.0, 0.0), (600.0, 1039.2), (-600.0, 1039.2), (-1200.0, 0.0), (-600.0, -1039.2), (600.0, -1039.2)]\n",
"粗采样复核：目标点 113 个，未覆盖 0 个，最坏命中 968.9 m，最近邻巡回 7.2 km\n"
]
}
],
"outputs": [],
"source": [
"def observe_omni(truth, station, r_eff, bearing_noise_deg=0.0):\n",
" \"\"\"全向源的观测语义（合成用）：返回 (result, svd_deg)。\"\"\"\n",
@@ -5563,25 +5406,9 @@
},
{
"cell_type": "code",
"execution_count": 33,
"id": "6460920f",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"第 1 次读数 no_signal 幸存格 34035 格心距真源 8.587 m（裕量 10.359 m） MEC 半径 1810.324 m\n",
"第 2 次读数 direction 幸存格 321 格心距真源 8.587 m（裕量 10.359 m） MEC 半径 687.185 m\n",
"第 3 次读数 direction 幸存格 15 格心距真源 8.587 m（裕量 10.359 m） MEC 半径 39.446 m\n",
"第 4 次读数 direction 幸存格 6 格心距真源 8.587 m（裕量 10.359 m） MEC 半径 20.718 m\n",
"\n",
"初始幸存格 47979；真源始终落在某个幸存格内：True\n",
"Voronoi 裕量 m = 10.359 m（格心到格内任一点的最大距离）\n",
"远端测点 (4000.0, 4000.0) 是否必 no_signal：True\n"
]
}
],
"outputs": [],
"source": [
"# ---- 9.2 网格幸存集的真源保留性（Voronoi 裕量定理的随机检验） ----------------\n",
"Random(20260913).seed(20260913)\n",
@@ -5619,24 +5446,9 @@
},
{
"cell_type": "code",
"execution_count": 34,
"id": "d37c4b2c",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"幸存集 MEC：圆心 (306.57, 409.12) 半径 20.718 m\n",
"网格清除证书阈值 9.141 m（= 20 − 裕量 10.359 − 工程余量 0.5）→ 可清除：False\n",
"near 读数后的凸证书：半径 5.001 m ≤ 19.499 m → True\n",
"沿来向偏移后清除点距真源 11.234 m <= 半径 20.718 + 偏移 0.000 = 20.718 m < 20 m\n",
"\n",
"七站全部 no_signal 后幸存格 0 → 该频道判缺席（无需等覆盖账本跑完）\n",
"只测其中 6 站仍有 3339 个幸存格 → 七站是刚好够用的最小解析覆盖\n"
]
}
],
"outputs": [],
"source": [
"# ---- 9.3 证书与缺席证明 -----------------------------------------------------\n",
"center, radius = pf.mec()\n",
@@ -5679,22 +5491,9 @@
},
{
"cell_type": "code",
"execution_count": 35,
"id": "6fc5cf54",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"第三问策略：覆盖计划 seven-r1200.0（7 站），网格间距 14.65 m\n",
"任务表：8 项（站点扫频 7 / 定位 1 / 清除 0）\n",
"排序后前 5 项： [('station', None), ('locate', 9), ('station', None), ('station', None), ('station', None)]\n",
"2-opt 前后路径耗时 2529.66 s -> 2246.77 s\n",
"信息增益选点：( 427.81, 413.89)\n"
]
}
],
"outputs": [],
"source": [
"# ---- 9.4 统一任务表与滚动排序（信息增益选点 + 2-opt） ------------------------\n",
"class _LogStub:\n",
@@ -5705,7 +5504,7 @@
" return []\n",
"\n",
"\n",
"client3 = SimulatorClient(\"2026001\", config=CONFIG_Q3, transport=None, log=_LogStub())\n",
"client3 = SimulatorClient(\"OFFLINE\", config=CONFIG_Q3, transport=None, log=_LogStub())\n",
"client3.state.position = (0.0, 0.0)\n",
"loop3 = BayesLoop(client3, CONFIG_Q3)\n",
"print(\"第三问策略：覆盖计划 %s（%d 站），网格间距 %.2f m\"\n",
@@ -5732,24 +5531,9 @@
},
{
"cell_type": "code",
