36. 有效的数独

目录

• 题目
• 法一、暴力法
• 法二、哈希表

题目

• 请你判断一个 9 x 9 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）
   
  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。
  空白格用 '.' 表示。

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。

法一、暴力法

class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        for i in range(9):                   #对每一行进行判断
            storage = []                     #每一行单独进行加载时，storage都置空
            for j in range(9):
                if board[i][j] == '.':        #如果该元素是空，继续下一个元素的判断
                    continue
                if board[i][j] in storage:    #如果该元素在列表中，返回False
                    return False
                else:
                    storage.append(board[i][j])    #如果该元素不是空且不在列表中，加入列表
        for i in range(9):                         #对每一列进行判断
            storage = []                           #每一列单独进行加载时，storage都置空
            for j in range(9):
                if board[j][i] == '.':
                    continue
                if board[j][i] in storage:
                    return False
                else:
                    storage.append(board[j][i])
        for i in range(0, 9, 3):                   #对九宫格是否重复进行判断
            for j in range(0, 9, 3):               #从0到9每隔3步取一次
                storage = []                       #每一块单独进行加载时，storage都置空
                for x in range(0, 3):
                    for y in range(0, 3):
                        if board[i + x][j + y] == '.':
                            continue
                        if board[i + x][j + y] in storage:
                            return False
                        else:
                            storage.append(board[i + x][j + y])
        return True

法二、哈希表

class Solution:
    def isValidSudoku(self, board):
        row = {}
        col = {}
        small = {}

        # 初始化字典
        for i in range(9):
          row[i] = set()
          col[i] = set()
          small[i] = set()
        for i in range(9):
            for j in range(9):
                val = board[i][j] #拷贝一份
                if val == '.':
                    continue
                point = i // 3 * 3 + j // 3#计算当前方格属于9宫格哪个，从0开始
                if val in row[i] or val in col[j] or val in small[point]:
                    return False
                row[i].add(val)#如果该元素不在，加入对应的行集合
                col[j].add(val)#如果该元素不在，加入对应的列集合
                small[point].add(val)#如果该元素不在，加入对应的方块集合
        return True