[LeetCode]题解（python）：037-Sudoku Solver

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题目来源

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https://leetcode.com/problems/sudoku-solver/

Write a program to solve a Sudoku puzzle by filling the empty cells.

Empty cells are indicated by the character '.'.

You may assume that there will be only one unique solution.

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题意分析

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Input:a unsolved Sudoku

Output: a solved Sudoku

Conditions:满足数独条件，只需要找到一个答案

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题目思路

用dfs的思路，对每一个空进行1-9的选择，如果不满足则回溯；满足条件为isValid（），就是满足该行，该列以及该小九方格没有使用过两个一样的元素（即数字）

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AC代码（Python）

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class Solution(object):
    def solveSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: void Do not return anything, modify board in-place instead.
        """
        def isValid(x, y):
            temp = board[x][y]
            board[x][y] = 'r'
            for i in range(9):
                if board[i][y] == temp:
                    return False
            for i in range(9):
                if board[x][i] == temp:
                    return False
            for i in range(3):
                for j in range(3):
                    if board[x / 3 * 3 + i][y / 3 * 3 + j] == temp:
                        return False
            board[x][y] = temp
            return True

        def dfs(board):
            for i in range(9):
                for j in range(9):
                    if board[i][j] == '.':
                        for k in '123456789':
                            board[i][j] = k
                            if isValid(i,j) and dfs(board):
                                return True
                            board[i][j] = '.'
                        return False
            return True
            
        dfs(board)