implement-trie-prefix-tree

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Algorithms

A <a href="https://en.wikipedia.org/wiki/Trie" target="_blank">trie</a> (pronounced as &quot;try&quot;) 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:

<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>

&nbsp;
Example 1:

<pre>
Input
[&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;]]
Output
[null, null, true, false, true, null, true]

Explanation
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>

&nbsp;
Constraints:

<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 * 104</code> calls in total will be made to <code>insert</code>, <code>search</code>, and <code>startsWith</code>.</li>
</ul>