結果

問題 No.2263 Perms
ユーザー lam6er
提出日時 2025-03-31 17:22:02
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 145 ms / 2,000 ms
コード長 2,521 bytes
コンパイル時間 181 ms
コンパイル使用メモリ 82,432 KB
実行使用メモリ 78,496 KB
最終ジャッジ日時 2025-03-31 17:23:04
合計ジャッジ時間 5,526 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
sample AC * 2
other AC * 39
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 collections import deque

def main():
    input = sys.stdin.read().split()
    ptr = 0
    N = int(input[ptr])
    M = int(input[ptr + 1])
    ptr += 2
    A = []
    for _ in range(N):
        row = list(map(int, input[ptr:ptr + N]))
        ptr += N
        A.append(row)
    
    # Check row sums
    for i in range(N):
        if sum(A[i]) != M:
            print(-1)
            return
    
    # Check column sums
    for j in range(N):
        total = sum(A[i][j] for i in range(N))
        if total != M:
            print(-1)
            return
    
    permutations = []
    for _ in range(M):
        # Build bipartite graph
        graph = [[] for _ in range(N)]
        for i in range(N):
            for j in range(N):
                if A[i][j] > 0:
                    graph[i].append(j)
        
        # Find perfect matching using Hopcroft-Karp
        pair_U = hopcroft_karp(graph, N, N)
        if not all(u != -1 for u in pair_U):
            print(-1)
            return
        
        permutation = [j + 1 for j in pair_U]
        permutations.append(permutation)
        
        # Update A matrix
        for i in range(N):
            j = pair_U[i]
            A[i][j] -= 1
    
    for p in permutations:
        print(' '.join(map(str, p)))

def hopcroft_karp(graph, U_size, V_size):
    pair_U = [-1] * U_size
    pair_V = [-1] * V_size
    dist = [0] * U_size
    
    def bfs():
        queue = deque()
        for u in range(U_size):
            if pair_U[u] == -1:
                dist[u] = 0
                queue.append(u)
            else:
                dist[u] = float('inf')
        dist_null = float('inf')
        while queue:
            u = queue.popleft()
            if dist[u] < dist_null:
                for v in graph[u]:
                    if pair_V[v] == -1:
                        dist_null = dist[u] + 1
                    elif dist[pair_V[v]] == float('inf'):
                        dist[pair_V[v]] = dist[u] + 1
                        queue.append(pair_V[v])
        return dist_null != float('inf')
    
    def dfs(u):
        for v in graph[u]:
            if pair_V[v] == -1 or (dist[pair_V[v]] == dist[u] + 1 and dfs(pair_V[v])):
                pair_U[u] = v
                pair_V[v] = u
                return True
        dist[u] = float('inf')
        return False
    
    while bfs():
        for u in range(U_size):
            if pair_U[u] == -1:
                dfs(u)
    return pair_U

if __name__ == '__main__':
    main()
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