208-implement-trie-prefix-tree.md

208. 实现 Trie (前缀树) - medium

Trie（发音类似 "try"）或者说 前缀树 是一种树形数据结构，用于高效地存储和检索字符串数据集中的键。这一数据结构有相当多的应用情景，例如自动补完和拼写检查。

请你实现 Trie 类：

• Trie() 初始化前缀树对象。
• void insert(String word) 向前缀树中插入字符串 word 。
• boolean search(String word) 如果字符串 word 在前缀树中，返回 true（即，在检索之前已经插入）；否则，返回 false 。
• boolean startsWith(String prefix) 如果之前已经插入的字符串 word 的前缀之一为 prefix ，返回 true ；否则，返回 false 。

 

示例：

输入
["Trie", "insert", "search", "search", "startsWith", "insert", "search"]
[[], ["apple"], ["apple"], ["app"], ["app"], ["app"], ["app"]]
输出
[null, null, true, false, true, null, true]

解释
Trie trie = new Trie();
trie.insert("apple");
trie.search("apple");   // 返回 True
trie.search("app");     // 返回 False
trie.startsWith("app"); // 返回 True
trie.insert("app");
trie.search("app");     // 返回 True

 

提示：

• 1 <= word.length, prefix.length <= 2000
• word 和 prefix 仅由小写英文字母组成
• insert、search 和 startsWith 调用次数 总计 不超过 3 * 104 次

Solutions

1. map 树

class Trie:

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


    def insert(self, word: str) -> None:
        """
        Inserts a word into the trie.
        """
        m = self.m
        n = Node()
        for s in word:
            n = m.get(s, Node())
            m[s] = n
            m = n.m
        n.f = True

    def search(self, word: str) -> bool:
        """
        Returns if the word is in the trie.
        """
        m = self.m
        n = Node()
        for s in word:
            if s not in m:
                return False
            n = m[s]
            m = n.m
        return n.f

    def startsWith(self, prefix: str) -> bool:
        """
        Returns if there is any word in the trie that starts with the given prefix.
        """
        m = self.m
        for s in prefix:
            if s not in m:
                return False
            m = m[s].m
        return True

class Node:
    def __init__(self, f=False):
        self.f = f
        self.m = {}

# Your Trie object will be instantiated and called as such:
# obj = Trie()
# obj.insert(word)
# param_2 = obj.search(word)
# param_3 = obj.startsWith(prefix)

题目中说明 word 和 prefix 只包含小写字母，可以将 map 替换为 list 节省存储空间。

class Trie:

    def __init__(self):
        """
        Initialize your data structure here.
        """
        self.isend = False
        self.children = [None] * 26

    def insert(self, word: str) -> None:
        """
        Inserts a word into the trie.
        """
        tn = self
        for s in word:
            idx = ord(s) - ord('a')
            if tn.children[idx] is None:
                tn.children[idx] = Trie()
            tn = tn.children[idx]
        tn.isend = True

    def _search(self, word: str) -> 'Trie':
        tn = self
        for s in word:
            idx = ord(s) - ord('a')
            if tn.children[idx] is None:
                return None
            tn = tn.children[idx]
        return tn

    def search(self, word: str) -> bool:
        """
        Returns if the word is in the trie.
        """
        tn = self._search(word)
        return bool(tn and tn.isend)

    def startsWith(self, prefix: str) -> bool:
        """
        Returns if there is any word in the trie that starts with the given prefix.
        """
        return self._search(prefix) is not None


# Your Trie object will be instantiated and called as such:
# obj = Trie()
# obj.insert(word)
# param_2 = obj.search(word)
# param_3 = obj.startsWith(prefix)