結果

問題 No.1392 Don't be together
ユーザー lam6er
提出日時 2025-03-20 20:31:28
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 927 ms / 2,000 ms
コード長 2,139 bytes
コンパイル時間 185 ms
コンパイル使用メモリ 82,568 KB
実行使用メモリ 70,624 KB
最終ジャッジ日時 2025-03-20 20:32:38
合計ジャッジ時間 4,390 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 27
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 #
プレゼンテーションモードにする

MOD = 998244353
def main():
    import sys
    sys.setrecursionlimit(1 << 25)
    N, M = map(int, sys.stdin.readline().split())
    P = list(map(int, sys.stdin.readline().split()))
    P = [p-1 for p in P]  # 0-based index
    
    # Cycle decomposition
    visited = [False] * N
    cycles = []
    for i in range(N):
        if not visited[i]:
            current = i
            cycle = []
            while not visited[current]:
                visited[current] = True
                cycle.append(current)
                current = P[current]
            cycles.append(cycle)
    
    # Check each cycle's min required colors
    max_min_color = 0
    for cycle in cycles:
        n = len(cycle)
        min_color = 2 if n % 2 == 0 else 3
        if min_color > max_min_color:
            max_min_color = min_color
    if M < max_min_color:
        print(0)
        return
    
    # Precompute factorial and inverse factorial modulo MOD
    max_n = M
    fact = [1] * (max_n + 1)
    for i in range(1, max_n + 1):
        fact[i] = fact[i-1] * i % MOD
    inv_fact = [1] * (max_n + 1)
    inv_fact[max_n] = pow(fact[max_n], MOD-2, MOD)
    for i in range(max_n-1, -1, -1):
        inv_fact[i] = inv_fact[i+1] * (i+1) % MOD
    
    def comb(n, k):
        if k < 0 or k > n:
            return 0
        return fact[n] * inv_fact[k] % MOD * inv_fact[n - k] % MOD
    
    # Calculate correct_color
    correct_color = 0
    for k in range(0, M+1):
        product = 1
        for cycle in cycles:
            n = len(cycle)
            min_color = 2 if n % 2 == 0 else 3
            if k < min_color:
                product = 0
                break
            term1 = pow(k-1, n, MOD)
            term2 = pow(-1, n, MOD) * (k-1) % MOD
            term = (term1 + term2) % MOD
            product = product * term % MOD
        c = comb(M, k)
        sign = pow(-1, M - k, MOD)
        correct_color = (correct_color + sign * c * product) % MOD
    
    # Compute answer as correct_color / M! mod MOD
    inv_m_fact = inv_fact[M]
    ans = correct_color * inv_m_fact % MOD
    print(ans)
    
if __name__ == "__main__":
    main()
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