leetcode 36. 有效的数独

发表于 2019-07-10

|

| 阅读次数:

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。

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。

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。

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

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: 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。

说明:
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。
给定数独序列只包含数字 1-9 和字符 ‘.’ 。
给定数独永远是 9x9 形式的。

使用三个二维数组 a, b, c 分别保存每行，每列，每个 3*3 区块中，相应数字出现的次数

示例代码(go)

func isValidSudoku(board [][]byte) bool {
    a := [9][9]int{}
    b := [9][9]int{}
    c := [9][9]int{}
    for i := 0; i < 9; i++ {
        for j := 0; j < 9; j++ {
            if board[i][j] == '.' {
                continue
            }
            num := board[i][j] - '0'
            k := (i / 3) * 3 + j / 3
            a[i][num-1]++
            b[j][num-1]++
            c[k][num-1]++
            if a[i][num-1] > 1 || b[j][num-1] > 1 || c[k][num-1] > 1 {
                return false
            }
        }
    }
    return true
}