class Solution:

     #         (x-1,y)

     # (x,y-1) (x,y) (x,y+1)

     #         (x+1,y)

     directions= [(0,-1),(-1,0),(0,1),(1,0)]

     def exist(self, board: List[List[str]], word: str) -> bool:

         m = len(board)

         if m == 0:

             return False

         n = len(board[0])

         marked = [[False for _ in range(n)] for _ in range(m)]

         # 对每一个格子都从头开始搜索

         for i in range(m):

             for j in range(n):

                 if self.__search_word(board,word,0,i,j,marked,m,n):

                     return True

         return False

     def  __search_word(self,board,word,index,start_x,start_y,marked,m,n):

         # 先写递归终止条件

         if index == len(word) -1:

             return board[start_x][start_y] == word[index]

         # 中间匹配了，再继续搜索

         if board[start_x][start_y] == word[index]:

             # 先占住这个位置，搜索不成功的话，要释放掉

             marked[start_x][start_y] = True

             for direction in self.directions:

                 new_x = start_x +direction[0]

                 new_y = start_y + direction[1]

                 ## 注意：如果这一次 search word 成功的话，就返回

                 if 0 <= new_x < m and 0 <= new_y < n and not marked[new_x][new_y] and self.__search_word(board,word,index+1,new_x,new_y,marked,m,n):

                     return True

             marked[start_x][start_y] = False

         return False