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.

class Trie {
public:
    struct TrieNode {

        TrieNode* children[26];
        bool isEndCharacter;

        TrieNode() {
            isEndCharacter = false;
            for (int i = 0; i < 26; i++)
                children[i] = NULL;
        }
    };

    TrieNode* root;
    
    Trie() { 
        root = new TrieNode(); 
    }

    // Idea is to make a N-ary tree where each nodes has 26 children.
    void insert(string word) {

        TrieNode* copy = root;
        for (int i = 0; i < word.size(); i++) {

            char ch = word[i];
            if (copy->children[ch - 'a'] == NULL) {
                copy->children[ch - 'a'] = new TrieNode();
            }
            copy = copy->children[ch - 'a'];
        }
        copy->isEndCharacter = true;
    }

    bool search(string word) {

        TrieNode* copy = root;
        for (int i = 0; i < word.size(); i++) {

            char ch = word[i];
            if (copy->children[ch - 'a'] == NULL)
                return false;

            copy = copy->children[ch - 'a'];
        }
        if (copy->isEndCharacter)
            return true;
        else
            return false;
    }

    bool startsWith(string prefix) {

        TrieNode* copy = root;
        for (int i = 0; i < prefix.size(); i++) {

            char ch = prefix[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);
 * bool param_2 = obj->search(word);
 * bool 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.

C++: Implement Trie (Prefix Tree)

Thought Process

Code Complexity

Time Complexity: O(n) (per operation)

Space Complexity: O(m*n)