Leetcode——37.解数独 [##]

---

@author: ZZQ
@software: PyCharm
@file: leetcode37_solveSudoku.py
@time: 2018/11/20 16:41
思路:递归回溯
首先，设置空矩阵bool_col，bool_row和bool_rect分别用于记录每一行，每一列，每个小方块里面已经被填进去的数字
然后，用回溯填空，如果填写的数组满足要求，则返回True，否则返回False. 直至便利完整个数组board。

import numpy


class Solution():
    def __init__(self):
        pass

    def solveSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: void Do not return anything, modify board in-place instead.
        """
        # 记录每一行，每一列，每个小方块里面已经被填进去的数字
        bool_col = numpy.zeros(shape=(9, 9))  # [[0] * 9] * 9
        bool_row = numpy.zeros(shape=(9, 9))
        bool_rect = numpy.zeros(shape=(9, 9))
        for i in range(9):
            for j in range(9):
                if board[i][j] != '.':
                    bool_col[i][ord(board[i][j])-ord('0')-1] = 1
                    bool_row[j][ord(board[i][j])-ord('0')-1] = 1
                    bool_rect[i/3*3+j/3][ord(board[i][j])-ord('0')-1] = 1

        self.dfs(board, bool_col, bool_row, bool_rect, 0, 0)
        return board

    # 回溯
    def dfs(self, board, bool_col, bool_row, bool_rect, i, j):
        while board[i][j] != '.':   # 找空位置
            j += 1
            if j >= 9:
                i += 1
                j = 0
            if i >= 9:
                return True
        for number in range(1, 10):
            if bool_col[i][number-1] != 1 and bool_row[j][number-1] != 1 and bool_rect[i/3*3+j/3][number-1] != 1:
                board[i][j] = str(number)
                bool_col[i][number-1] = 1
                bool_row[j][number-1] = 1
                bool_rect[i / 3 * 3 + j / 3][number-1] = 1
                if self.dfs(board, bool_col, bool_row, bool_rect, i, j):
                    return True
                else:  # 回溯，当前值不行，继续换下一个值进行尝试
                    board[i][j] = '.'
                    bool_col[i][number-1] = 0
                    bool_row[j][number-1] = 0
                    bool_rect[i / 3 * 3 + j / 3][number-1] = 0
        return False


if __name__ == "__main__":
    answer = Solution()
    for i in answer.solveSudoku([
        ["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"]
    ]):
       print(i)