Implement Trie (Prefix Tree)

A trie (pronounced "try") or prefix tree is a tree data structure used to efficiently store and retrieve keys in a dataset of strings. There are various applications of this data structure, such as autocomplete and spellchecker.

Implement the Trie class:

• Trie() — Initializes the trie object.
• void insert(String word) — Inserts the string word into the trie.
• boolean search(String word) — Returns true if the string word is in the trie (i.e., was inserted before), and false otherwise.
• boolean startsWith(String prefix) — Returns true if there is a previously inserted string word that has the prefix prefix, and false otherwise.

Example 1:

Input:
["Trie", "insert", "search", "search", "startsWith", "insert", "search"]
[[], ["apple"], ["apple"], ["app"], ["app"], ["app"], ["app"]]
Output: [null, null, true, false, true, null, true]
Explanation:
Trie trie = new Trie();
trie.insert("apple");   // Inserts "apple" into the trie
trie.search("apple");   // Returns true
trie.search("app");     // Returns false ("app" was not inserted)
trie.startsWith("app"); // Returns true ("apple" starts with "app")
trie.insert("app");     // Inserts "app" into the trie
trie.search("app");     // Returns true ("app" is now in the trie)