Given a n*n adjacency array. it will give you a maximum flow. This version use BFS to search path. Assume the first is the source and the last is the sink. Time complexity - O(Ef) example graph = [[0, 16, 13, 0, 0, 0], [0, 0, 10, 12, 0, 0], [0, 4, 0, 0, 14, 0], [0, 0, 9, 0, 0, 20], [0, 0, 0, 7, 0, 4], [0, 0, 0, 0, 0, 0]] answer should be 23 """ import copy import queue import math def maximum_flow_bfs(adjacency_matrix): """ Get the maximum flow through a graph using a breadth first search """ #initial setting new_array=copy.deepcopy(adjacency_matrix) total=0 whileTrue: #setting min to max_value min_flow=math.inf #save visited nodes visited= [0]*len(new_array) #save parent nodes path= [0]*len(new_array) #initialize queue for BFS bfs=queue.Queue() #initial setting visited[0] =1 bfs.put(0) #BFS to find path whilebfs.qsize() >0: #pop from queue src=bfs.get() forkinrange(len(new_array)): #checking capacity and visit if(new_array[src][k] >0andvisited[k] ==0 ): #if not, put into queue and chage to visit and save path visited[k] =1 bfs.put(k) path[k] =src #if there is no path from src to sink ifvisited[len(new_array) -1] ==0: break #initial setting tmp=len(new_array) -1.

In this implementation, the maximum_flow_bfs function takes an adjacency matrix as input and…

Answered: t will give you a maximum flow. This…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Given a n*n adjacency array.
	it will give you a maximum flow.
	This version use BFS to search path.

	Assume the first is the source and the last is the sink.

	Time complexity - O(Ef)

	example

	graph = [[0, 16, 13, 0, 0, 0],
	[0, 0, 10, 12, 0, 0],
	[0, 4, 0, 0, 14, 0],
	[0, 0, 9, 0, 0, 20],
	[0, 0, 0, 7, 0, 4],
	[0, 0, 0, 0, 0, 0]]

	answer should be

	23

	"""
	import copy
	import queue
	import math

	def maximum_flow_bfs(adjacency_matrix):
	"""
	Get the maximum flow through a graph using a breadth first search
	"""
	#initial setting
	new_array=copy.deepcopy(adjacency_matrix)
	total=0

	whileTrue:
	#setting min to max_value
	min_flow=math.inf
	#save visited nodes
	visited= [0]*len(new_array)
	#save parent nodes
	path= [0]*len(new_array)

	#initialize queue for BFS
	bfs=queue.Queue()

	#initial setting
	visited[0] =1
	bfs.put(0)

	#BFS to find path
	whilebfs.qsize() >0:
	#pop from queue
	src=bfs.get()
	forkinrange(len(new_array)):
	#checking capacity and visit
	if(new_array[src][k] >0andvisited[k] ==0 ):
	#if not, put into queue and chage to visit and save path
	visited[k] =1
	bfs.put(k)
	path[k] =src

	#if there is no path from src to sink
	ifvisited[len(new_array) -1] ==0:
	break

	#initial setting
	tmp=len(new_array) -1.

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