211. 添加与搜索单词 – 数据结构设计

请你设计一个数据结构，支持 添加新单词 和 查找字符串是否与任何先前添加的字符串匹配 。

实现词典类WordDictionary：

• WordDictionary()初始化词典对象
• void addWord(word)将word添加到数据结构中，之后可以对它进行匹配
• bool search(word)如果数据结构中存在字符串与word匹配，则返回true；否则，返回false。word中可能包含一些'.'，每个.都可以表示任何一个字母。

示例：

**输入：**
["WordDictionary","addWord","addWord","addWord","search","search","search","search"]
[[],["bad"],["dad"],["mad"],["pad"],["bad"],[".ad"],["b.."]]
**输出：**
[null,null,null,null,false,true,true,true]

**解释：**
WordDictionary wordDictionary = new WordDictionary();
wordDictionary.addWord("bad");
wordDictionary.addWord("dad");
wordDictionary.addWord("mad");
wordDictionary.search("pad"); // return False
wordDictionary.search("bad"); // return True
wordDictionary.search(".ad"); // return True
wordDictionary.search("b.."); // return True

提示：

• 1 <= word.length <= 500
• addWord中的word由小写英文字母组成
• search中的word由'.'或小写英文字母组成
• 最多调用50000次addWord和search

1.字典树
Python解答：

class WordDictionary:

    def __init__(self):
        """
        Initialize your data structure here.
        """
        self.trie = {}
        self.is_word = False

    def addWord(self, word: str) -> None:
        i = 0
        p = self
        while i < len(word):
            if word[i] not in p.trie.keys():
                p.trie[word[i]] = WordDictionary()
            p = p.trie[word[i]]
            i += 1
        p.is_word = True

    def search(self, word: str) -> bool:
        def helper(adic, word, i):
            if i == len(word):
                if adic.is_word:
                    return True
                else:
                    return False
            else:
                if word[i] != '.' and word[i] not in adic.trie.keys():
                    return False
                elif word[i] != '.' and word[i] in adic.trie.keys():
                    return helper(adic.trie[word[i]], word, i+1)
                else:
                    for c in adic.trie.keys():
                        if helper(adic.trie[c], word, i+1):
                            return True
                return False
        return helper(self, word, 0)

# Your WordDictionary object will be instantiated and called as such:
# obj = WordDictionary()
# obj.addWord(word)
# param_2 = obj.search(word)

构造时间复杂度：O(n*k)
查询时间复杂度：O(k)