<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>

class Solution {
public:
    vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
        
        
        //1) create adjacency List 
        set<int> MHTRoots;
        vector<int> height(n,0);
        
        vector<vector<int>> adjList(n);
        
        for (int e=0;e<n-1;++e){
            int a=edges[e][0];
            int b=edges[e][1];
            adjList[a].push_back(b);
            adjList[b].push_back(a);
        } 
        
        //2) add all leaf nodes to the queue
        queue<int> leafQ;
        for (int i=0;i<n;++i){
            MHTRoots.insert(i);
            if (adjList[i].size()==1)
                leafQ.push(i);
        }
        
        
        // 3)in each round dequeue a leaf node and update the adjecency list of its parent. if the parent has degree 1 add it to the queue.
        while (MHTRoots.size()>2){
            int leaf=leafQ.front();
            leafQ.pop();
            MHTRoots.erase(leaf);
            int parent=adjList[leaf][0];
            adjList[parent].erase(
                remove(adjList[parent].begin(), adjList[parent].end(), leaf), 
                adjList[parent].end());
            
            height[parent]=max(height[leaf]+1,height[parent]);
           
            if(adjList[parent].size()==1){
                leafQ.push(parent);
            }
        }

        // do until there is olny one or two nodes in a graph and return them as the root of MHT
        vector <int> roots(MHTRoots.begin(),MHTRoots.end());
        if (MHTRoots.size()==2&& height[roots[0]]<height[roots[1]]){
            roots.erase(roots.begin());
        }
        else if (MHTRoots.size()==2&& height[roots[0]]>height[roots[1]]){
            roots.erase(roots.end());
        }
        return roots;
    
    }
};
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