<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 {
private:
    vector<vector<int>> g;
    vector<int> dis;
    vector<int> par;
    
    void dfs(int node, int parent, int d){
        dis[node] = d;
        par[node] = parent;
        for (int ngbh: g[node]){
            if (ngbh == parent) continue;
            if (dis[ngbh] != -1) continue;
            dfs(ngbh, node, d+1);
        }
        return;
    }

    int farnode(int root, vector<int>& dis, int n){
        int ans = root;
        for (int i = 0; i < n; i++){
            if (dis[ans] < dis[i]) ans = i;
        }
        return ans;
    }

public:
    vector<int> findMinHeightTrees(int n, vector<vector<int>>& ed) {
        g.resize(n);
        par.assign(n, -1);
        dis.assign(n, -1);

        for (int i = 0; i < (int)ed.size(); i++){
            int n0 = ed[i][0]; int n1 = ed[i][1];
            g[n0].push_back(n1);
            g[n1].push_back(n0);
        }

        dfs(0, -1, 0);
        int d1 = farnode(0, dis, n);

        par.assign(n, -1);
        dis.assign(n, -1);
        
        dfs(d1, -1, 0);
        int d2 = farnode(d1,dis, n);

        int dia = dis[d2];
        vector<int> ans;
        int node = d2;
        for (int i = 0; i < dia/2;i++){
            node = par[node];
        }
        ans.push_back(node);
        if (dia % 2 == 1) ans.push_back(par[node]);

        return ans;
    }
};
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