leetcode pyhton数组：有效的数独

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

这道题第一眼看挺懵的，感觉只能行、列、3*3块分别检测，后来想到3*3块就没办法了

从网上寻找答案，将索引到位置利用整数除法框定范围判定是否存在相同的数字

v1.0时间复杂度O(n^3)

class Solution:
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        for i in range(9):
            for j in range(9):
                if board[i][j]!= '.':
                    
                    #判断行重复性
                    for k in range(j+1,9):
                        if board[i][j] == board[i][k]:
                            return False
                    for h in range(i+1,9):
                        if board[i][j] == board[h][j]:
                            return False

                        
                    a = board[i][j]
                    board[i][j] = 0
                    for p in range(i//3*3, i//3*3+3): #//返回不大于结果的最大整数
                        for q in range(j//3*3, j//3*3+3):
                            if a== board[p][q]:
                                return False
        return True

时间少用了很多，减少了数据读取

def isValidSudoku(board):
    dic_row = [{},{},{},{},{},{},{},{},{}]
    dic_column =[{},{},{},{},{},{},{},{},{}]
    dic_box = [{},{},{},{},{},{},{},{},{}]
    
    for i in range(9):
        for j in range(9):
            num = board[i][j]
            if num  == '.':
                continue
            if num not in dic_row[i] and num not in dic_column[j] and num not in dic_box[3*(i//3)+(j//3)]:
                #判定key是否存在
                dic_row[i][num] =1
                dic_column[j][num] = 1
                dic_box[3*(i//3)+(j//3)][num] = 1
            else:
                return False
    return True

利用字典的方法，每一行即为一个字典，将第i行或者第j列的key= num 时设为1

判定若num存在相同的key值，即为存在重复

v3.0 v2.0另一种实现方法

def isValidSudoku(board):
        Cell = [[] for i in range(9)]                   # 没有必要用dict,我们只某个数字关心有没有出现过
        Col =  [[] for i in range(9)]
        Row =  [[] for i in range(9)]

        for i,row in enumerate(board):                  # 将一个可遍历的数据对象(如列表、元组或字符串)组合为一个索引序列，同时列出数据和数据下标，一般用在 for 循环当中
            for j,num in enumerate(row):
                if num != '.':
                    k = (i//3)*3 + j//3
                    if num in Row[i] + Col[j] + Cell[k]:    # list的骚操作,将三个list顺序的拼接 
                        return False
                    Row[i].append(num)
                    Col[j].append(num)
                    Cell[k].append(num)

        return True

设定行列与块cell分别为9个

        for i,row in enumerate(board):                  # 将一个可遍历的数据对象(如列表、元组或字符串)组合为一个索引序列，同时列出数据和数据下标，一般用在 for 循环当中
            for j,num in enumerate(row):

同时输出输入对象的行列和结果值进行处理

判定num是否存在于与Row[i] + Col[j] + Cell[k]中

不存在之后执行调加

存在直接返回False

leetcode pyhton数组：有效的数独

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