Trie

Animation: https://www.cs.usfca.edu/~galles/visualization/Trie.html it use an Array of TrieNode in every node: TrieNode[] children = new TrieNode[26]

basic: https://leetcode.com/problems/implement-trie-prefix-tree/description/

Template

class Trie {
    TrieNode root;
    /** Initialize your data structure here. */
    public Trie() {
        root = new TrieNode();
    }

    /** Inserts a word into the trie. */
    public void insert(String word) {
        TrieNode r = root;
        for (int i = 0; i < word.length(); i++) {
            int pos = word.charAt(i) - 'a';
            if (r.next[pos] == null) r.next[pos] = new TrieNode();
            r = r.next[pos];
        }
        r.isWord = true;
    }

    /** Returns if the word is in the trie. */
    public boolean search(String word) {
        TrieNode r = root;
        for (int i = 0; i < word.length(); i++) {
            int pos = word.charAt(i) - 'a';
            if (r.next[pos] == null) return false;
            r = r.next[pos];
        }
        return r.isWord;
    }

    /** Returns if there is any word in the trie that starts with the given prefix. */
    public boolean startsWith(String prefix) {
        TrieNode r = root;
        for (int i = 0; i < prefix.length(); i++) {
            int pos = prefix.charAt(i) - 'a';
            if (r.next[pos] == null) return false;
            r = r.next[pos];
        }

        // prefix is word
        if (r.isWord) return true;

        // iterate next[]
        for (TrieNode t : r.next) {
            if (t != null) return true;
        }

        return false;
    }
}

class TrieNode {
    TrieNode[] next;
    boolean isWord;
    public TrieNode() {
        next = new TrieNode[26];
    }
}

DFS to build Trie

211-Add and Search Word - Data structure design

public void insert(String word, int index) {
    if (index == word.length()) {
        this.hasWord = true;
        return;
    }
    int pos = word.charAt(index) - 'a';
    if (children[pos] == null) children[pos] = new TrieNode();
    children[pos].insert(word, index+1);
}

Applications

Words dictionary, then look up a word

• 212-Word Search II

• 472-Concatenated Words

Extension: numbers, binary

• 386-Lexicographical Numbers

• 421-Maximum XOR of Two Numbers in an Array

https://leetcode.com/problems/add-and-search-word-data-structure-design/description/ https://leetcode.com/problems/implement-magic-dictionary https://leetcode.com/problems/replace-words/description/ https://leetcode.com/problems/maximum-xor-of-two-numbers-in-an-array