Break the tree into forest of event trees

even_tree.py

import fileinput

inputs = fileinput.input()
input_vals = []

for n in inputs:
	input_vals.append(n.replace('\n', ''))

numVertices, numEdges = [int(k) for k in input_vals[0].split(' ')]

edges = []

for i in range(numEdges):
	edges.append(tuple([int(k) for k in input_vals[i+1].split(' ')]))

def find_node_group(i, edges, removedEdge):
	count = 1
	stack = [i]

	while stack:
		item = stack.pop()
		for edge in edges:
			if edge in removedEdge:
				continue
			if edge[0] == item:
				stack.append(edge[1])
				removedEdge.add(edge)
				count += 1
			elif edge[1] == item:
				stack.append(edge[0])
				removedEdge.add(edge)
				count += 1
	return count

countEdges = 0
for edge in edges:
	group1NodesCount = find_node_group(edge[0], edges, set(tuple([edge])))
	group2NodesCount = find_node_group(edge[1], edges, set(tuple([edge])))
	if group2NodesCount % 2 == 0 and group1NodesCount % 2 == 0:
		countEdges += 1

print countEdges