#263 Implement Prefix Tree (Trie)

Implement a prefix tree (trie) that supports string insertion and search operations.

The PrefixTree class should support:

• insert(word): Adds a word to the trie
• search(word): Returns true if word exists in trie
• startsWith(prefix): Returns true if any word starts with prefix

Constraints:

• 1 ≤ word.length, prefix.length ≤ 1000
• All strings contain only lowercase English letters

Examples:

const trie = new PrefixTree();
trie.insert("dog");
trie.search("dog");     // returns true

trie.search("do");      // returns false

trie.startsWith("do"); // returns true

trie.insert("do");
trie.search("do");      // returns true