LeetCode——有效的数独

题目：

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。

思路：

这种限定了数字的个数并且是正整数的，首先要想到用数组来判断数字的个数是否超标，比如1的个数，那么就判断num[1]中的大小就可以了。根据数独的规则，我们只要判断每行，每列和每个3*3方格是否满足就行。

代码：

class Solution:
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        numlist = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
        #先求列是否重复
        for i in range(0,9):
            numlist = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
            for row in board:
                if row[i] != '.':
                    numlist[int(row[i])] += 1
                    if numlist[int(row[i])] > 1:
                        return False
        #求行是否重复
        for i in range(0,9):#得到某一行
            numlist = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
            for index, num in enumerate(board[i]):
                if num != '.':
                    numlist[int(num)] += 1
                    if numlist[int(num)] > 1:
                        return False
        #得到每一个3*3方格
        for i in range(0, 9):
            #得到x，y的上下限
            minX = (int(i/3)) *3
            minY = (i % 3)*3
            maxX = (int(i/3)+1) *3-1
            maxY = (i % 3+1)*3 -1
            numlist = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
            index1 = minX
            while index1 <= maxX:
                index2 = minY
                while index2 <= maxY:
                    if board[index1][index2] !='.':
                        numlist[int(board[index1][index2] )] += 1
                        if numlist[int(board[index1][index2] )] > 1:
                            return False
                    index2 += 1
                index1 += 1
        return True






if __name__ =="__main__":
    res = Solution()
    print(res.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"]
]))
    pass

LeetCode——有效的数独

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