Sudoku Solver

问题：给定一个9*9的二维数组，数组元素为1~9的字符串，“.”代表该位置为空，将“.”替换为1~9的字符串，使数组中的数据满足数独的规则

示例：

解决思路：先进行一次9*9的遍历，统计已有的数据，再进行遍历，如果该位置为空，则循环 使用1~9中的字符串进行填充，递归的填充后面的空位，如果某个位置不能正确填充，说明前面的填充有误，则前面的填充需要重新选择 

Python代码：

class Solution(object):
    def solveSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: None Do not return anything, modify board in-place instead.
        """
        row = {i:{str(j):0 for j in range(1,10)} for i in range(9)}
        col = {i:{str(j):0 for j in range(1,10)} for i in range(9)}
        part = {m:{j:{str(i):0 for i in range(1,10)} for j in range(3)} for m in range(3)}
        for i in range(9):
            for j in range(9):
                ele = board[i][j]
                if ele != ".":
                    row[i][ele] += 1
                    col[j][ele] += 1
                    part[i//3][j//3][ele] += 1                    
        self.solve(board,row,col,part)
        
    def solve(self,board,row,col,part,start_row=0):
        for i in range(start_row,9):
            for j in range(9):
                if board[i][j] == ".":       
                    for m in "123456789":
                        if row[i][m] + col[j][m] + part[i//3][j//3][m] == 0:
                            board[i][j] = m
                            row[i][m] += 1
                            col[j][m] += 1
                            part[i//3][j//3][m] += 1
                            if self.solve(board,row,col,part,i):
                                return True
                            board[i][j] = "."
                            row[i][m] -= 1
                            col[j][m] -= 1
                            part[i//3][j//3][m] -= 1
                    return False
        return True