"""问题二算例：随机首次示向度（全向源）。"""

from __future__ import annotations

import math
import random

from mcm26b.config import ProblemConfig


def random_case(seed: int, config: ProblemConfig | None = None) -> dict:
    """随机检测点 s 与示向度 θ：默认让真源与读数一致（误差 ±1° 内）。"""
    config = config or ProblemConfig()
    rng = random.Random(seed)
    radius = config.field.omega_radius_m
    # 检测点可在目标域内或域外；这里取域内，符合题目常规场景
    angle_s = rng.uniform(0, 2 * math.pi)
    distance_s = radius * math.sqrt(rng.random()) * 0.9
    station = (distance_s * math.cos(angle_s), distance_s * math.sin(angle_s))
    # 真源与检测点距离落在 [60, 1500) 且仍在 Ω 内
    while True:
        bearing_true = rng.uniform(0, 2 * math.pi)
        source_distance = rng.uniform(60, config.field.r_eff_max_m - 1)
        target = (station[0] + source_distance * math.cos(bearing_true),
                  station[1] + source_distance * math.sin(bearing_true))
        if math.hypot(*target) <= radius:
            break
    error = math.radians(rng.uniform(-0.95, 0.95))
    bearing_deg = math.degrees(bearing_true + error) % 360.0
    return {"id": f"q2-{seed}", "station": [round(station[0], 2), round(station[1], 2)],
            "bearing_deg": round(bearing_deg, 2), "half_angle_deg": 1.0,
            "true_source": [round(target[0], 2), round(target[1], 2)]}


def random_cases(count: int, base_seed: int = 4200,
                 config: ProblemConfig | None = None) -> list[dict]:
    return [random_case(base_seed + index, config) for index in range(count)]