dfs 解决（隐式）图搜索问题

132. 单词搜索 II

中文

English

给出一个由小写字母组成的矩阵和一个字典。找出所有同时在字典和矩阵中出现的单词。一个单词可以从矩阵中的任意位置开始，可以向左/右/上/下四个相邻方向移动。一个字母在一个单词中只能被使用一次。且字典中不存在重复单词

样例

样例 1:

输入：["doaf","agai","dcan"]，["dog","dad","dgdg","can","again"]
输出：["again","can","dad","dog"]
解释：
  d o a f
  a g a i
  d c a n
矩阵中查找，返回 ["again","can","dad","dog"]。

样例 2:

输入：["a"]，["b"]
输出：[]
解释：
 a
矩阵中查找，返回 []。

挑战

使用单词查找树来实现你的算法

 

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DIRECTIONS = [(0, -1), (0, 1), (-1, 0), (1, 0)]   class Solution:     """     @param board: A list of lists of character     @param words: A list of string     @return: A list of string     """     def wordSearchII(self, board, words):         if board is None or len(board) == 0:             return []                   word_set = set(words)         prefix_set = set()         for word in words:             for i in range(len(word)):                 prefix_set.add(word[:i + 1])                   result = set()         for i in range(len(board)):             for j in range(len(board[0])):                 c = board[i][j]                 self.search(                     board,                     i,                     j,                     board[i][j],                     word_set,                     prefix_set,                     set([(i, j)]),                     result,                 )                           return list(result)               def search(self, board, x, y, word, word_set, prefix_set, visited, result):         if word not in prefix_set:             return                   if word in word_set:             result.add(word)                   for delta_x, delta_y in DIRECTIONS:             x_ = x + delta_x             y_ = y + delta_y                           if not self.inside(board, x_, y_):                 continue             if (x_, y_) in visited:                 continue                           visited.add((x_, y_))             self.search(                 board,                 x_,                 y_,                 word + board[x_][y_],                 word_set,                 prefix_set,                 visited,                 result,             )             visited.remove((x_, y_))                   def inside(self, board, x, y):         return 0 <= x < len(board) and 0 <= y < len(board[0])

 注意使用prefix hash map来剪枝。

使用trie的解法：

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

DIRECTIONS = [(0, -1), (0, 1), (-1, 0), (1, 0)]   class TrieNode:         #定义字典树的节点     def __init__(self):         self.children = {}         self.is_word = False         self.word = None                     class Trie:     def __init__(self):         self.root = TrieNode()               def add(self, word):        #字典树插入单词         node = self.root         for c in word:             if c not in node.children:                 node.children[c] = TrieNode()   #在此节点申请节点             node = node.children[c]             #继续遍历         node.is_word = True         node.word = word        #存入单词               def find(self, word):           node = self.root         for c in word:             node = node.children.get(c)             if node is None:                 return None                           return node             class Solution:     """     @param board: A list of lists of character     @param words: A list of string     @return: A list of string     """     def wordSearchII(self, board, words):         if board is None or len(board) == 0:             return []                       trie = Trie()         for word in words:          #插入单词             trie.add(word)           result = set()         for i in range(len(board)):             #遍历字母矩阵，将每个字母作为单词首字母开始搜索             for j in range(len(board[0])):                 c = board[i][j]                 self.search(                     board,                     i,                     j,                     trie.root.children.get(c),                     set([(i, j)]),                     result,                 )                           return list(result)               def search(self, board, x, y, node, visited, result):           #在字典树上dfs查找         if node is None:             return                   if node.is_word:             result.add(node.word)                   for delta_x, delta_y in DIRECTIONS:             #向四个方向查找             x_ = x + delta_x             y_ = y + delta_y                           if not self.inside(board, x_, y_):                 continue             if (x_, y_) in visited:                 continue                           visited.add((x_, y_))             self.search(                 board,                 x_,                 y_,                 node.children.get(board[x_][y_]),                 visited,                 result,             )             visited.remove((x_, y_))                   def inside(self, board, x, y):         return 0 <= x < len(board) and 0 <= y < len(board[0])