Implement Trie (Prefix Tree)

Thought Process

A Trie is a tree-like data structure that stores strings by breaking them down into individual characters. Each node represents a character and has 26 children (for English letters). The 'insert' operation adds characters level by level, creating new nodes as needed and marking the end with a boolean. For 'search', we traverse the tree checking if all characters exist and verify the end marker. The 'startsWith' operation is similar but doesn't require the end marker.

// Make a Trie Node
class TrieNode{

    TrieNode[] children;
    boolean isEndCharacter;

    TrieNode(){
        children = new TrieNode[26];
        isEndCharacter = false;
    }
}

class Trie {

    TrieNode root;
    public Trie() {
        root = new TrieNode();
    }
    
    public void insert(String word) {
        
        TrieNode copy = root;
        for(int i=0;i<word.length();i++){

            char ch = word.charAt(i);
            // if Node doesn't exist
            if(copy.children[ch-'a']==null)
                copy.children[ch-'a'] = new TrieNode();
            
            copy = copy.children[ch-'a'];
            // For the last character, make it as end.
            if(i==(word.length()-1))
                copy.isEndCharacter = true;
        }
    }
    
    public boolean search(String word) {
        
        TrieNode copy = root;
        for(int i=0;i<word.length();i++){

            char ch = word.charAt(i);
            if(copy.children[ch-'a']==null)
                return false;
            else
                copy = copy.children[ch-'a'];
        }
        // Whether last node field for 'isEndCharacter' is True or not.
        if(copy.isEndCharacter==true)
            return true;
        else
            return false;
    }
    
    public boolean startsWith(String prefix) {
        
        TrieNode copy = root;
        for(int i=0;i<prefix.length();i++){

            char ch = prefix.charAt(i);
            if(copy.children[ch-'a']==null){
                return false;
            }
            copy = copy.children[ch-'a'];
        }
        return 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);
 */

Code Complexity

Time Complexity: O(n) (per operation)

Each operation (insert/search/startsWith) processes each character exactly once, where 'n' is the length of the input string.

Space Complexity: O(m*n)

Where 'm' is average word length and 'n' is number of words, as each character may require a new node.

Java: Implement Trie (Prefix Tree)

Thought Process

Code Complexity

Time Complexity: O(n) (per operation)

Space Complexity: O(m*n)