36-有效的数独

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。

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。

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。

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示例

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

示例 2:

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。

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解法

核心思想：使用三个哈希表进行计数，三个表中所有的value均不大于1时，返回True。

如何计算Box的索引值?

按照上图将9x9的数独分成0-8共九个3x3：则索引值为：

box_index = row//3*3+column//3

完整代码：

class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        rows_ls = [{} for i in range(9)]
        columns_ls = [{} for i in range(9)]
        boxes_ls = [{} for i in range(9)]
        for row in range(9):
            for column in range(9):
                num = board[row][column]
                if num != ".":
                    num = int(num)
                    box_index = row//3*3+column//3
                    rows_ls[row][num] = rows_ls[row].get(num, 0) + 1
                    columns_ls[column][num] = columns_ls[column].get(
                        num, 0) + 1
                    boxes_ls[box_index][num] = boxes_ls[box_index].get(
                        num, 0) + 1
                    # check valid
                    if rows_ls[row][num] > 1 or columns_ls[column][num] > 1 or boxes_ls[box_index][num] > 1:
                        return False
        return True

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来源

LeetCode中该题地址，Click here!