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208. 实现 Trie (前缀树)

English Version

题目描述

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

解法

前缀树每个节点包括两部分：

  1. 指向子节点的指针数组 children，对于本题而言，数组长度为 26，即小写英文字母的数量。children[0] 对应小写字母 a，...，children[25] 对应小写字母 z。
  2. 布尔字段 isEnd，表示该节点是否为字符串的结尾。

1. 插入字符串

我们从字典树的根开始，插入字符串。对于当前字符对应的子节点，有两种情况：

  • 子节点存在。沿着指针移动到子节点，继续处理下一个字符。
  • 子节点不存在。创建一个新的子节点，记录在 children 数组的对应位置上，然后沿着指针移动到子节点，继续搜索下一个字符。

重复以上步骤，直到处理字符串的最后一个字符，然后将当前节点标记为字符串的结尾。

2. 查找前缀

我们从字典树的根开始，查找前缀。对于当前字符对应的子节点，有两种情况：

  • 子节点存在。沿着指针移动到子节点，继续搜索下一个字符。
  • 子节点不存在。说明字典树中不包含该前缀，返回空指针。

重复以上步骤，直到返回空指针或搜索完前缀的最后一个字符。

若搜索到了前缀的末尾，就说明字典树中存在该前缀。此外，若前缀末尾对应节点的 isEnd 为真，则说明字典树中存在该字符串。

Python3

class Trie:

    def __init__(self):
        self.children = [None] * 26
        self.is_end = False

    def insert(self, word: str) -> None:
        node = self
        for c in word:
            idx = ord(c) - ord('a')
            if node.children[idx] is None:
                node.children[idx] = Trie()
            node = node.children[idx]
        node.is_end = True

    def search(self, word: str) -> bool:
        node = self._search_prefix(word)
        return node is not None and node.is_end

    def startsWith(self, prefix: str) -> bool:
        node = self._search_prefix(prefix)
        return node is not None

    def _search_prefix(self, prefix: str):
        node = self
        for c in prefix:
            idx = ord(c) - ord('a')
            if node.children[idx] is None:
                return None
            node = node.children[idx]
        return node

# 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)

Java

class Trie {
    private Trie[] children;
    private boolean isEnd;

    public Trie() {
        children = new Trie[26];
    }
    
    public void insert(String word) {
        Trie node = this;
        for (char c : word.toCharArray()) {
            int idx = c - 'a';
            if (node.children[idx] == null) {
                node.children[idx] = new Trie();
            }
            node = node.children[idx];
        }
        node.isEnd = true;
    }
    
    public boolean search(String word) {
        Trie node = searchPrefix(word);
        return node != null && node.isEnd;
    }
    
    public boolean startsWith(String prefix) {
        Trie node = searchPrefix(prefix);
        return node != null;
    }

    private Trie searchPrefix(String s) {
        Trie node = this;
        for (char c : s.toCharArray()) {
            int idx = c - 'a';
            if (node.children[idx] == null) {
                return null;
            }
            node = node.children[idx];
        }
        return node;
    }
}

/**
 * Your Trie object will be instantiated and called as such:
 * Trie obj = new Trie();
 * obj.insert(word);
 * boolean param_2 = obj.search(word);
 * boolean param_3 = obj.startsWith(prefix);
 */

JavaScript

/**
 * Initialize your data structure here.
 */
var Trie = function() {
    this.children = {};
};

/**
 * Inserts a word into the trie. 
 * @param {string} word
 * @return {void}
 */
Trie.prototype.insert = function(word) {
    let node = this.children;
    for (let char of word) {
        if (!node[char]) {
            node[char] = {};
        }
        node = node[char];
    }
    node.isEnd = true;
};

/**
 * Returns if the word is in the trie. 
 * @param {string} word
 * @return {boolean}
 */
Trie.prototype.search = function(word) {
    let node = this.searchPrefix(word);
    return node != undefined && node.isEnd != undefined;
};

Trie.prototype.searchPrefix = function (prefix) {
    let node = this.children;
    for (let char of prefix) {
        if (!node[char]) return false;
        node = node[char];
    }
    return node;
}

/**
 * Returns if there is any word in the trie that starts with the given prefix. 
 * @param {string} prefix
 * @return {boolean}
 */
Trie.prototype.startsWith = function(prefix) {
    return this.searchPrefix(prefix);
};

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

C++

class Trie {
private:
    vector<Trie*> children;
    bool isEnd;

    Trie* searchPrefix(string s) {
        Trie* node = this;
        for (char c : s)
        {
            int idx = c - 'a';
            if (!node->children[idx]) return nullptr;
            node = node->children[idx];
        }
        return node;
    }

public:
    Trie() : children(26), isEnd(false) {}
    
    void insert(string word) {
        Trie* node = this;
        for (char c : word)
        {
            int idx = c - 'a';
            if (!node->children[idx]) node->children[idx] = new Trie();
            node = node->children[idx];
        }
        node->isEnd = true;
    }
    
    bool search(string word) {
        Trie* node = searchPrefix(word);
        return node != nullptr && node->isEnd;
    }
    
    bool startsWith(string prefix) {
        Trie* node = searchPrefix(prefix);
        return node != nullptr;
    }
};

/**
 * Your Trie object will be instantiated and called as such:
 * Trie* obj = new Trie();
 * obj->insert(word);
 * bool param_2 = obj->search(word);
 * bool param_3 = obj->startsWith(prefix);
 */

Go

type Trie struct {
	children [26]*Trie
	isEnd    bool
}

func Constructor() Trie {
	return Trie{}
}

func (this *Trie) Insert(word string) {
	node := this
	for _, c := range word {
		idx := c - 'a'
		if node.children[idx] == nil {
			node.children[idx] = &Trie{}
		}
		node = node.children[idx]
	}
	node.isEnd = true
}

func (this *Trie) Search(word string) bool {
	node := this.SearchPrefix(word)
	return node != nil && node.isEnd
}

func (this *Trie) StartsWith(prefix string) bool {
	node := this.SearchPrefix(prefix)
	return node != nil
}

func (this *Trie) SearchPrefix(s string) *Trie {
	node := this
	for _, c := range s {
		idx := c - 'a'
		if node.children[idx] == nil {
			return nil
		}
		node = node.children[idx]
	}
	return node
}

/**
 * Your Trie object will be instantiated and called as such:
 * obj := Constructor();
 * obj.Insert(word);
 * param_2 := obj.Search(word);
 * param_3 := obj.StartsWith(prefix);
 */

C#

public class Trie {
    bool isEnd;
    Trie[] children = new Trie[26];

    public Trie() {

    }

    public void Insert(string word) {
        Trie node = this;
        foreach (var c in word)
        {
            var idx = c - 'a';
            node.children[idx] ??= new Trie();
            node = node.children[idx];
        }
        node.isEnd = true;
    }

    public bool Search(string word) {
        Trie node = SearchPrefix(word);
        return node != null && node.isEnd;
    }

    public bool StartsWith(string prefix) {
        Trie node = SearchPrefix(prefix);
        return node != null;
    }

    private Trie SearchPrefix(string s) {
        Trie node = this;
        foreach (var c in s)
        {
            var idx = c - 'a';
            if (node.children[idx] == null)
            {
                return null;
            }
            node = node.children[idx];
        }
        return node;
    }
}

/**
 * Your Trie object will be instantiated and called as such:
 * Trie obj = new Trie();
 * obj.Insert(word);
 * bool param_2 = obj.Search(word);
 * bool param_3 = obj.StartsWith(prefix);
 */

...