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解数独

1、程序简介

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：

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 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）

注：数独部分空格内已填入了数字，空白格用 ‘.’ 表示。

示例：

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

2、程序代码

# -*- coding: utf-8 -*-
"""
Created on Fri Dec  3 15:33:29 2021
Function:
@author: 小梁aixj
"""
class Solution(object):def solveSudoku(self, board):def isvaild(i,j):for m in range(9):if m!=i and board[m][j]==board[i][j]:return Falsefor n in range(9):if n!=j and board[i][n]==board[i][j]:return Falsefor m in range(i//3*3,i//3*3+3):for n in range(j//3*3,j//3*3+3):if m!=i and n!=j and board[m][n]==board[i][j]:return Falsereturn Truedef f(a,b,board):for i in range(a,9):for j in range(b,9):if board[i][j]=='.':for c in '123456789':board[i][j]=cif isvaild(i,j):if f(a,b,board):return Trueelse: board[i][j]='.'else: board[i][j]='.'return Falsereturn Truef(0,0,board)return board
#%%
s=Solution()
board=[['5','3','.','.','7','.','.','.','.'],['6','.','.','1','9','5','.','.','.'],['.','9','8','.','.','.','.','.','.'],['8','.','.','.','6','.','.','.','3'],['4','.','.','8','.','3','.','.','1'],['7','.','.','.','2','.','.','.','6'],['.','6','.','.','.','.','2','8','.'],['.','.','.','4','1','9','.','.','5'],['.','.','.','.','8','.','.','7','9']]print('按原样输出：')
print(s.solveSudoku(board))
print('格式化输出：')
#格式化输出
a=s.solveSudoku(board)
for x in range(9):for y in range(9):print(a[x][y], end="  ")print()

3、运行结果

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