Implement Trie (Prefix Tree)

A trie (pronounced "try") is a tree data structure used to efficiently store and retrieve keys in a dataset of strings. 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 word is in the trie (was inserted before), false otherwise.
• boolean startsWith(String prefix) Returns true if there is a previously inserted word that has prefix as a prefix, false otherwise.

Example:

Input:
["Trie", "insert", "search", "search", "startsWith", "insert", "search"]
[[], ["apple"], ["apple"], ["app"], ["app"], ["app"], ["app"]]
Output:
[null, null, true, false, true, null, true]

Constraints:

• 1 ≤ word.length, prefix.length ≤ 2000
• word and prefix consist only of lowercase English letters
• At most 3 × 10⁴ calls in total will be made to insert, search, and startsWith