当前位置： 面试刷题>> 有效的数独(经典算法150题)
### 题目描述
**有效的数独**
编写一个函数来判断一个9x9的数独是否有效。只需要根据以下规则进行判断：
1. 数独板上的数字1-9在每一行只能出现一次。
2. 数独板上的数字1-9在每一列只能出现一次。
3. 数独板上的数字1-9在每一个3x3的子矩阵（也称“宫”或“块”）中只能出现一次。
**注意**：一个空数独板是有效的。
### 示例
**示例 1**:
```
输入:
[
["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: true
```
**示例 2**:
```
输入:
[
["8","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: false
解释: 第二行的第一个数字与第一行的第一个数字相同，因此无效。
```
### PHP 示例代码
```php
function isValidSudoku($board) {
$rows = array_fill(0, 9, array_fill(0, 9, false));
$cols = array_fill(0, 9, array_fill(0, 9, false));
$boxes = array_fill(0, 9, array_fill(0, 9, false));
for ($i = 0; $i < 9; $i++) {
for ($j = 0; $j < 9; $j++) {
$num = $board[$i][$j];
if ($num == '.') continue;
$num = intval($num) - 1;
$boxIndex = floor($i / 3) * 3 + floor($j / 3);
if ($rows[$i][$num] || $cols[$j][$num] || $boxes[$boxIndex][$num]) {
return false;
}
$rows[$i][$num] = true;
$cols[$j][$num] = true;
$boxes[$boxIndex][$num] = true;
}
}
return true;
}
```
### Python 示例代码
```python
def isValidSudoku(board):
rows = [set() for _ in range(9)]
cols = [set() for _ in range(9)]
boxes = [set() for _ in range(9)]
for i in range(9):
for j in range(9):
num = board[i][j]
if num == '.':
continue
num = int(num) - 1
box_index = (i // 3) * 3 + (j // 3)
if num in rows[i] or num in cols[j] or num in boxes[box_index]:
return False
rows[i].add(num)
cols[j].add(num)
boxes[box_index].add(num)
return True
```
### JavaScript 示例代码
```javascript
function isValidSudoku(board) {
const rows = new Array(9).fill(0).map(() => new Set());
const cols = new Array(9).fill(0).map(() => new Set());
const boxes = new Array(9).fill(0).map(() => new Set());
for (let i = 0; i < 9; i++) {
for (let j = 0; j < 9; j++) {
const num = board[i][j];
if (num === '.') continue;
const numInt = parseInt(num) - 1;
const boxIndex = Math.floor(i / 3) * 3 + Math.floor(j / 3);
if (rows[i].has(numInt) || cols[j].has(numInt) || boxes[boxIndex].has(numInt)) {
return false;
}
rows[i].add(numInt);
cols[j].add(numInt);
boxes[boxIndex].add(numInt);
}
}
return true;
}
```
以上代码示例均实现了对9x9数独有效性的判断，符合题目要求。