有效的数独

题目

请你判断一个 9 x 9 的数独是否有效。只需要 根据以下规则 ，验证已经填入的数字是否有效即可。

• 数字 1-9 在每一行只能出现一次。
• 数字 1-9 在每一列只能出现一次。
• 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）

注意：

一个有效的数独（部分已被填充）不一定是可解的。 只需要根据以上规则，验证已经填入的数字是否有效即可。 空白格用 '.' 表示。

示例 1：

输入：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"]]
输出：true

示例 2：

输入：board =
[["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：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字（1-9）或者 '.'

题解

解题思路

新建三个二维数组，分别用于标记 第i行是否有当前数字，第j列是否有当前数字，第n个九宫格是否有当前数字，如果这三者相互冲突，说明不是有效的数独，返回 false。

/**
 * 有效的数独
 * @param {character[][]} board
 * @return {boolean}
 */
export default function(board: string[][]): boolean {
  const lineNumber: boolean[][] = [[],[],[],[],[],[],[],[],[]]
  const colNumber: boolean[][] = [[],[],[],[],[],[],[],[],[]]
  const blockNumber: boolean[][] = [[],[],[],[],[],[],[],[],[]]
  for (let i = 0; i < board.length; i++) {
    for (let j = 0; j < board[i].length; j++) {
      if (board[i][j] === '.') continue
      // 计算是第几个九宫格
      const n = Math.floor(i / 3) * 3 + Math.floor(j / 3)
      // 当前格子的数字
      const number = Number(board[i][j])
      if (lineNumber[i][number] || colNumber[j][number] || blockNumber[n][number]) return false
      lineNumber[i][number] = colNumber[j][number] = blockNumber[n][number] = true
    }
  }
  return true
}