8-1

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。

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。
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。

A readable and understandable python solution:

class Solution(object):
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        return (self.is_row_valid(board) and
                self.is_col_valid(board) and
                self.is_square_valid(board))

    def is_row_valid(self, board):
        for row in board:
            if not self.is_unit_valid(row):
                return False
        return True

    def is_col_valid(self, board):
        for col in zip(*board):
            if not self.is_unit_valid(col):
                return False
        return True

    def is_square_valid(self, board):
        for i in (0, 3, 6):
            for j in (0, 3, 6):
                square = [board[x][y] for x in range(i, i + 3) for y in range(j, j + 3)]
                if not self.is_unit_valid(square):
                    return False
        return True

    def is_unit_valid(self, unit):
        unit = [i for i in unit if i != '.']
        return len(set(unit)) == len(unit)

分析：

（1）该代码分别对行、列及每个3x3的方块区域进行判断。在判断列的时候，使用了zip方法，其用法详见：菜鸟教程，它在此处的主要功能是提取数独中每一列的元素，函数返回的是一个tuple型的list。

（2）如何取出每个3x3的小方格？这里i和j采用了“跳跃式”的取法，每次间隔为3，然后在构建square的for循环中，控制横向和纵向每次只取相邻的三个数，如此即可实现取出所有的3x3小方格。

转载于:https://www.cnblogs.com/tbgatgb/p/11144156.html