Implement Trie (Prefix Tree)
<p>A <a href="https://en.wikipedia.org/wiki/Trie" target="_blank"><strong>trie</strong></a> (pronounced as &quot;try&quot;) or <strong>prefix tree</strong> 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.</p>

<p>Implement the Trie class:</p>

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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;Trie&quot;, &quot;insert&quot;, &quot;search&quot;, &quot;search&quot;, &quot;startsWith&quot;, &quot;insert&quot;, &quot;search&quot;]
[[], [&quot;apple&quot;], [&quot;apple&quot;], [&quot;app&quot;], [&quot;app&quot;], [&quot;app&quot;], [&quot;app&quot;]]
<strong>Output</strong>
[null, null, true, false, true, null, true]

<strong>Explanation</strong>
Trie trie = new Trie();
trie.insert(&quot;apple&quot;);
trie.search(&quot;apple&quot;);   // return True
trie.search(&quot;app&quot;);     // return False
trie.startsWith(&quot;app&quot;); // return True
trie.insert(&quot;app&quot;);
trie.search(&quot;app&quot;);     // return True
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= word.length, prefix.length &lt;= 2000</code></li>
	<li><code>word</code> and <code>prefix</code> consist only of lowercase English letters.</li>
	<li>At most <code>3 * 10<sup>4</sup></code> calls <strong>in total</strong> will be made to <code>insert</code>, <code>search</code>, and <code>startsWith</code>.</li>
</ul>
Design; Trie; Hash Table; String
public class Trie {
    bool isEnd;
    Trie[] children = new Trie[26];

    public Trie() {

    }

    public void Insert(string word) {
        Trie node = this;
        foreach (var c in word)
        {
            var idx = c - 'a';
            node.children[idx] ??= new Trie();
            node = node.children[idx];
        }
        node.isEnd = true;
    }

    public bool Search(string word) {
        Trie node = SearchPrefix(word);
        return node != null && node.isEnd;
    }

    public bool StartsWith(string prefix) {
        Trie node = SearchPrefix(prefix);
        return node != null;
    }

    private Trie SearchPrefix(string s) {
        Trie node = this;
        foreach (var c in s)
        {
            var idx = c - 'a';
            if (node.children[idx] == null)
            {
                return null;
            }
            node = node.children[idx];
        }
        return node;
    }
}

/**
 * Your Trie object will be instantiated and called as such:
 * Trie obj = new Trie();
 * obj.Insert(word);
 * bool param_2 = obj.Search(word);
 * bool param_3 = obj.StartsWith(prefix);
 */
