結果

問題 No.283 スライドパズルと魔方陣
ユーザー gew1fw
提出日時 2025-06-12 16:59:12
言語 PyPy3
(7.3.15)
結果
WA  
実行時間 -
コード長 2,635 bytes
コンパイル時間 382 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 66,816 KB
最終ジャッジ日時 2025-06-12 16:59:21
合計ジャッジ時間 6,975 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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ファイルパターン 結果
other AC * 6 WA * 33
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ソースコード

diff # 

def generate_magic_square_odd(n):
    magic = [[0 for _ in range(n)] for _ in range(n)]
    i, j = 0, n // 2
    num = 1
    while num <= n * n:
        magic[i][j] = num
        num += 1
        ni, nj = i - 1, j + 1
        if ni < 0:
            ni = n - 1
        if nj >= n:
            nj = 0
        if magic[ni][nj] != 0:
            ni, nj = i + 1, j
        i, j = ni, nj
    return magic

def generate_magic_square_4():
    return [
        [16, 3, 2, 13],
        [5, 10, 11, 8],
        [9, 6, 7, 12],
        [4, 15, 14, 1]
    ]

def is_magic_square(grid):
    n = len(grid)
    magic_sum = n * (n**2 + 1) // 2
    for row in grid:
        if sum(row) != magic_sum:
            return False
    for j in range(n):
        col_sum = 0
        for i in range(n):
            col_sum += grid[i][j]
        if col_sum != magic_sum:
            return False
    diag1 = sum(grid[i][i] for i in range(n))
    diag2 = sum(grid[i][n - 1 - i] for i in range(n))
    if diag1 != magic_sum or diag2 != magic_sum:
        return False
    return True

def main():
    import sys
    input = sys.stdin.read().split()
    idx = 0
    N = int(input[idx])
    idx +=1
    grid = []
    for _ in range(N):
        row = list(map(int, input[idx:idx+N]))
        grid.append(row)
        idx += N
    
    if N == 2:
        print("impossible")
        return
    
    if N % 2 == 1:
        B = generate_magic_square_odd(N)
    elif N == 4:
        B = generate_magic_square_4()
    else:
        print("impossible")
        return
    
    A = [row[:] for row in grid]
    for i in range(N):
        for j in range(N):
            if A[i][j] == 0:
                A[i][j] = N * N
    
    if is_magic_square(A):
        print("possible")
        for row in A:
            print(' '.join(map(str, row)))
        return
    
    flat_A = [num for row in A for num in row]
    flat_B = [num for row in B for num in row]
    
    value_to_index = {val: idx for idx, val in enumerate(flat_A)}
    P = [value_to_index[val] for val in flat_B]
    
    inversions = 0
    n = len(P)
    for i in range(n):
        for j in range(i + 1, n):
            if P[i] > P[j]:
                inversions += 1
    
    blank_i, blank_j = -1, -1
    for i in range(N):
        for j in range(N):
            if grid[i][j] == 0:
                blank_i, blank_j = i, j
                break
        if blank_i != -1:
            break
    
    if (inversions + (N - 1 - blank_i)) % 2 == 0:
        print("possible")
        for row in B:
            print(' '.join(map(str, row)))
    else:
        print("impossible")

if __name__ == "__main__":
    main()
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