Leetcode36. 有效的数独

原创已于 2022-06-29 18:49:10 修改 · 164 阅读

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于 2020-03-13 11:24:30 首次发布

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本文详细解析了LeetCode36题——有效数独的解决方案，介绍了如何使用行、列和宫格记录的方法来验证9x9数独的有效性，确保每个数字在行、列和宫格中只出现一次。

Leetcode36. 有效的数独

题目：
判断一个 9x9 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。
在这里插入图片描述
上图是一个部分填充的有效的数独。

数独部分空格内已填入了数字，空白格用 ‘.’ 表示。
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

题解：
可以使用 box_index = (row / 3) * 3 + columns / 3，其中 / 是整数除法。
在这里插入图片描述
java代码：

  public static boolean isValidSudoku(char[][] board) {
        int[][] row = new int[9][9];
        int[][] col = new int[9][9];
        int[][][] box = new int[3][3][9];

        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                char c = board[i][j];
                if (c != '.') {
                    int index = c - '0' - 1;
                    row[i][index]++;
                    col[j][index]++;
                    box[i / 3][j / 3][index]++;
                    if (row[i][index] > 1 || col[j][index] > 1 || box[i / 3][j / 3][index] > 1) {
                        return false;
                    }
                }
            }
        }
        return true;
    }

scala代码：

/**
    *
    * @param board
    * @return
    */
  def isValidSudoku(board: Array[Array[Char]]): Boolean = {
    val row = new Array[mutable.HashMap[Int, Int]](9)
    val col = new Array[mutable.HashMap[Int, Int]](9)
    val box = new Array[mutable.HashMap[Int, Int]](9)
    for(i<-0 until 9){
        row(i)= new mutable.HashMap[Int,Int]()
        col(i)= new mutable.HashMap[Int,Int]()
        box(i)= new mutable.HashMap[Int,Int]()
      }

    var flag = true
    for (i <- 0 until 9; if (flag)) {
      for (j <- 0 until 9; if (flag)) {
        val char = board(i)(j)
        if (char != '.') {
          val num: Int = char-'0'

          val box_index = (i / 3) * 3 + (j / 3)
          row(i).put(num, row(i).getOrElse(num, 0) + 1)
          col(j).put(num, col(j).getOrElse(num, 0) + 1)
          box(box_index).put(num, box(box_index).getOrElse(num, 0) + 1)
          if (row(i).getOrElse(num, 0) > 1 || col(j).getOrElse(num, 0) > 1 || box(box_index).getOrElse(num, 0) > 1) {
            flag = false
          }
        }
      }
    }
    flag
  }