Question: We again consider directed graphs, with nodes 1..n and with a edges (this time without weights). Our aim is now to reverse the graph; that

We again consider directed graphs, with nodes 1..n and with a

We again consider directed graphs, with nodes 1..n and with a edges (this time without weights). Our aim is now to reverse the graph; that is, from a given graph (V, E) we want to construct a graph (V, E) such that for all i and k in V, E contains an edge fro to k iff E contains an edge from k toi 1. (10p) First assume the graph is represented as an adjacency matrix A, with the boolean A(i, k) true iff the graph has an edge fromi to k. Write an algorithm to implement this specification, and analyze its running time, as a function of n and of a 2. (5p) Next assume the graph is represented as adjacency lists L (that is, for cachi e 1..n, the list L[i] contains the targets of edges with source i). Then the specification can be implemented by the algorithm below (where CONs adds an edge to a list of edges) whose running time, as a function of n and of a, you must analyze. for k 1 to n ,[A] EMPTY or i 1 to n foreach k E Li

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Text: 2.(10p). We shall now consider directed graphs, where each edge has a weight (a positive integer). The algorithm below takes as input a directed graph G with nodes 1..n and with a edges, and...

Consider the algorithm below whose input is a directed graph G with nodes 1..n and with a edges, and which for each i 1..n computes in A[i] the number of incoming edges to i. for i 1 to n A[i] 0 for...

Discrete Math Directed Graphs Let us first give the formal definition: Definition (Directed graph). A directed graph is given by a set of vertices V and a transition relation T C V x V. We write 9 =...

everything above this is background information and everything below that says #grade is what i need help with Graphs In graph theory, a graph is a set of nodes ("vertices") that are connected to one...

The algorithm used in lecture was minimum spanning arborescence. 5. (a) Find a directed graph where Prims algorithm doesn't yield the arborescence of minimum cost. Your example graph should not...

1 . ( a ) For a graph G , consider two edge - weight functions w 1 and w 2 such that w 1 ( e ) w 1 ( e ) w 2 ( e ) w 2 ( e ) for all edges e , e E . Show that T is an MST wrt w 1 iff it is an MST wrt...

This question tests the following learning outcomes: Apply general-purpose data structures and algorithmic techniques to efficiently solve computational problems. Explain in a clear and succinct way...

For this assignment, you will write a program to find a maximum flow in a flow network. User Requirements The user is a start-up software company that specializes in software for combinatorial...

( a ) For a graph G , consider two edge - weight functions w 1 and w 2 such that w 1 ( e ) w 1 ( e ' ) L o n g l e f t r i g h t a r r o w w 2 ( e ) w 2 ( e ' ) for all edges e , e ' inE. Show that T...

nodes, but at least its bias can be quantified by Markov Chain L. INTRODUCTION analysis and thus can be corrected via appropriate re-weighting The popularity of online social networks (OSNs) in...

Comment on the following statement, which is attributed to Robert Heinlein: "A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a...

A gas mixture is found to contain two diatomic A and B species for which the partial pressures of both are 0.05065MPa (0.5atm). This mixture is to be enriched in the partial pressure of the A species...

According to the Census Bureau, in October 2 0 1 6 , the average house price in the United States was $ 2 8 , 4 5 8 . 7 years earlier, the average price was $ 2 2 , 3 0 8 . What was theannual...

Which of the following are problems with identifying users of ABC? Multiple select question. ABC means different things to different organizations. Organizations will announce the discontinuance of...

2-15 Describe the Information systems and IT infrastructure at Income after migrating to the fully digital system. NTUC Income (Income), one of Singapores largest insurers, has over 2 million policy...

2-17 How well is Income prepared for the future? Are the problems described in the case likely to be repeated? NTUC Income (Income), one of Singapores largest insurers, has over 2 million policy...

2-16 What benefits did Income reap from the new system? NTUC Income (Income), one of Singapores largest insurers, has over 2 million policy holders with total assets of S$31.3 billion. The insurer...