208\. Implement Trie (Prefix Tree)

Medium

A [**trie**](https://en.wikipedia.org/wiki/Trie) (pronounced as "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"); trie.search("apple"); // return True
    trie.search("app"); // return False
    trie.startsWith("app"); // return True
    trie.insert("app");
    trie.search("app"); // return True 

**Constraints:**

*   `1 <= word.length, prefix.length <= 2000`
*   `word` and `prefix` consist only of lowercase English letters.
*   At most <code>3 * 10<sup>4</sup></code> calls **in total** will be made to `insert`, `search`, and `startsWith`.