<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:

    // int calculateHeight(unordered_map<int, vector<int>>& graph, int n,int min_ind){
    //     queue<int> start;
    //     vector<int>visit(n,0);
    //     start.push(min_ind);
    //     int level=0;
    //     while(!start.empty()){
    //         int size=start.size();
    //         for(int i=0;i<size;i++){
    //             int temp=start.front();
    //             start.pop();
    //             if(!visit[temp]){
    //                 visit[temp]=1;
    //                 for(int i:graph[temp]){
    //                     start.push(i);
    //                 }
    //             }
    //         }
    //         if(start.size()>0){
    //             level++;
    //         }
    //     }
    //     return level;
    // }

    // vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
    //     if(n==1){
    //         return {0};
    //     }
    //     unordered_map<int, vector<int>> graph;
    //     vector<int> conDeg(n);
    //     for(auto &edg : edges){
    //         conDeg[edg[0]]++;
    //         conDeg[edg[1]]++;
    //         graph[edg[0]].push_back(edg[1]);
    //         graph[edg[1]].push_back(edg[0]);
    //     }
    //     map<int,vector<int>>res;
    //     vector<int> cat;
    //     for(int i=0;i<n;i++){
    //         int c=calculateHeight(graph,n,i);
    //         cat.push_back(c);
    //         res[c].push_back(i);
    //     }
    //     auto min_it = min_element(cat.begin(), cat.end());
    //     return res[*min_it];
    // }
    vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
    if (n == 1) {
        return {0};
    }

    // Build the graph
    vector<unordered_set<int>> graph(n);
    for (const auto& edge : edges) {
        graph[edge[0]].insert(edge[1]);
        graph[edge[1]].insert(edge[0]);
    }

    // Initialize leaves
    vector<int> leaves;
    for (int i = 0; i < n; ++i) {
        if (graph[i].size() == 1) {
            leaves.push_back(i);
        }
    }

    // Trim the leaves until we reach the centroids
    int remainingNodes = n;
    while (remainingNodes > 2) {
        vector<int> newLeaves;
        remainingNodes -= leaves.size();
        for (int leaf : leaves) {
            int neighbor = *graph[leaf].begin();
            graph[neighbor].erase(leaf);
            if (graph[neighbor].size() == 1) {
                newLeaves.push_back(neighbor);
            }
        }
        leaves = newLeaves;
    }

    return leaves;
}
};
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