結果

問題 No.1428 PeRmutation Question
ユーザー lam6er
提出日時 2025-04-16 15:59:39
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 73 ms / 2,000 ms
コード長 2,104 bytes
コンパイル時間 521 ms
コンパイル使用メモリ 82,208 KB
実行使用メモリ 84,480 KB
最終ジャッジ日時 2025-04-16 16:02:02
合計ジャッジ時間 3,194 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff # 

MOD = 10**9 + 7

def main():
    import sys
    input = sys.stdin.read().split()
    idx = 0
    N = int(input[idx])
    idx += 1
    P = list(map(int, input[idx:idx+N]))
    idx += N
    
    # Precompute factorials up to N
    max_n = N
    fact = [1] * (max_n + 1)
    for i in range(2, max_n + 1):
        fact[i] = fact[i-1] * i % MOD
    
    # Compute cycle decomposition
    visited = [False] * (N + 1)
    cycle_counts = {}
    for i in range(1, N+1):
        if not visited[i]:
            current = i
            cycle_length = 0
            while not visited[current]:
                visited[current] = True
                current = P[current - 1]  # P is 0-based in list, but elements are 1-based
                cycle_length += 1
            if cycle_length in cycle_counts:
                cycle_counts[cycle_length] += 1
            else:
                cycle_counts[cycle_length] = 1
    
    # Check if there exists m with (m even and a_m >=1) or (m odd and a_m >=2)
    has_odd_centralizer = False
    for m in cycle_counts:
        a_m = cycle_counts[m]
        if (m % 2 == 0 and a_m >= 1) or (m % 2 == 1 and a_m >= 2):
            has_odd_centralizer = True
            break
    
    if has_odd_centralizer:
        # Compute denominator
        denominator = 1
        for m in cycle_counts:
            a_m = cycle_counts[m]
            denominator = denominator * pow(m, a_m, MOD) % MOD
            denominator = denominator * fact[a_m] % MOD
        size = fact[N] * pow(denominator, MOD-2, MOD) % MOD
        print(size)
    else:
        if N == 1:
            print(1)
        else:
            # Compute denominator
            denominator = 1
            for m in cycle_counts:
                a_m = cycle_counts[m]
                denominator = denominator * pow(m, a_m, MOD) % MOD
                denominator = denominator * fact[a_m] % MOD
            size = fact[N] * pow(denominator, MOD-2, MOD) % MOD
            inv_2 = 500000004  # Modular inverse of 2 mod 1e9+7
            ans = size * inv_2 % MOD
            print(ans)

if __name__ == "__main__":
    main()
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