0037：解数独（★★）

Ian

2015-02-06 约 714 字预计阅读 2 分钟次阅读

力扣第 37 题

题目

编写一个程序，通过填充空格来解决数独问题。

数独的解法需 遵循如下规则：

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）

数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1：

输入：board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
输出：[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
解释：输入的数独如上图所示，唯一有效的解决方案如下所示：

提示：

board.length == 9
board[i].length == 9
board[i][j] 是一位数字或者 '.'
题目数据保证输入数独仅有一个解

相似问题：

分析

回溯法的典型应用。可以直接遍历空格位置，节省时间。

解答

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class Solution:
    def solveSudoku(self, board: List[List[str]]) -> None:
        """
        Do not return anything, modify board in-place instead.
        """
        R,C,B = ([[0]*10 for _ in range(9)] for _ in range(3))
        A = []
        for i in range(9):
            for j in range(9):
                k = i//3*3+j//3
                if board[i][j]=='.':
                    A.append((i,j,k))
                else:
                    x = int(board[i][j])
                    R[i][x]=C[j][x]=B[k][x]=1

        def dfs(w):
            if w==len(A):
                return True
            i,j,k = A[w]
            for x in range(1,10):
                if R[i][x]==C[j][x]==B[k][x]==0:
                    board[i][j]=str(x)
                    R[i][x]=C[j][x]=B[k][x]=1
                    if dfs(w+1):
                        return True
                    R[i][x]=C[j][x]=B[k][x]=0
            return False
        dfs(0)

77 ms

目录

0037：解数独（★★）

题目

分析

解答