"""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,
    }