208. Implement Trie (Prefix Tree)

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

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.