<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) {
    //     // unordered_map<int, vector<int>> links;
    //     vector<vector<int>> graph (n, vector<int>());
    //     vector<int> degree (n, 0);

    //     int remainingGraph = n;

    //     for (int i=0; i< edges.size(); i++){
    //         graph[edges[i][0]].push_back(edges[i][1]);
    //         graph[edges[i][1]].push_back(edges[i][0]);
    //         degree[edges[i][0]]++;
    //         degree[edges[i][1]]++;
    //     }

    //     queue<int> leafs;


    //     for (int i=0 ; i < n; i++){
    //         if (degree[i]==1) leafs.push(i);
    //     }


    //     while (remainingGraph== 1 || remainingGraph == 2){
    //         queue<int> pLeafs;

    //         while (!leafs.empty()){
    //             int currLeaf = leafs.pop();
    //             remainingGraph--;

    //             for (int i=0; i< graph[currLeaf].size(); i++){
    //                 if (graph[currLeaf][i]!=-1){
    //                     int parent = graph[currLeaf][i];
    //                     graph[currLeaf][i] = -1;


    //                 }
    //             }
    //         }
    //     } 




    // }

    vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {

        vector<unordered_set<int>> graph (n, unordered_set<int>());


        for ( int i=0; i< edges.size(); i++){
            graph[edges[i][0]].insert(edges[i][1]);
            graph[edges[i][1]].insert(edges[i][0]);
        }

        queue<int> leafs;
        queue<int> pLeafs;

        for (int i=0; i<n ; i++){
            if (graph[i].size()==1) pLeafs.push(i);
        }

        int remainingGraph = n;
        

        // int round=1;
        // cout << "test " << remainingGraph <<endl;
        while (remainingGraph > 2) {
            // cout << "round" << round << endl;
            
            while ( !pLeafs.empty() ){
                leafs.push( pLeafs.front()); pLeafs.pop();
            }
            while ( !leafs.empty() ) {
                
                int leaf =  leafs.front(); leafs.pop();
                // cout << leaf << " " ;
                remainingGraph--;
                int parent = *graph[leaf].begin();

                graph[parent].erase(leaf);
                graph[leaf].erase(parent);
                if (graph[parent].size()==1){
                    pLeafs.push(parent);
                }
            }
            // cout << endl;

            
        }

        vector<int> ans;

        if (n==1){
            ans.push_back(0); return ans;
        }

        while (!pLeafs.empty()){
            ans.push_back(pLeafs.front()); pLeafs.pop();
        }

        return ans;
        
    }


};
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