baseline

project/q1/baseline.py

@@ -0,0 +1,98 @@
+"""问题一基线实现：网格采样 + 轴对齐包围盒（bbox）代理。
+
+这是"先上手"的朴素做法，常见于直接对可行点打网格再读包围盒：
+
+1. 在固定大框上按步长采样，保留满足全部角域约束的点；
+2. 直径用包围盒对角线代理 —— 只要区域是斜的/细长的就会系统性高估；
+3. 覆盖判断用"包围盒中心 + 代理直径"的圆 —— 因为包围盒自身对其中心对称，
+   该判据几乎恒为"能覆盖"，从而丢掉问题一真正要考的反例。
+
+本实现刻意保留这些结构性缺陷，作为``optimal.py``的对照；它不读取最优实现的
+任何中间量，两条代码路径完全独立。
+"""
+
+from __future__ import annotations
+
+import math
+from time import perf_counter
+
+import numpy as np
+
+from mcm26b.geometry.localization import Measurement, halfplanes
+
+from project.common import Method
+
+METHOD = Method(
+    key="baseline",
+    name="网格采样 + bbox 对角线代理",
+    kind="baseline",
+    note="轴对齐包围盒近似直径与覆盖，O(盒面积/步长²)，与参考解同分辨率",
+)
+
+BOX_M = 2600.0
+STEP_M = 5.0
+
+
+def solve_case(case: dict) -> dict:
+    start = perf_counter()
+    measurements = [Measurement(row["x"], row["y"], row["bearing_deg"],
+                                row.get("half_angle_deg", 1.0))
+                    for row in case["measurements"]]
+    planes = [plane for m in measurements for plane in halfplanes(m)]
+
+    xs = np.arange(-BOX_M, BOX_M + STEP_M, STEP_M)
+    grid_x, grid_y = np.meshgrid(xs, xs)          # 行=y，列=x
+    mask = np.ones(grid_x.shape, dtype=bool)
+    for a, b, c in planes:
+        mask &= (a * grid_x + b * grid_y <= c)
+
+    result = _evaluate(mask, xs)
+    result["method"] = METHOD.key
+    result["runtime_ms"] = round((perf_counter() - start) * 1000.0, 4)
+    result["algorithm"] = METHOD.name
+    return result
+
+
+def _evaluate(mask: np.ndarray, axis: np.ndarray) -> dict:
+    if not mask.any():
+        return _empty("empty")
+    # 可行点触到采样框边界 => 区域至少延伸到框外，判无界
+    if (mask[0, :].any() or mask[-1, :].any()
+            or mask[:, 0].any() or mask[:, -1].any()):
+        return _empty("unbounded")
+
+    rows, cols = np.nonzero(mask)
+    x_min, x_max = axis[cols].min(), axis[cols].max()
+    y_min, y_max = axis[rows].min(), axis[rows].max()
+    width, height = x_max - x_min, y_max - y_min
+    diameter = math.hypot(width, height)          # 包围盒对角线代理
+    center = ((x_min + x_max) / 2.0, (y_min + y_max) / 2.0)
+    px = axis[cols]
+    py = axis[rows]
+    max_distance = float(np.max(np.hypot(px - center[0], py - center[1])))
+    return {
+        "status": "polygon" if mask.sum() >= 2 else "point",
+        "diameter_m": diameter,
+        "diameter_infinite": False,
+        "covers": bool(max_distance <= diameter / 2.0 + 1e-9),
+        "mec_radius_m": None,
+        "max_excess_m": round(max_distance - diameter / 2.0, 6),
+        "outside_vertex_count": None,
+        "vertex_count": int(mask.sum()),
+        "bbox_width_m": round(width, 3),
+        "bbox_height_m": round(height, 3),
+        "runtime_ms": None,
+    }
+
+
+def _empty(status: str) -> dict:
+    return {
+        "status": status,
+        "diameter_m": None,
+        "diameter_infinite": status == "unbounded",
+        "covers": None,
+        "mec_radius_m": None,
+        "max_excess_m": None,
+        "outside_vertex_count": None,
+        "vertex_count": 0,
+    }