"execution_count": 36,
"id": "5a06d133",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"第四问覆盖计划 q4_mincover_v2：31 点\n",
"证书采样分辨率 15 m / 72 档，目标 (p,h) 3256200 个，缺口 0，最坏命中 990.051 m\n",
"最近邻巡回 23.9 km（虚拟移动 4776.8 s）→ 发现阶段的移动代价下界\n",
"设计裕量：r_design 965 m、前向角裕量 5.0°；校核用 r_eff 1000 m、角裕量 0.0°\n",
"\n",
"对照 q4_mincover_v1：同样 31 点，但证书采样只有 75 m / 24 档，细网格复检有 125 个缺口\n",
"→ 采样分辨率必须与证书一致，否则'删掉一个关键点仍看似覆盖'（校核退化为装饰）\n"
]
}
],
"outputs": [],
"source": [
"# ---- 9.5 覆盖计划证书：离线全分辨率生成，运行期按同分辨率复核 ----------------------------------\n",
"plan_v2 = plan_instance(\"q4_mincover_v2\", verify=False)\n",
@@ -5774,7 +5558,6 @@
},
{
"cell_type": "markdown",
"id": "7b3fdca8",
"metadata": {},
"source": [
"## 10. 问题四：含定向源的闭环\n",
@@ -5794,19 +5577,9 @@
},
{
"cell_type": "code",
"execution_count": 37,
"id": "96d693ce",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"最小命中集 31 点，粗采样复核 (p,h) 1356 个：未覆盖 0，最坏命中 922.0 m\n",
"对照 700 m 方格 49 点：同样未覆盖 0，巡回 36.4 km vs 23.9 km\n"
]
}
],
"outputs": [],
"source": [
"# ---- 10.1 定向覆盖最小命中集的覆盖语义 --------------------------------------\n",
"plan_q4 = plan_instance(\"q4_mincover_v2\", verify=False)\n",
@@ -5825,26 +5598,9 @@
},
{
"cell_type": "code",
"execution_count": 38,
"id": "c1860693",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"测点方位 115.0° 距离 900 m → direction（预期 direction）幸存格 339 真源格偏移 6.088 m（裕量 10.359 m）朝向档 13 个 含真源朝向档：True\n",
"测点方位 285.0° 距离 700 m → direction（预期 direction）幸存格 63 真源格偏移 6.088 m（裕量 10.359 m）朝向档 2 个 含真源朝向档：True\n",
"测点方位 200.0° 距离 600 m → direction（预期 direction）幸存格 9 真源格偏移 6.088 m（裕量 10.359 m）朝向档 2 个 含真源朝向档：True\n",
"测点方位 230.0° 距离 1050 m → direction（预期 direction）幸存格 9 真源格偏移 6.088 m（裕量 10.359 m）朝向档 2 个 含真源朝向档：True\n",
"测点方位 140.0° 距离 400 m → direction（预期 direction）幸存格 7 真源格偏移 6.088 m（裕量 10.359 m）朝向档 2 个 含真源朝向档：True\n",
"测点方位 330.0° 距离 800 m → no_signal（预期 no_signal）幸存格 7 真源格偏移 6.088 m（裕量 10.359 m）朝向档 2 个 含真源朝向档：True\n",
"测点方位 200.0° 距离 1250 m → no_signal（预期 no_signal）幸存格 7 真源格偏移 6.088 m（裕量 10.359 m）朝向档 2 个 含真源朝向档：True\n",
"\n",
"联合集规模 7 格，抽样平均朝向档 2.00 / 24\n"
]
}
],
"outputs": [],
"source": [
"# ---- 10.2 (位置 × 朝向) 联合可行集的保守性随机检验 --------------------------\n",
"truth4 = (420.0, -260.0) # 真源位置\n",
@@ -5893,27 +5649,9 @@
},
{
"cell_type": "code",
"execution_count": 39,
"id": "19dea4e3",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"探点可见性概率（越高越可能在该点收到信号）：\n",
" ( -2000.0, 0.0) prob_detect = 0.0000\n",
" ( 0.0, 0.0) prob_detect = 0.0833\n",
" ( 420.0, -260.0) prob_detect = 0.0417\n",
" ( 1500.0, -900.0) prob_detect = 0.0000\n",
" ( -331.8, -533.6) prob_detect = 0.0833\n",
"\n",
