<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>

'''
Need to keep filtering out nodes until we have nodes with degree 0 or 1

1. Create adj list for all nodes [node:[list of edges]]
2. Get leaf nodes for the tree and keep removing them until you have 0 or 1 nodes left (using bfs)
3. Return the remaining nodes as answer
'''
from collections import defaultdict
class Solution:
    def findMinHeightTrees(self, n: int, edges: List[List[int]]) -> List[int]:
        if n < 2:
            return [0]
        #create adjList
        adjList = defaultdict(list)
        for e1,e2 in edges:
            adjList[e1].append(e2)
            adjList[e2].append(e1)
        #Get all leaf nodes
        leaf = []
        for e in adjList:
            if len(adjList[e]) == 1:
                leaf.append(e)
        #do a bfs and remove nodes from leaf
        #remove the popped node from all its connected nodes
        #if the connected nodes size is size is 1 add it to leaf
        newLeaf = []
        # while n > 2:
        #     n -= len(leaf)
        #     newLeaf = []
        #     for e in leaf:
        #         connectedNode = adjList[e].pop()
        #         adjList[connectedNode].remove(e)
        #         if len(adjList[connectedNode]) == 1:
        #             newLeaf.append(connectedNode)
        #         leaf = newLeaf

        while n > 2:
            n -= len(leaf)
            newLeaf = []
            # current = leaf.pop(0)
            # if not leaf:
            #     leaf = newLeaf
            #     newLeaf = []
            # modify = adjList[current]
            for e in leaf:
                connectedNode = adjList[e].pop(0)
                adjList[connectedNode].remove(e)
                if len(adjList[connectedNode]) == 1:
                     newLeaf.append(connectedNode)
                leaf = newLeaf                                        
        return leaf


        
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