LeetCode 208. Implement Trie (Prefix Tree)

[Woodyiiiiiii]

Implement a trie with insert, search, and startsWith methods.

Example:

Trie trie = new Trie();

trie.insert("apple");
trie.search("apple");   // returns true
trie.search("app");     // returns false
trie.startsWith("app"); // returns true
trie.insert("app");   
trie.search("app");     // returns true

Note:

• You may assume that all inputs are consist of lowercase letters a-z.
• All inputs are guaranteed to be non-empty strings.

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这道题是字典树(Trie) 的入门题目，又称前缀树(prefix tree)或者单词查找树。字典树是一个用来检索字符串(验证一个字符串是否在一堆字符串中或者是前缀)、字符串最长公共前缀等功能的数据结构。

Trie是一个用空间换取时间的应用，插入、查找的时间复杂度均为O(N)，其中N为字符串长度，而 空间复杂度是26^n级别的，非常庞大（可采用双数组实现改善）。

详细资料可以观看参考资料。LeetCode中还有关于字典树的类似题目还有No.211题，其中难点在于如何解决正则表达式中的“.”表达，使用了典型的DFS方法，参数表示下标而不再是字符串我没有想出来，太蠢了。

具体如何实现看如下代码：

class Trie {
    
    TreeNode root;
    
    class TreeNode {
        TreeNode[] nodes = new TreeNode[26];
        boolean end = false;
    }

    /** Initialize your data structure here. */
    public Trie() {
        root = new TreeNode();
    }
    
    /** Inserts a word into the trie. */
    public void insert(String word) {
        TreeNode tmp = root;
        for (int i = 0; i < word.length(); ++i) {
            int idx = word.charAt(i) - 'a';
            if (tmp.nodes[idx] == null) {
                tmp.nodes[idx] = new TreeNode();
            }
            tmp = tmp.nodes[idx];
        }
        tmp.end = true;
    }
    
    private TreeNode searchNode(String word) {
        TreeNode tmp = root;
        for (int i = 0; i < word.length(); ++i) {
            int idx = word.charAt(i) - 'a';
            if (tmp.nodes[idx] == null) {
                return null;
            }
            tmp = tmp.nodes[idx];
        }
        return tmp;
    }
    
    /** Returns if the word is in the trie. */
    public boolean search(String word) {
        TreeNode tmp = searchNode(word);
        return tmp == null ? false : tmp.end;
    }
    
    /** Returns if there is any word in the trie that starts with the given prefix. */
    public boolean startsWith(String prefix) {
        return searchNode(prefix) == null ? false : true;
    }
}

/**
 * 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);
 */

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类似题目：

• 211. Add and Search Word - Data structure design

参考资料：

• https://leetcode.com/problems/implement-trie-prefix-tree/
• https://www.cnblogs.com/grandyang/p/4491665.html
• http://dongxicheng.org/structure/trietree/