【LeetCode 】: 36. 有效的数独（Valid Sudoku）

36. 有效的数独（Valid Sudoku）

问题描述：

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。

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。

思路：

首先需要一个辅助函数，验证一维数组中的重复元素

    def containsDuplicate(self, nums):
        return len(nums) != len(set(nums))

然后使用两个for循环，遍历每个行，把每行出现的元素存入到一维数组中，判断是否存在重复元素

     # 验证行元素是否重复
     for i in range(0,9):
         for j in range(0,9):
             if(board[i][j] != '.'):
                 test.append(int(board[i][j]))
         if(self.containsDuplicate(test)):
             return False
         test.clear()

同理，判断列元素是否包含重复元素

	# 验证列元素是否重复
	for i in range(0,9):
	    for j in range(0,9):
	        if(board[j][i] != '.'):
	            test.append(int(board[j][i]))
	    if(self.containsDuplicate(test)):
	        return False
	    test.clear()

最后，我们来判断3*3宫格内的重复元素。代码如下：

        # 验证3x3宫格是否重复
        for i in range(0,3):
            for j in range(0, 3):
                for x in range(i*3,i*3+3):
                    for y in range(j*3,j*3+3):
                        if(board[x][y] != "."):
                            test.append(int(board[x][y]))
                if (self.containsDuplicate(test)):
                    return False
                test.clear()

完整代码：

class Solution(object):

    def containsDuplicate(self, nums):
        return len(nums) != len(set(nums))

    def isValidSudoku(self, board):
        test = []

        # 验证行元素是否重复
        for i in range(0,9):
            for j in range(0,9):
                if(board[i][j] != '.'):
                    test.append(int(board[i][j]))
            if(self.containsDuplicate(test)):
                return False
            test.clear()


        # 验证列元素是否重复
        for i in range(0,9):
            for j in range(0,9):
                if(board[j][i] != '.'):
                    test.append(int(board[j][i]))
            if(self.containsDuplicate(test)):
                return False
            test.clear()

        # 验证3x3宫格是否重复
        for i in range(0,3):
            for j in range(0, 3):
                for x in range(i*3,i*3+3):
                    for y in range(j*3,j*3+3):
                        if(board[x][y] != "."):
                            test.append(int(board[x][y]))
                if (self.containsDuplicate(test)):
                    return False
                test.clear()

        return True

if __name__ == '__main__':
    s = Solution()
    print(s.isValidSudoku([
  ["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"]
]))

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