[数据结构与算法]leetcode:36. 有效的数独

题目

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/valid-sudoku

请你判断一个 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。（请参考示例图）
数独部分空格内已填入了数字，空白格用 ‘.’ 表示。

注意：
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。

示例 1：

输入：board =
[[“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：board =
[[“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。

提示：

board.length == 9
board[i].length == 9
board[i][j] 是一位数字或者 ‘.’

解法

左右遍历，上下遍历，以及判断小方块中是否有重复的

如何确定是哪一个小方块，通过横纵坐标能得到：

j // 3 + i // 3 * 3

参考：

• python

class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        row = [[0]*10 for _ in range(9)]
        col = [[0]*10 for _ in range(9)]
        box = [[0]*10 for _ in range(9)]  #这里*10 是由于数字9  // 1 2 3 4 5 6 7 8 9 
        for i in range(9):
            for j in range(9):
                if board[i][j] == '.':
                    continue
                curNum = int(board[i][j])
                if row[i][curNum] != 0 or col[j][curNum] != 0 or box[j//3+ i//3 * 3][curNum] != 0:
                    return False
                row[i][curNum] = 1
                col[j][curNum] = 1
                box[j//3 + i//3*3][curNum] = 1
        return True

复杂度分析

• 时间复杂度：O(1)，固定9x9大小的问题，计算量不随数据发生明显变化
• 空间复杂度：O(1)， 固定9x9大小的问题， 空间里不随数据发生明显变化