## Valid Sudoku

### 描述

Determine if a Sudoku is valid, according to: Sudoku Puzzles - The Rules .

The Sudoku board could be partially filled, where empty cells are filled with the character `'.'`.

![Valid Sudoku](../../images/sudoku.png)

### 分析

### 代码

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

{% if book.cpp %}
```cpp
// Valid Sudoku
// 时间复杂度O(n^2)，空间复杂度O(1)
class Solution {
public:
bool isValidSudoku(const vector>& board) {
bool used[9];

for (int i = 0; i < 9; ++i) {
fill(used, used + 9, false);

for (int j = 0; j < 9; ++j) // 检查行
if (!check(board[i][j], used))
return false;

fill(used, used + 9, false);

for (int j = 0; j < 9; ++j) // 检查列
if (!check(board[j][i], used))
return false;
}

for (int r = 0; r < 3; ++r) // 检查 9 个子格子
for (int c = 0; c < 3; ++c) {
fill(used, used + 9, false);

for (int i = r * 3; i < r * 3 + 3; ++i)
for (int j = c * 3; j < c * 3 + 3; ++j)
if (!check(board[i][j], used))
return false;
}

return true;
}

bool check(char ch, bool used[9]) {
if (ch == '.') return true;

if (used[ch - '1']) return false;

return used[ch - '1'] = true;
}
};
```
{% endif %}

### 相关题目

* [Sudoku Solver](sudoku-solver.md)