当前位置： 面试刷题>> 判断数独是否合法 (经典算法题500道)
### 题目描述补充
题目：**判断数独是否合法**
给定一个9x9的二维数组表示的数独棋盘，数组中的每个元素是一个字符（'1'-'9'表示数字，'.'表示空位）。请编写一个函数来判断这个数独是否合法。数独合法的条件是：
1. 每行必须恰好包含数字1-9各一次。
2. 每列必须恰好包含数字1-9各一次。
3. 9个3x3的子方格（也称“宫”）必须各自恰好包含数字1-9各一次。
### 示例代码
#### PHP 示例
```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);
$boxIndex = floor($i / 3) * 3 + floor($j / 3);
if ($rows[$i][$num - 1] || $cols[$j][$num - 1] || $boxes[$boxIndex][$num - 1]) {
return false;
}
$rows[$i][$num - 1] = true;
$cols[$j][$num - 1] = true;
$boxes[$boxIndex][$num - 1] = true;
}
}
return true;
}
// 示例用法
$board = [
["5","3",".",".","7",".",".",".","."],
["6",".",".","1","9","5",".",".","."],
[".","9","8",".",".",".",".","6","."],
["8",".",".",".","6",".",".",".","3"],
["4",".",".","8",".","3",".",".","1"],
["7",".",".",".","2",".",".",".","6"],
[".","6",".",".",".",".","2","8","."],
[".",".",".","4","1","9",".",".","5"],
[".",".",".",".","8",".",".","7","9"]
];
echo isValidSudoku($board) ? "数独合法" : "数独不合法";
```
#### Python 示例
```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)
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
# 示例用法
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"]
]
print("数独合法" if isValidSudoku(board) else "数独不合法")
```
#### JavaScript 示例
```javascript
function isValidSudoku(board) {
const rows = Array.from({ length: 9 }, () => new Set());
const cols = Array.from({ length: 9 }, () => new Set());
const boxes = Array.from({ length: 9 }, () => 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, 10);
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;
}
// 示例用法
const 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"]
];
console.log(isValidSudoku(board) ? "数独合法" : "数独不合法");
```
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