from collections import deque

class Solution:

  # build a unidrictional graph 
  def build_graph(self, nodes, edges):
    graph, indegree = {}, {}
    for i in range(nodes):
      graph[i] = []
      indegree[i] = 0 
    for node1, node2 in edges:
      graph[node1].append(node2)
      graph[node2].append(node1)
      indegree[node1] += 1
      indegree[node2] += 1
    return(graph, indegree)
   
  def findTrees(self, nodes, edges):
    if nodes == 1:
      return [0]

    graph, indegree = self.build_graph(nodes, edges)
    q = deque([x for x in indegree if indegree[x] == 1])

    result = []
    
    # topological ordering can be done on unidirectional graph too
    # for that we should do indegree[neighbor] == 1 as edge nodes are linked
    # topological finds the center of graph in unidirectional graph 
    # e.g. A -- B -- C --- D 
    # topological ordering will start with A and D as edge nodes and goes to the center [B,C]
    # the center can have one or more nodes. so we go level by level "its a BFS at the end"
    # center nodes will give you the shortest trees for sure!
    while q:
      result.clear()
      for _ in range(len(q)): # for each level
        node = q.popleft()
        result.append(node) # the result contains the level nodes = last level 
        for neighbor in graph[node]:
          indegree[neighbor] -= 1
          if indegree[neighbor] == 1:
            q.append(neighbor)
    
    return result