baseline

project/q1/optimal.py

@@ -0,0 +1,59 @@
+"""问题一最优实现：复用生产几何内核 ``mcm26b.geometry.localization.solve``。
+
+算法（已由 ``tests/test_geometry.py`` / ``tests/test_geometry_certificates.py``
+固化，本模块只做输入输出适配，不重写）：
+
+1. 每条带 ±δ 误差的示向度写成前向角域的三条半平面约束（含 0°/360° 跨界）；
+2. 枚举全部边界直线交点，保留满足全部约束者，单调链求凸包；
+3. 检查是否存在非零衰退方向判定无界；否则枚举凸包顶点对取精确直径；
+4. 用直径两端点中点圆检验覆盖，并给出圆外顶点、最大超出距离等反例见证；
+5. Welzl 增量法求最小包围圆，给出 20 m 清除余量证书。
+"""
+
+from __future__ import annotations
+
+from time import perf_counter
+
+from mcm26b.geometry.localization import Measurement, solve
+
+from project.common import Method
+
+METHOD = Method(
+    key="optimal",
+    name="精确半平面交 + 顶点对直径 + MEC",
+    kind="optimal",
+    note="生产内核 mcm26b.geometry.localization.solve",
+)
+
+
+def solve_case(case: dict) -> dict:
+    """输入 case["measurements"]，输出归一化结果。"""
+    measurements = [Measurement(row["x"], row["y"], row["bearing_deg"],
+                                row.get("half_angle_deg", 1.0))
+                    for row in case["measurements"]]
+    start = perf_counter()
+    result = solve(measurements)
+    elapsed_ms = (perf_counter() - start) * 1000.0
+    return normalize(result, elapsed_ms)
+
+
+def normalize(result: dict, elapsed_ms: float) -> dict:
+    status = result["status"]
+    diameter = result.get("diameter_m")
+    circle = result.get("diameter_circle") or {}
+    mec = result.get("minimum_enclosing_circle") or {}
+    covers = circle.get("covers") if status in ("point", "segment", "polygon") else None
+    return {
+        "method": METHOD.key,
+        "status": status,
+        "diameter_m": diameter,
+        "diameter_infinite": result.get("diameter_infinite"),
+        "covers": covers,
+        "mec_radius_m": mec.get("radius_m"),
+        "max_excess_m": circle.get("max_excess_m"),
+        "outside_vertex_count": len(circle.get("outside_vertex_indices", []))
+        if circle else None,
+        "vertex_count": len(result.get("vertices", [])),
+        "runtime_ms": round(elapsed_ms, 4),
+        "algorithm": METHOD.name,
+    }