結果

問題 No.2445 奇行列式
ユーザー qwewe
提出日時 2025-04-24 12:22:59
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 2,876 bytes
コンパイル時間 319 ms
コンパイル使用メモリ 82,016 KB
実行使用メモリ 372,448 KB
最終ジャッジ日時 2025-04-24 12:25:08
合計ジャッジ時間 6,825 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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ファイルパターン 結果
other AC * 13 TLE * 1 -- * 6
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 # 

import sys
from itertools import combinations

def compute_permanent(A, N, mod):
    # Precompute masks for each number of set bits
    masks = [[] for _ in range(N+1)]
    for mask in range(1 << N):
        cnt = bin(mask).count('1')
        masks[cnt].append(mask)
    
    dp = [0] * (1 << N)
    dp[0] = 1  # Base case: empty mask
    
    for i in range(N):
        new_dp = [0] * (1 << N)
        current_masks = masks[i]
        for mask in current_masks:
            current_val = dp[mask]
            if current_val == 0:
                continue
            # Iterate over all possible columns j not in mask
            for j in range(N):
                if not (mask & (1 << j)):
                    new_mask = mask | (1 << j)
                    new_dp[new_mask] = (new_dp[new_mask] + current_val * A[i][j]) % mod
        dp = new_dp
    return dp[(1 << N) - 1]

def compute_determinant(A, N, mod):
    # Precompute masks for each number of set bits
    masks = [[] for _ in range(N+1)]
    for mask in range(1 << N):
        cnt = bin(mask).count('1')
        masks[cnt].append(mask)
    
    # dp[mask][parity] where parity is 0 (even) or 1 (odd)
    dp = [[0] * 2 for _ in range(1 << N)]
    dp[0][0] = 1  # Base case: empty mask, even parity
    
    for i in range(N):
        new_dp = [[0] * 2 for _ in range(1 << N)]
        current_masks = masks[i]
        for mask in current_masks:
            for parity in 0, 1:
                current_val = dp[mask][parity]
                if current_val == 0:
                    continue
                # Iterate over all possible columns j not in mask
                for j in range(N):
                    if not (mask & (1 << j)):
                        # Calculate the number of set bits higher than j
                        cnt = (mask >> (j + 1)).bit_count()
                        new_parity = (parity + cnt) % 2
                        new_mask = mask | (1 << j)
                        contribution = (current_val * A[i][j]) % mod
                        new_dp[new_mask][new_parity] = (new_dp[new_mask][new_parity] + contribution) % mod
        dp = new_dp
    
    full_mask = (1 << N) - 1
    determinant = 0
    for parity in 0, 1:
        sign = 1 if parity % 2 == 0 else -1
        term = (sign * dp[full_mask][parity]) % mod
        determinant = (determinant + term) % mod
    return determinant

def main():
    input = sys.stdin.read().split()
    ptr = 0
    N = int(input[ptr])
    ptr += 1
    B = int(input[ptr])
    ptr += 1
    A = []
    for _ in range(N):
        row = list(map(int, input[ptr:ptr+N]))
        ptr += N
        A.append(row)
    
    mod = 2 * B
    permanent = compute_permanent(A, N, mod)
    determinant = compute_determinant(A, N, mod)
    
    diff = (permanent - determinant) % mod
    ans = (diff // 2) % B
    print(ans)

if __name__ == "__main__":
    main()
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