<h2><a href="https://leetcode.com/problems/height-of-binary-tree-after-subtree-removal-queries/">2458. Height of Binary Tree After Subtree Removal Queries</a></h2><h3>Hard</h3><hr><div><p>You are given the <code>root</code> of a <strong>binary tree</strong> with <code>n</code> nodes. Each node is assigned a unique value from <code>1</code> to <code>n</code>. You are also given an array <code>queries</code> of size <code>m</code>.</p>

<p>You have to perform <code>m</code> <strong>independent</strong> queries on the tree where in the <code>i^th</code> query you do the following:</p>

<ul>

<li><strong>Remove</strong> the subtree rooted at the node with the value <code>queries[i]</code> from the tree. It is <strong>guaranteed</strong> that <code>queries[i]</code> will <strong>not</strong> be equal to the value of the root.</li>

</ul>

<p>Return <em>an array </em><code>answer</code><em> of size </em><code>m</code><em> where </em><code>answer[i]</code><em> is the height of the tree after performing the </em><code>i^th</code><em> query</em>.</p>

<p><strong>Note</strong>:</p>

<ul>

<li>The queries are independent, so the tree returns to its <strong>initial</strong> state after each query.</li>

<li>The height of a tree is the <strong>number of edges in the longest simple path</strong> from the root to some node in the tree.</li>

</ul>

<p>&nbsp;</p>

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

<img alt="" src="https://assets.leetcode.com/uploads/2022/09/07/binaryytreeedrawio-1.png" style="width: 495px; height: 281px;">

<pre><strong>Input:</strong> root = [1,3,4,2,null,6,5,null,null,null,null,null,7], queries = [4]

<strong>Output:</strong> [2]

<strong>Explanation:</strong> The diagram above shows the tree after removing the subtree rooted at node with value 4.

The height of the tree is 2 (The path 1 -&gt; 3 -&gt; 2).

</pre>

<p><strong class="example">Example 2:</strong></p>

<img alt="" src="https://assets.leetcode.com/uploads/2022/09/07/binaryytreeedrawio-2.png" style="width: 301px; height: 284px;">

<pre><strong>Input:</strong> root = [5,8,9,2,1,3,7,4,6], queries = [3,2,4,8]

<strong>Output:</strong> [3,2,3,2]

<strong>Explanation:</strong> We have the following queries:

- Removing the subtree rooted at node with value 3. The height of the tree becomes 3 (The path 5 -&gt; 8 -&gt; 2 -&gt; 4).

- Removing the subtree rooted at node with value 2. The height of the tree becomes 2 (The path 5 -&gt; 8 -&gt; 1).

- Removing the subtree rooted at node with value 4. The height of the tree becomes 3 (The path 5 -&gt; 8 -&gt; 2 -&gt; 6).

- Removing the subtree rooted at node with value 8. The height of the tree becomes 2 (The path 5 -&gt; 9 -&gt; 3).

</pre>

<p>&nbsp;</p>

<p><strong>Constraints:</strong></p>

<ul>

<li>The number of nodes in the tree is <code>n</code>.</li>

<li><code>2 &lt;= n &lt;= 10⁵</code></li>

<li><code>1 &lt;= Node.val &lt;= n</code></li>

<li>All the values in the tree are <strong>unique</strong>.</li>

<li><code>m == queries.length</code></li>

<li><code>1 &lt;= m &lt;= min(n, 10⁴)</code></li>

<li><code>1 &lt;= queries[i] &lt;= n</code></li>

<li><code>queries[i] != root.val</code></li>

</ul>

</div>