結果

問題 No.1413 Dynamic Sushi
ユーザー lam6er
提出日時 2025-04-16 16:33:40
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,096 ms / 4,000 ms
コード長 4,933 bytes
コンパイル時間 564 ms
コンパイル使用メモリ 81,892 KB
実行使用メモリ 78,124 KB
最終ジャッジ日時 2025-04-16 16:37:31
合計ジャッジ時間 21,918 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
other AC * 25
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ソースコード

diff # 

import math

def main():
    import sys
    input = sys.stdin.read().split()
    idx = 0
    N = int(input[idx])
    idx += 1
    W = int(input[idx])
    idx += 1

    sushi = []
    for _ in range(N):
        X = int(input[idx])
        Y = int(input[idx+1])
        R = int(input[idx+2])
        V = int(input[idx+3])
        A = int(input[idx+4])
        sushi.append((X, Y, R, V, A))
        idx +=5

    INF = float('inf')
    dp = [[INF] * N for _ in range(1 << N)]

    # Precompute initial times for each sushi
    for i in range(N):
        X, Y, R, V, A = sushi[i]
        low = 0.0
        high = 0.0
        theta = (V * 0 + A) * math.pi / 180
        x = X + R * math.cos(theta)
        y = Y + R * math.sin(theta)
        dist_sq = x**2 + y**2
        if dist_sq <= 0.0:
            T_i = 0.0
        else:
            high = 1.0
            found = False
            for _ in range(100):
                theta_high = (V * high + A) * math.pi / 180
                x_high = X + R * math.cos(theta_high)
                y_high = Y + R * math.sin(theta_high)
                dist_sq_high = x_high**2 + y_high**2
                if dist_sq_high <= (W * high)**2:
                    found = True
                    break
                high *= 2
                if high > 1e20:
                    break
            if not found:
                continue
            for _ in range(100):
                mid = (low + high) / 2
                theta_mid = (V * mid + A) * math.pi / 180
                x_mid = X + R * math.cos(theta_mid)
                y_mid = Y + R * math.sin(theta_mid)
                dist_sq_mid = x_mid**2 + y_mid**2
                if dist_sq_mid <= (W * mid)**2:
                    high = mid
                else:
                    low = mid
            T_i = high
        if T_i < INF:
            mask = 1 << i
            dp[mask][i] = T_i

    # Process all masks
    for mask in range(1 << N):
        for j in range(N):
            if not (mask & (1 << j)) or dp[mask][j] == INF:
                continue
            current_time = dp[mask][j]
            Xj, Yj, Rj, Vj, Aj = sushi[j]
            theta_j = (Vj * current_time + Aj) * math.pi / 180
            xj = Xj + Rj * math.cos(theta_j)
            yj = Yj + Rj * math.sin(theta_j)
            for i in range(N):
                if mask & (1 << i):
                    continue
                Xi, Yi, Ri, Vi, Ai = sushi[i]
                low = current_time
                high = current_time
                theta_i = (Vi * current_time + Ai) * math.pi / 180
                xi = Xi + Ri * math.cos(theta_i)
                yi = Yi + Ri * math.sin(theta_i)
                dx = xj - xi
                dy = yj - yi
                dist_sq = dx**2 + dy**2
                time_diff = current_time - current_time
                if dist_sq <= (W * time_diff)**2:
                    T_i = current_time
                else:
                    high = current_time + 1.0
                    found = False
                    for _ in range(100):
                        t = high
                        theta_i_high = (Vi * t + Ai) * math.pi / 180
                        xi_high = Xi + Ri * math.cos(theta_i_high)
                        yi_high = Yi + Ri * math.sin(theta_i_high)
                        dx_high = xj - xi_high
                        dy_high = yj - yi_high
                        dist_sq_high = dx_high**2 + dy_high**2
                        time_diff_high = t - current_time
                        if dist_sq_high <= (W * time_diff_high)**2:
                            found = True
                            break
                        high *= 2
                        if high > current_time + 1e20:
                            break
                    if not found:
                        continue
                    for _ in range(100):
                        mid = (low + high) / 2
                        theta_i_mid = (Vi * mid + Ai) * math.pi / 180
                        xi_mid = Xi + Ri * math.cos(theta_i_mid)
                        yi_mid = Yi + Ri * math.sin(theta_i_mid)
                        dx_mid = xj - xi_mid
                        dy_mid = yj - yi_mid
                        dist_sq_mid = dx_mid**2 + dy_mid**2
                        time_diff_mid = mid - current_time
                        if dist_sq_mid <= (W * time_diff_mid)**2:
                            high = mid
                        else:
                            low = mid
                    T_i = high
                if T_i < INF:
                    new_mask = mask | (1 << i)
                    if T_i < dp[new_mask][i]:
                        dp[new_mask][i] = T_i

    full_mask = (1 << N) - 1
    min_time = INF
    for j in range(N):
        if dp[full_mask][j] < min_time:
            min_time = dp[full_mask][j]
    print("{0:.11f}".format(min_time))

if __name__ == '__main__':
    main()
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