<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>

'''
Min height tree the main logic can be translated to:
 - keep removing all nodes having a degree of 1 until you are left with 2 or less nodes
 - these nodes are the sol

1. For each edge find the node connectivity
    -1a. Use defaultdict(list) for each node and add one node to the connectivity of the other node and vice versa
2. Identify all the leaf nodes from the graph
3. Keep removing leaf nodes from the graph, decrease the degree of the other nodes
4. Continue step 3 until we have 2 or less nodes  
'''
class Solution:
    def findMinHeightTrees(self, n: int, edges: List[List[int]]) -> List[int]:
      if n < 3:
        return [i for i in range(n)]
      adjNodes = defaultdict(list)
      leaf = []

      for e in edges:
        adjNodes[e[0]].append(e[1])
        adjNodes[e[1]].append(e[0])

      for i in range(n):
        if len(adjNodes[i]) == 1:
          leaf.append(i)
        
      while n > 2:
        n -= len(leaf)
        newLeaf = []
        for e in leaf:
          connectedNode = adjNodes[e].pop()
          adjNodes[connectedNode].remove(e)
          if len(adjNodes[connectedNode]) == 1:
            newLeaf.append(connectedNode)
          leaf = newLeaf
      return leaf
27300