<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> dfs(int u, int p, vector<int> adj[], vector<vector<int>> &h){
        int mx1=0, mx2=0;
        for(auto e:adj[u]){
            if(e==p) continue;
            int hc=1+dfs(e,u,adj,h)[0];
            if(hc>mx2){
                swap(hc,mx2);
                if(mx2>mx1)
                  swap(mx1,mx2);
            }

        }
        return h[u]={mx1,mx2};
    }


    void dpp(int u, int p, vector<int> adj[], vector<vector<int>> &h){


    
            if(p!=-1){
                int best=h[p][0]+1;
                if(h[u][0]+1==h[p][0]) best=h[p][1]+1;
                if(h[u][1]<best){
                    swap(h[u][1],best);
                    if(h[u][0]<h[u][1])
                        swap(h[u][0],h[u][1]);
                }
            }

        for(auto e:adj[u]){
            if(e==p) continue;
            dpp(e,u,adj,h);
        }


    }


    vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
        vector<int> adj[n+1];
        for(auto e:edges){
            adj[e[0]].push_back(e[1]);
            adj[e[1]].push_back(e[0]);
        }

        vector<vector<int>> h(n);
        dfs(0,-1, adj,h);
        for(auto e:h) cout<<e[0]<<" "<<e[1]<<"\n";
        cout<<"done \n";

        dpp(0, -1, adj, h);
        map<int,vector<int>> mp;

        for(auto e:h) cout<<e[0]<<" "<<e[1]<<"\n";
        cout<<"\n";

        for(int i=0;i<n;i++){
            mp[h[i][0]].push_back(i);
        }

        return (mp.begin())->second;

        return {-1};


    }
};
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