text: # -*- coding: utf-8 -*-
  
  """
  
  For a undirected graph with tree characteristics, we can choose any node as the root. The result graph is then a rooted tree. Among all possible rooted trees, those with minimum height are called minimum height trees (MHTs). Given such a graph, write a function to find all the MHTs and return a list of their root labels.
  
  Format
  The graph contains n nodes which are labeled from 0 to n - 1. You will be given the number n and a list of undirected edges (each edge is a pair of labels).
  
  You can assume that no duplicate edges will appear in edges. Since all edges are undirected, [0, 1] is the same as [1, 0] and thus will not appear together in edges.
  
  Example 1:
  
  Given n = 4, edges = [[1, 0], [1, 2], [1, 3]]
  
          0
          |
          1
         / \
        2   3
  return [1]
  
  Example 2:
  
  Given n = 6, edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]
  
       0  1  2
        \ | /
          3
          |
          4
          |
          5
  return [3, 4]
  
  Hint:
  
  How many MHTs can a graph have at most?
  Note:
  
  (1) According to the definition of tree on Wikipedia: “a tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any connected graph without simple cycles is a tree.”
  
  (2) The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.
  
  """
  
  class Solution(object):
  	
  	"""
  	:type n: int
  	:type edges: List[List[int]]
  	:rtype: List[int]
  	"""
  	def findMinHeightTrees(self, n, edges):
  		# the idea is to move from the leave nodes and move
  		# in-ward till we end up with either one or two roots
  		# same idea as topological sort
  		
  		# base case
  		if n == 1: return [0]
  		
  		# keep track of the the undirected edges
  		adj = [set() for i in range(n)]
  		for i, j in edges:
  			adj[i].add(j)
  			adj[j].add(i)
  
  		# leaves are those nodes that have in-degree of length 1
  		leaves = [i for i in range(n) if len(adj[i]) == 1]
  
  		# do BFS topological sorting
  		while n > 2:
  			n -= len(leaves)
  			
  			# next level to the current leaves
  			next_leaves = []
  			
  			# visit all neighbors to each leave
  			for i in leaves:
  				
  				# no need to visit all i neighbors, we are only insterested
  				# in the shortest path so any neighbor is valid
  				j = adj[i].pop()
  				adj[j].remove(i)
  			
  				# new leave found
  				if len(adj[j]) == 1: 
  					next_leaves.append(j)
  
  			# set next level to be visited
  			leaves = next_leaves
  		
  		return leaves
  		
  		
  		
  s = Solution()		
  print s.findMinHeightTrees(4, [[1,0],[1,2],[1,3]])