• ㊗️
• 大家
• offer
• 多多！

## Problem

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

A sudoku solution must satisfy all the following rules:

Each of the digits 1-9 must occur exactly once in each row. Each of the digits 1-9 must occur exactly once in each column. Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid. The ‘.’ character indicates empty cells.

Example 1:

Input: 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"]]
Output: [["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"]]
Explanation: The input board is shown above and the only valid solution is shown below:


Constraints:

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit or ‘.’.
• It is guaranteed that the input board has only one solution.

## Code

class Solution {
public void solveSudoku(char[][] board) {
solve(board);
}

private boolean solve(char[][] board){
for(int i = 0; i < 9; i++){
for(int j = 0; j < 9; j++){
if(board[i][j] == '.'){
for(char c = '1'; c <= '9'; c++){
if(isValid(board, i, j, c)){
board[i][j] = c;
if(solve(board)){
return true;
} else {
board[i][j] = '.';
}
}
}
// 试了所有的组合都不行
return false;
}
}
}
// 没有.的位置，也就是有效的解
return true;
}

private boolean isValid(char[][] board, int row, int col, char c){
for(int j = 0; j < 9; j++){
if(col != j && board[row][j] == c) return false;
}

for(int i = 0; i < 9; i++){
if(row != i && board[i][col] == c) return false;
}

int rowIndex = 3 * (row / 3);
int colIndex = 3 * (col / 3);

for(int i = rowIndex; i < rowIndex + 3; i++){
for(int j = colIndex; j < colIndex + 3; j++){
if(i != row && j != col && board[i][j] == c) return false;
}
}
return true;
}
}