36. 有效的数独

题目来源：36. 有效的数独

请你判断一个 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。（请参考示例图）

数独部分空格内已填入了数字，空白格用 '.' 表示。

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。

/**
 * @param {character[][]} board
 * @return {boolean}
 */
var isValidSudoku = function(board) {
  let row = new Array(9).fill(0).map(()=>new Map());
  let col = new Array(9).fill(0).map(()=>new Map());
  let box = new Array(9).fill(0).map(()=>new Map());
  
  for(let i = 0;i < 9; i++){
    for(let j = 0; j < 9; j++){
      let cur = board[i][j];
      if(cur == '.'){
        continue;
      }
      let boxIndex = parseInt(3*parseInt(j/3)+i/3);
      if(row[i].has(cur)){
        return false;
      }
      row[i].set(cur, 1);

      if(col[j].has(cur)){
        return false;
      }
      col[j].set(cur, 1);

      if(box[boxIndex].has(cur)){
        return false;
      }
      box[boxIndex].set(cur,1);      
    }
    
  }
  return true;
};

 

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。

 python3

from typing import List


class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
      rows = [{} for i in range(9)]
      columns = [{} for i in range(9)]
      boxes = [{} for i in range(9)]
      for i in range(9):
        for j in range(9):
          num = board[i][j]
          if num != '.':
            num = int(num)
            boxIndex = (i//3)*3 + j//3

            rows[i][num] = rows[i].get(num, 0) + 1
            columns[j][num] = columns[j].get(num, 0) + 1
            boxes[boxIndex][num] = boxes[boxIndex].get(num, 0) + 1

            if rows[i][num] > 1 or columns[j][num] > 1 or boxes[boxIndex][num] > 1:
              return False            

      return True


if __name__ == '__main__':
  so = Solution()
  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(so.isValidSudoku(board))

  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"]]
print(so.isValidSudoku(board))

 

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字或者 '.'