## Sudoku Solver

### 描述

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.

![A sudoku puzzle...](../images/sudoku.png)

![...and its solution numbers marked in red](../images/sudoku-solution.png)

### 分析

### 代码

{% if book.java %}
{% codesnippet "./code/sudoku-solver."+book.suffix, language=book.suffix %}{% endcodesnippet %}
{% endif %}

{% if book.cpp %}
```cpp
// Sudoku Solver
// 时间复杂度O(9^4)，空间复杂度O(1)
class Solution {
public:
void solveSudoku(vector > &board) {
_solveSudoku(board);
}
private:
bool _solveSudoku(vector > &board) {
for (int i = 0; i < 9; ++i)
for (int j = 0; j < 9; ++j) {
if (board[i][j] == '.') {
for (int k = 0; k < 9; ++k) {
board[i][j] = '1' + k;
if (isValid(board, i, j) && _solveSudoku(board))
return true;
board[i][j] = '.';
}
return false;
}
}
return true;
}
// 检查 (x, y) 是否合法
bool isValid(const vector > &board, int x, int y) {
int i, j;
for (i = 0; i < 9; i++) // 检查 y 列
if (i != x && board[i][y] == board[x][y])
return false;
for (j = 0; j < 9; j++) // 检查 x 行
if (j != y && board[x][j] == board[x][y])
return false;
for (i = 3 * (x / 3); i < 3 * (x / 3 + 1); i++)
for (j = 3 * (y / 3); j < 3 * (y / 3 + 1); j++)
if ((i != x || j != y) && board[i][j] == board[x][y])
return false;
return true;
}
};
```
{% endif %}

### 相关题目

* [Valid Sudoku](valid-sudoku.md)