<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<vector<int>> g;
    
    void dfs(int level, int node, int par, vector<int> &dist, vector<int> &parent) {
        dist[node] = level;
        parent[node]=par;
        for(auto x: g[node]){
            if(x!=par){
                dfs(level+1, x, node, dist, parent);
            }
        }
    }
    vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
        g.resize(n+1);
        for(auto e: edges){
            g[e[0]+1].push_back(e[1]+1);
            g[e[1]+1].push_back(e[0]+1);
        }

        if(n==1) return {0};

        vector<int> dist(n+1, 1e9);
        vector<int> par(n+1, 0);
        dfs(0, 1, 0, dist, par);
        int maxm = dist[1], x1 = 1;
        for(int i=1; i<=n; i++){
            if(maxm<dist[i]){
                maxm=dist[i];
                x1=i;
            }
        }

        dfs(0, x1, 0, dist, par);
        maxm = dist[x1]; int x2 = x1;
        for(int i=1; i<=n; i++){
            if(maxm<dist[i]){
                maxm=dist[i];
                x2=i;
            }
        }


        if(maxm%2==0) {
            int ans = x2;
            int mv = maxm/2;
            while(mv--){
                ans = par[ans];
            }
            return {ans-1};
        } 


        int ans1 = x2;
        int mv = maxm/2;
        while(mv--) {
            ans1 = par[ans1];
        }
        int ans2 = par[ans1];
        return {ans1-1, ans2-1};
        
    }
};
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