"""问题二基线实现：两个朴素但常见的对照。

- ``candidate_perp``：沿首次示向度垂直方向、距检测点约 1000 m 取点。
  这是"尽量把交会角做成 90°"的教科书启发式，**但它忽略接收距离保证**：
  真源可能落在首次角域的远端（≤1500 m），此时第二点距离可超过 1000 m，
  第二次测量直接 ``no_signal``，几何收益落空。
- ``candidate_mec``：退到候选集最小包围圆圆心。它确实落在保证接收盘内
  （ρ≤1000 时），但交会角可能接近 0°、后验几乎不收缩，代表"最保守"一端。
"""

from __future__ import annotations

import math

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

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

PERP = Method(
    key="baseline_perp",
    name="垂直 1000 m 最大交会角",
    kind="baseline",
    note="忽略接收保证的几何启发式",
)
MEC = Method(
    key="baseline_mec",
    name="候选集 MEC 圆心",
    kind="baseline",
    note="保证接收但交会角最差的保守基线",
)
METHODS = (PERP, MEC)


def _region(case: dict, config: ProblemConfig):
    return first_bearing_region(case, config)


def candidate_perp(case: dict, config: ProblemConfig | None = None) -> dict:
    config = config or problem_config()
    region = _region(case, config)
    station = (case["station"][0], case["station"][1])
    theta = math.radians(case["bearing_deg"] + 90.0)
    distance = config.field.r_eff_min_m
    position = (station[0] + distance * math.cos(theta),
                station[1] + distance * math.sin(theta))
    return {
        "method": PERP.key,
        "position": [round(position[0], 4), round(position[1], 4)],
        "worst_posterior_radius_m": None,   # 由 compare 统一评估
        "move_cost_s": None,
        "safe_disk_radius_m": safe_disk_radius(region, config),
        "initial_radius_m": region.mec()[1],
        "reason": "沿首次示向度法向 1000 m 取 90° 交会点",
    }


def candidate_mec(case: dict, config: ProblemConfig | None = None) -> dict:
    config = config or problem_config()
    region = _region(case, config)
    center, radius = region.mec()
    return {
        "method": MEC.key,
        "position": [round(center[0], 4), round(center[1], 4)],
        "worst_posterior_radius_m": None,
        "move_cost_s": None,
        "safe_disk_radius_m": safe_disk_radius(region, config),
        "initial_radius_m": radius,
        "reason": "取候选集最小包围圆圆心，保证接收但交会角可能最差",
    }