"""问题二最优实现：保证接收盘内的最坏后验半径最小化选点（生产实现）。

复用 ``mcm26b.planner.select_measurement_point``：

1. 在"保证接收盘" B(mec_center, 1000-ρ) 内环形采样候选点；
2. 对每个候选，用"目标边界点 × 读数区间端点（+near 分支）"估计
   最坏后验最小包围半径，并以移动时间同分决胜；
3. 选定后按 1/4 间距加密复核，返回位置、后验半径与理由。

采样是启发式（不是连续问题全局最优证明），但保证接收是严格的。
"""

from __future__ import annotations

from mcm26b.config import ProblemConfig
from mcm26b.planner import safe_disk_radius, select_measurement_point

from project.common import Method, problem_config
from project.q2.region import first_bearing_region

METHOD = Method(
    key="optimal",
    name="保证接收盘内最小最坏后验半径",
    kind="optimal",
    note="生产实现 mcm26b.planner.select_measurement_point",
)


def candidate(case: dict, config: ProblemConfig | None = None) -> dict:
    config = config or problem_config()
    region = first_bearing_region(case, config)
    station = (case["station"][0], case["station"][1])
    plan = select_measurement_point(region, station, config)
    return {
        "method": METHOD.key,
        "position": [round(plan.position[0], 4), round(plan.position[1], 4)],
        "worst_posterior_radius_m": plan.worst_posterior_radius_m,
        "move_cost_s": plan.move_cost_s,
        "safe_disk_radius_m": safe_disk_radius(region, config),
        "initial_radius_m": region.mec()[1],
        "reason": plan.reason,
    }