<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 Solution0 {
public:
    // Function to find the nodes that form trees with the minimum height
    vector<int> findMinHeightTrees(int numNodes, vector<vector<int>>& edges) {
        // Base case: if there's only one node, it's the root of a minHeightTree
        if (numNodes == 1) return {0};

        // Each node will be an index in an adjacency list
        vector<vector<int>> adjacencyList(numNodes);
        // The degree count for each node
        vector<int> degrees(numNodes, 0);

        // Construct the graph
        for (const auto& edge : edges) {
            int nodeA = edge[0], nodeB = edge[1];
            adjacencyList[nodeA].push_back(nodeB);
            adjacencyList[nodeB].push_back(nodeA);
            degrees[nodeA]++;
            degrees[nodeB]++;
        }

        // Initialize a queue for processing leaf nodes (nodes with degree 1)
        queue<int> processingQueue;
        for (int i = 0; i < numNodes; ++i) {
            if (degrees[i] == 1) {
                processingQueue.push(i);
            }
        }

        // Vector to hold the minimum height tree roots
        vector<int> minHeightRoots;

        // Process the graph
        while (!processingQueue.empty()) {
            // Start a new level
            minHeightRoots.clear();
            int levelSize = processingQueue.size(); // Number of nodes in the current level

            // Process all nodes in the current level
            for (int i = 0; i < levelSize; ++i) {
                int currentNode = processingQueue.front();
                processingQueue.pop();

                // Add the current node to this level's results
                minHeightRoots.push_back(currentNode);

                // Decrease the degree of adjacent nodes and enqueue new leaf nodes
                for (int adjacentNode : adjacencyList[currentNode]) {
                    if (--degrees[adjacentNode] == 1) { // If it becomes a leaf node
                        processingQueue.push(adjacentNode);
                    }
                }
            }
        }

        // minHeightRoots now contains the roots of tree who have the minimum height
        return minHeightRoots;
    }
};

class Solution1 {
public:
    vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
        return {};
    }
};

class Solution {
public:
vector<int> findMinHeightTrees(int n, vector<vector<int> >& edges) {
    if (n == 1) return {0};
    vector<int> res;
    vector<unordered_set<int>> adj(n);
    queue<int> q;
    for (auto edge : edges) {
        adj[edge[0]].insert(edge[1]);
        adj[edge[1]].insert(edge[0]);
    }
    for (int i = 0; i < n; ++i) {
        if (adj[i].size() == 1) q.push(i);
    }
    while (!q.empty()) {
        res.clear();
        int size = q.size();
        n -= size;
        for (int i = 0; i < size; ++i) {
            int t = q.front(); q.pop();
            res.push_back(t);
            cout <<"Remove " << t << "\n";
            for (auto a : adj[t]) {
            adj[a].erase(t);
            if (adj[a].size() == 1) q.push(a);
            }
        }
    }
    //while (!q.empty()) {
      //  res.push_back(q.front()); q.pop();
    //}
    return res;
}
};
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