"候选集外包框 820 m × 820 m，20 m 网格覆盖 171 格（外包框枚举上界 1936）\n",
"格内任意点到最近格心 <= 14.14 m < 20 m → 逐格 /clear 至少命中一次\n",
"外包框内落在候选集中的随机点，被某个格心 20 m 覆盖：96 个\n"
]
}
],
"outputs": [],
"source": [
"# ---- 10.3 可见性选点取代固定阶梯；后备清除兜底 ------------------------------\n",
"print(\"探点可见性概率（越高越可能在该点收到信号）：\")\n",
@@ -5952,26 +5690,12 @@
},
{
"cell_type": "code",
"execution_count": 40,
"id": "9a7b1181",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"第四问策略：覆盖计划 q4_mincover_v2（31 点），联合信念开关 True，探点口径 nearest_visible\n",
"后备清除硬顶 400 格，单轮遮挡探点预算 4 次，定位步数上限 8\n",
"\n",
"频道 3 候选集半径 750.1 m，可清除：False\n",
"保证接收盘半径 249.9 m（盘内必收到信号 -> 静默即遮挡）\n",
"被遮挡后梯子升级到的探点：( 71.58, -134.29)\n"
]
}
],
"outputs": [],
"source": [
"# ---- 10.4 第四问闭环装配（不连模拟器：只检查策略对象初始化） ----------------\n",
"client4 = SimulatorClient(\"2026001\", config=CONFIG, transport=None, log=_LogStub())\n",
"client4 = SimulatorClient(\"OFFLINE\", config=CONFIG, transport=None, log=_LogStub())\n",
"client4.state.position = (0.0, 0.0)\n",
"loop4 = DirectionalExtension(client4, CONFIG)\n",
"print(\"第四问策略：覆盖计划 %s（%d 点），联合信念开关 %s，探点口径 %s\"\n",
@@ -5998,7 +5722,6 @@
},
{
"cell_type": "markdown",
"id": "18a6a561",
"metadata": {},
"source": [
"# 第四部分 · 总览与自检\n",
@@ -6036,8 +5759,8 @@
"\n",
"```bash\n",
"# 对接官方模拟器（演练/正式）\n",
"python -m mcm26b.run --robot-id <队号> --problem 3 # 第三问：bayes 闭环\n",
"python -m mcm26b.run --robot-id <队号> --problem 4 # 第四问：directional 闭环\n",
"python -m mcm26b.cli run --robot-id <队号> --problem 3 # 第三问：bayes 闭环\n",
"python -m mcm26b.cli run --robot-id <队号> --problem 4 # 第四问：directional 闭环\n",
"```\n",
"\n",
"成绩口径是**虚拟时间**：`avg_locate_clear_time_s = 全程虚拟时长 / 已清除源数`，\n",
@@ -6046,35 +5769,9 @@
},
{
"cell_type": "code",
"execution_count": 41,
"id": "25656b6b",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"四问核心自检：\n",
" [通过] 问1 角域交会有界且直径有限\n",
" [通过] 问1 三点交会可原地清除（MEC ≤ 20 m）\n",
" [通过] 问1 直径圆反例被识别（covers=False）\n",
" [通过] 问2 第二点在保证接收盘内\n",
" [通过] 问2 追加三点后最坏后验半径 ≤ 20 m\n",
" [通过] 问3 七站解析覆盖上界 < 1000 m\n",
" [通过] 问3 七站计划粗采样无缺口\n",
" [通过] 问3 粒子滤波保留真源\n",
" [通过] 问3 空幸存集给出缺席证明\n",
" [通过] 问3 2-opt 不劣于原任务序\n",
" [通过] 问4 最小命中集 31 点、证书 0 缺口\n",
" [通过] 问4 粗采样复核定向覆盖无缺口\n",
" [通过] 问4 联合信念保留真源朝向档\n",
" [通过] 问4 后备清除格数在硬顶内\n",
" [通过] 问4 闭环装配成功（定向覆盖计划已加载）\n",
"\n",
"全部 15 项通过。\n"
]
}
],
"outputs": [],
"source": [
"# ---- 总自检：把四问的核心结论再跑一遍，全部通过才算整理成功 ----------------\n",
"checks = []\n",
@@ -6121,21 +5818,21 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"name": "python",
"version": "3.10",
"mimetype": "text/x-python",
"file_extension": ".py",
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.9"
}
}
},
"nbformat": 4,