<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:

    void DFS(vector<int>& hights, vector<vector<int>>& adj_list, int v, int p) {
        for (auto u : adj_list[v]) {
            if (u == p) {
                continue;
            }
            DFS(hights, adj_list, u, v);
        }
        for (auto u : adj_list[v]) {
            if (u == p) {
                continue;
            }
            hights[v] = max(hights[v], hights[u] + 1);
        }
    }

    vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
        vector<int> hights(n, 0);
        vector<vector<int>> adj_list(n);
        for (auto& edge : edges) {
            adj_list[edge[0]].push_back(edge[1]);
            adj_list[edge[1]].push_back(edge[0]);
        }
        DFS(hights, adj_list, 0, -1);
        vector<int> result;
        result.push_back(0);
        int parent = 0;
        while (true) {
        int min_hight = hights[parent];
        int hight_vert = -1;
        for (auto u : adj_list[parent]) {
            if (hights[u] == min_hight - 1) {
                if (hight_vert == -1) {
                    hight_vert = u;
                } else {
                    return result;
                }
            }
        }
        int new_hight_for_parent = 0;
        for (auto u : adj_list[parent]) {
            if (u == hight_vert) {
                continue;
            }
            new_hight_for_parent = max(new_hight_for_parent, hights[u] + 1);
        }
        int new_hight = max(min_hight - 1, new_hight_for_parent + 1);
        if (new_hight > min_hight) {
            return result;
        }
        if (new_hight == min_hight) {
            result.push_back(hight_vert);
            return result;
        }
        result.clear();
        result.push_back(hight_vert);
        hights[parent] = new_hight_for_parent;
        parent = hight_vert;
        }

        return result;
    }
};
57434