36. Valid Sudoku

1. Question

Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

1. Each row must contain the digits 1-9 without repetition.
2. Each column must contain the digits 1-9 without repetition.
3. Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.

2. Note

• A Sudoku board (partially filled) could be valid but is not necessarily solvable.
• Only the filled cells need to be validated according to the mentioned rules.

3. Examples

Example 1:

Input: 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"]]
Output: true

Example 2:

Input: 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"]]
Output: false
Explanation: Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

4. Constraints

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit 1-9 or '.'.

5. References

来源：力扣（LeetCode） 链接：https://leetcode-cn.com/problems/valid-sudoku 著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

6. Solutions

行、列、方块中1-9计数

class Solution {
  public boolean isValidSudoku(char[][] board) {
    int[][] row = new int[9][9];
    int[][] col = new int[9][9];
    int[][][] arr = new int[3][3][9];
    for (int i = 0; i < board.length; i++) {
      for (int j = 0; j < board[0].length; j++) {
        if (board[i][j] == '.') {
          continue;
        }
        // 下标从0开始
        int val = board[i][j] - '0' - 1;
        row[i][val] += 1;
        col[j][val] += 1;
        arr[i / 3][j / 3][val] += 1;
        if (row[i][val] > 1 || col[j][val] > 1 || arr[i / 3][j / 3][val] > 1) {
          return false;
        }
      }
    }
    return true;
  }
}