<p>A tree is an undirected graph in which any two vertices are connected by&nbsp;<i>exactly</i>&nbsp;one path. In other words, any connected graph without simple cycles is a tree.</p>

<p>Given a tree of <code>n</code> nodes&nbsp;labelled from <code>0</code> to <code>n - 1</code>, and an array of&nbsp;<code>n - 1</code>&nbsp;<code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an undirected edge between the two nodes&nbsp;<code>a<sub>i</sub></code> and&nbsp;<code>b<sub>i</sub></code> in the tree,&nbsp;you can choose any node of the tree as the root. When you select a node <code>x</code> as the root, the result tree has height <code>h</code>. Among all possible rooted trees, those with minimum height (i.e. <code>min(h)</code>)&nbsp; are called <strong>minimum height trees</strong> (MHTs).</p>

<p>Return <em>a list of all <strong>MHTs&#39;</strong> root labels</em>.&nbsp;You can return the answer in <strong>any order</strong>.</p>

<p>The <strong>height</strong> of a rooted tree is the number of edges on the longest downward path between the root and a leaf.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/01/e1.jpg" style="width: 800px; height: 213px;" />
<pre>
<strong>Input:</strong> n = 4, edges = [[1,0],[1,2],[1,3]]
<strong>Output:</strong> [1]
<strong>Explanation:</strong> As shown, the height of the tree is 1 when the root is the node with label 1 which is the only MHT.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/01/e2.jpg" style="width: 800px; height: 321px;" />
<pre>
<strong>Input:</strong> n = 6, edges = [[3,0],[3,1],[3,2],[3,4],[5,4]]
<strong>Output:</strong> [3,4]
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>edges.length == n - 1</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>All the pairs <code>(a<sub>i</sub>, b<sub>i</sub>)</code> are distinct.</li>
	<li>The given input is <strong>guaranteed</strong> to be a tree and there will be <strong>no repeated</strong> edges.</li>
</ul>

#include <vector>
#include <unordered_map>
#include <unordered_set>
#include <queue>

class Solution {
public:
    std::vector<int> findMinHeightTrees(int n, std::vector<std::vector<int>>& edges) {
        if (n == 1) return {0}; // A single node is always a root of MHT
        if (n == 2) return {0, 1}; // Two nodes are both roots of MHT
        
        // Build the adjacency list
        std::unordered_map<int, std::unordered_set<int>> adj;
        for (const auto& edge : edges) {
            adj[edge[0]].insert(edge[1]);
            adj[edge[1]].insert(edge[0]);
        }
        
        // Initialize the leaves (nodes with one connection)
        std::queue<int> q;
        for (const auto& pair : adj) {
            if (pair.second.size() == 1) {
                q.push(pair.first);
            }
        }
        
        int remainingNodes = n;
        while (remainingNodes > 2) {
            int leavesCount = q.size();
            remainingNodes -= leavesCount;
            for (int i = 0; i < leavesCount; ++i) {
                int leaf = q.front();
                q.pop();
                // Remove the leaf from its neighbor
                int neighbor = *adj[leaf].begin();
                adj[neighbor].erase(leaf);
                if (adj[neighbor].size() == 1) {
                    q.push(neighbor);
                }
            }
        }
        
        // Remaining nodes in the queue are the roots of the MHTs
        std::vector<int> result;
        while (!q.empty()) {
            result.push_back(q.front());
            q.pop();
        }
        
        return result;
    }
};

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