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

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

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

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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