import numpy as np


def createFirstInstance():
	"""
	Transforms the given instance of the min flow cost problem into 
	another one by adding a node to ensure the existence of a inital 
	tree solution
	"""
	pass
	
def computeNodeCosts():
	pass
	
def checkOptimality():
	"""
	Checks if the current tree solution is optimal, if not a non-optimal
	edge is returned
	Output:
	edgeNr - (-1) if solution is optimal, else the index of the edge
	"""
	pass

def updateTreeSolution():
	"""
	"""
	pass
