結果

問題 No.155 生放送とBGM
ユーザー lam6er
提出日時 2025-04-16 00:16:26
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 2,066 bytes
コンパイル時間 261 ms
コンパイル使用メモリ 81,900 KB
実行使用メモリ 275,680 KB
最終ジャッジ日時 2025-04-16 00:18:13
合計ジャッジ時間 14,695 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
other TLE * 1 -- * 14
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ソースコード

diff # 

import sys

def main():
    from math import factorial

    N, L = map(int, sys.stdin.readline().split())
    L_seconds = L * 60
    S_list = []
    total_S = 0
    for s in sys.stdin.readline().split():
        mm, ss = map(int, s.split(':'))
        total = mm * 60 + ss
        S_list.append(total)
        total_S += total

    K = L_seconds // total_S if total_S != 0 else 0
    R = L_seconds % total_S if total_S != 0 else L_seconds

    if K >= 1:
        print(N)
        return

    # Precompute combinations using Pascal's triangle
    max_n = N - 1
    comb = [[0] * (max_n + 1) for _ in range(max_n + 1)]
    for i in range(max_n + 1):
        comb[i][0] = 1
        for j in range(1, i + 1):
            comb[i][j] = comb[i - 1][j - 1] + comb[i - 1][j]

    expected = 0.0

    for idx in range(N):
        s_i = S_list[idx]
        other_s = S_list[:idx] + S_list[idx + 1:]
        n = len(other_s)
        if n == 0:
            # Only this song, check if R >=1
            expected += 1.0 if s_i >= 1 else 0.0
            continue

        # DP to compute C(m): number of ways to choose m songs with sum < R
        R_current = R
        dp = [ [0] * (R_current) for _ in range(n + 1) ]
        dp[0][0] = 1
        for s in other_s:
            for m in range(n - 1, -1, -1):
                for t in range(R_current):
                    if dp[m][t]:
                        nt = t + s
                        if nt < R_current:
                            dp[m + 1][nt] += dp[m][t]

        # Compute C(m)
        C = [0] * (n + 1)
        for m in range(n + 1):
            C[m] = sum(dp[m][t] for t in range(R_current))

        # Calculate sum(C[m] / comb(n, m)) for m from 0 to n
        total = 0.0
        for m in range(n + 1):
            if comb[n][m] == 0:
                continue
            if C[m] == 0:
                continue
            total += C[m] / comb[n][m]

        # Probability for this song
        prob = total / N
        expected += prob

    print("{0:.10f}".format(expected))

if __name__ == '__main__':
    main()
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