<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 Node:
    def __init__(self):
        self.neighbors = set()
class Solution:
    def findMinHeightTrees(self, n: int, edges: List[List[int]]) -> List[int]:
        if n <= 1:
            return [0]
        nodes = defaultdict(list)
        # create adjacency list
        for n1, n2 in edges:
            nodes[n1].append(n2)
            nodes[n2].append(n1)
        # print(nodes)

        leaves = deque()
        edge_count = {}
        for node, neighs in nodes.items():
            if len(neighs) == 1:
                leaves.append(node)
            edge_count[node] = len(neighs)

        while leaves:
            if n <= 2:
                return list(leaves)
            for i in range(len(leaves)):
                curr_node = leaves.popleft()
                n -= 1
                for nei in nodes[curr_node]:
                    edge_count[nei] -= 1
                    if edge_count[nei] == 1:
                        leaves.append(nei)

        


        # iterate thru nz
        # iterate through its neighbors
        # dfs until the current node is null
        # increment counter every time
        # set maxHeight
        # if it is a new maxHeight, reset the result array 
        # if it is equal to maxHeight, add to result array

        

        # for i, node in nodes.items():
        #     print(i, node.neighbors)
        #     visited = set()
        #     visited.add(i)
        #     currH = findMinHeight(node, 0, visited)
        #     print(i, currH)
            # if currH > maxH:
            #     maxH = currH
            #     maxNodes = [node]
            # elif currH == maxH:
            #     maxNodes.append(node)
        # f(4, 0)
        #   f(5, 1) 
        #       => 2
        #   f(3, 1) 
        #       f(0,2) => 3
        #       f(1,2) => 3
        #       f(2,2) => 3
        #       => 3
        #   => 3

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