"""第四问覆盖证书与最小命中集搜索（CLI；核心实现见 mcm26b.guarantee.cover）。 第四问的定向源在"读点位于源的前向半平面内"时才可能被检出，因此 "某频道在所有被访点都 no_signal ⟹ 该频道不存在源"的缺席证明，等价于要求 被访点集合 S 满足 ∀ p ∈ Ω, ∀ h ∈ [0,360): ∃ c ∈ S, |c − p| ≤ r_eff_min(1000) 且 (c − p)·u(h) ≥ 0 （题面规定朝向覆盖"两侧各 90 度，含边界"，故取 ≥ 0）。现役 49 点方格的 "单元对角 ≤ 1000"是**充分**条件但远非必要；本脚本用贪心击中集求等价覆盖的 更小点集，并输出可复现证书。 uv run python scripts/verify_q4_cover.py # 校核 + 搜索 + 打印 uv run python scripts/verify_q4_cover.py --spacing 200 --write-plan q4_mincover_v1 uv run python scripts/verify_q4_cover.py --check-json my_points.json """ from __future__ import annotations import argparse import hashlib import json from pathlib import Path from mcm26b.config import ProblemConfig from mcm26b.guarantee import (CERTIFY_HEADINGS, CERTIFY_STEP_M, R_EFF_MIN_M, CoverageCertificate, CoveragePlan, candidate_lattice, coverage_masks, forward_targets, greedy_cover, omega_positions, plan_names, square_49_plan, verify_full_disk, verify_forward_half_disk, verify_plan, write_plan) ROOT = Path(__file__).resolve().parents[1] DEFAULT_PLAN_DIR = ROOT / "src/mcm26b/guarantee/plans" def _report(points, kind: str, step_m: float, headings: int, r_eff: float = R_EFF_MIN_M, heading_margin_deg: float = 0.0) -> dict: """按覆盖语义校核点集，返回证书字典。""" if kind == "forward_half_disk": certificate = verify_forward_half_disk(points, step_m, headings, r_eff=r_eff, heading_margin_deg=heading_margin_deg) else: certificate = verify_full_disk(points, step_m, r_eff) return certificate.as_dict() def prune_redundant(masks: list[int], chosen: list[int]) -> list[int]: """贪心结果冗余剪枝：删掉任何"其余点已完全覆盖其目标"的点。""" full = 0 for index in chosen: full |= masks[index] pruned = list(chosen) changed = True while changed: changed = False for index in list(pruned): rest = 0 for other in pruned: if other != index: rest |= masks[other] if rest == full: pruned.remove(index) changed = True return pruned def fine_prune(points, step_m: float, headings: int, r_eff: float, heading_margin_deg: float): """证书分辨率上的冗余剪枝：删掉任何点后校核仍 0 缺口才真删。 粗网格（搜索用）上的冗余判据偏保守，会在证书分辨率下留下可删的点； 本步每个候选删除都用**证书同一口径**复核，因此不削弱证书。 """ points = list(points) improved = True while improved: improved = False for index in range(len(points)): trial = points[:index] + points[index + 1:] certificate = verify_forward_half_disk( trial, step_m, headings, r_eff=r_eff, heading_margin_deg=heading_margin_deg) if certificate.uncovered == 0: points = trial improved = True print(f" 精细剪枝：删点后仍 0 缺口，剩 {len(points)} 点", flush=True) break return points def main() -> int: parser = argparse.ArgumentParser(description=__doc__.splitlines()[0]) parser.add_argument("--spacing", type=float, default=200.0, help="贪心候选点网格间距（米）") parser.add_argument("--radius", type=float, default=2850.0, help="候选点所在圆盘半径（米）") parser.add_argument("--target-step", type=float, default=CERTIFY_STEP_M, help="搜索用采样位置步长（米）") parser.add_argument("--headings", type=int, default=CERTIFY_HEADINGS, help="搜索用采样朝向档数") parser.add_argument("--verify-step", type=float, default=None, help="证书校核位置步长（默认等于 --target-step）") parser.add_argument("--verify-headings", type=int, default=None, help="证书校核朝向档数（默认等于 --headings）") parser.add_argument("--design-radius", type=float, default=None, help="搜索时的设计距离（默认 1000；<1000 即留裕量）") parser.add_argument("--heading-margin", type=float, default=0.0, help="搜索时的前向角裕量（度）") parser.add_argument("--verify-radius", type=float, default=None, help="证书校核距离（默认 1000；<1000 即留裕量）") parser.add_argument("--verify-heading-margin", type=float, default=0.0, help="证书校核前向角裕量（度）；应 ≥ 180/verify_headings/2") parser.add_argument("--no-prune", action="store_true", help="关闭冗余剪枝") parser.add_argument("--fine-prune", action="store_true", help="在证书分辨率上再做一轮冗余剪枝（删点后仍 0 缺口才删）") parser.add_argument("--coverage", choices=("forward_half_disk", "full_disk"), default="forward_half_disk", help="覆盖语义") parser.add_argument("--check-json", type=Path, default=None, help="只校核给定点集（[[x,y],...] 或 {\"points\":[...]}）") parser.add_argument("--write-plan", default=None, help="把贪心最小集写成覆盖计划（名称，落 src/mcm26b/guarantee/plans/）") parser.add_argument("--out", type=Path, default=None, help="证书 JSON 输出路径") args = parser.parse_args() verify_step = (args.verify_step if args.verify_step is not None else args.target_step) verify_headings = (args.verify_headings if args.verify_headings is not None else args.headings) design_radius = (args.design_radius if args.design_radius is not None else R_EFF_MIN_M) verify_radius = (args.verify_radius if args.verify_radius is not None else R_EFF_MIN_M) if args.check_json is not None: payload = json.loads(args.check_json.read_text(encoding="utf-8")) raw = payload.get("points") if isinstance(payload, dict) else payload points = [tuple(map(float, p)) for p in raw] report = _report(points, args.coverage, verify_step, verify_headings, verify_radius, args.verify_heading_margin) print(json.dumps(report, ensure_ascii=False, indent=2)) return 0 if report["uncovered"] == 0 else 1 shipped = square_49_plan() shipped_report = _report(shipped.points, "forward_half_disk", verify_step, verify_headings, verify_radius, args.verify_heading_margin) print(f"目标空间：{shipped_report['targets']} 个 (p,h)" f"（校核位置步长 {verify_step} m，朝向 {verify_headings} 档，" f"r_verify={verify_radius:.0f} m，角裕量 " f"{args.verify_heading_margin}°）") print(f"现役 {shipped.name}：{len(shipped.points)} 点，" f"缺口 {shipped_report['uncovered']}，" f"NN 巡回 {shipped_report['nn_tour_m'] / 1000:.1f} km" f"（{shipped_report['nn_tour_virtual_s']:.0f} s 移动）", flush=True) targets = forward_targets(args.target_step, args.headings) candidates = candidate_lattice(args.spacing, args.radius) print(f"候选点 {len(candidates)}（{args.spacing} m 网格，半径 {args.radius} m）；" f"设计裕量 r_design={design_radius:.0f} m，前向角裕量 " f"{args.heading_margin}°", flush=True) masks = coverage_masks(targets, candidates, r_eff=design_radius, heading_margin_deg=args.heading_margin) chosen = greedy_cover(masks, len(targets)) if not args.no_prune: chosen = prune_redundant(masks, chosen) best_points = [candidates[i] for i in chosen] if args.fine_prune: best_points = fine_prune(best_points, verify_step, verify_headings, verify_radius, args.verify_heading_margin) best_report = _report(best_points, "forward_half_disk", verify_step, verify_headings, verify_radius, args.verify_heading_margin) print(f"设计裕量最小命中集：{len(best_points)} 点，缺口 {best_report['uncovered']}，" f"NN 巡回 {best_report['nn_tour_m'] / 1000:.1f} km" f"（{best_report['nn_tour_virtual_s']:.0f} s 移动）", flush=True) if best_report["uncovered"] != 0: print("贪心结果未通过证书校核，拒绝生成计划。") return 1 generator = {"script": "scripts/verify_q4_cover.py", "spacing_m": args.spacing, "radius_m": args.radius, "target_step_m": args.target_step, "headings": args.headings, "design_r_eff_m": design_radius, "heading_margin_deg": args.heading_margin, "pruned": not args.no_prune, "verify_step_m": verify_step, "verify_headings": verify_headings, "verify_r_eff_m": verify_radius, "verify_heading_margin_deg": args.verify_heading_margin, "code_sha256": hashlib.sha256( Path(__file__).read_bytes()).hexdigest()} certificate = CoverageCertificate( kind=best_report["kind"], target_step_m=verify_step, headings=verify_headings, r_eff_min_m=verify_radius, targets=best_report["targets"], uncovered=best_report["uncovered"], worst_hit_distance_m=best_report["worst_hit_distance_m"], nn_tour_m=best_report["nn_tour_m"], generator_sha256=generator["code_sha256"], verify_heading_margin_deg=args.verify_heading_margin) plan = CoveragePlan( name=args.write_plan or "q4_mincover_draft", problem=4, kind="certified", coverage="forward_half_disk", note=(f"设计裕量最小命中集：{len(best_points)} 点，" f"r_design={design_radius:.0f} m / 前向角裕量 {args.heading_margin}°；" f"证书按 {verify_step:.0f} m/{verify_headings} 档、r_verify=" f"{verify_radius:.0f} m、角裕量 {args.verify_heading_margin}° " f"校核缺口 0（同一证书口径复核，含精细剪枝）；最坏命中 " f"{best_report['worst_hit_distance_m']:.0f} m，" f"NN 巡回 {best_report['nn_tour_m'] / 1000:.1f} km"), generator=generator, certificate=certificate, points=tuple(best_points)) payload = {"model": {"r_omega_m": 1800.0, "r_eff_min_m": 1000.0}, "design": {"r_design_m": design_radius, "heading_margin_deg": args.heading_margin}, "verify": {"r_eff_m": verify_radius, "heading_margin_deg": args.verify_heading_margin, "step_m": verify_step, "headings": verify_headings}, "shipped": shipped_report, "mincover": best_report} if args.out is not None: out = args.out if args.out.is_absolute() else ROOT / args.out out.parent.mkdir(parents=True, exist_ok=True) out.write_text(json.dumps(payload, ensure_ascii=False, indent=2) + "\n", encoding="utf-8") print(f"证书已写入 {out}") if args.write_plan: target = DEFAULT_PLAN_DIR / f"{args.write_plan}.json" write_plan(plan, target) verified = verify_plan(plan) print(f"计划已写入 {target}；运行期分辨率复核缺口 {verified.uncovered}") print("已注册计划：" + "，".join(plan_names())) _ = (ProblemConfig(), omega_positions) # 保持公开入口可发现性 return 0 if __name__ == "__main__": raise SystemExit(main())