Question

Help with Q3 please!

3 (9 pts) For the graph G (VE) in question 2 (above), construct the adjacency lists for G (using alphabetical ordering) and the corresponding reverse graph GR Adjacency list for G (alphabetical ordering): Adjacency list for G. V = {A, B, C, D, G, H, S) V - {A, B, C, D, G, H, S) E A = { EB = EC) - E[D] = {C,G) E[G] - [ ECH - E[S { EA = { ERB - (CS) ERC - E D ERG = { EH- E [S] - Write (using pseudcode) a function reverse (G) to perform the following task: Input: A directed graph G = (VE) Output: The edge list Ek of the adjacency list for the reverse graph GR of G Determine the run-time of the algorithm Ollogno (n) O(nalog n) (1.6) (na)

Answer 1

As I can see the graph for Question 3 , the first thing that comes to my mind is to make a adjacency Matrix which will simplify the graph the graph and can see each vertex clearly , this will also help us to reverse the graph.

So the adjacency Matrix for the graph is

| 이 (0) A (0) | 0 | B(1) | 1 C(2) | 0 D(3) | 0 G(4) 10 H(5) | 0 | S (6) | 0 | (1) | (2) | (3) | (4) | (5) | (6) 0 | 1 | 0 0 101 10 |0 |1 |0 | 0 |1 |0 | 0 |0 10 | 0 |1|0 11 10 |0 |1 10 10 |1 10 10 10 10 | 1 |0|0 0 10 10

in this , as you can see that (A,C)=1 that means Edge A points to C

and this is same for all edges where 1 is filled.

so now as we have this Matrix we can easily fill Adjacency List for G graph

E{A}={C}

E{B}={A,D}

E{C}={B}

E{D}={C,G}

E{G}={C,H}

E{H}={S}

E{S}={B}

So till here we have filled the adjacency table for G graph now we to make a function that will take Adjacency matrix and give us Gr(G reversed graph).

Pseudo Code:-

1) Function will be taking the 2 dimentional Matrix which is our Adjacency matrix as a parameter with a return type of 2D matrix so that it can return the reversed graph adjacency matrix .

Adjacency Matrix with Index

| 이 (0) A (0) | 0 | B(1) | 1 C(2) | 0 D(3) | 0 G(4) 10 H(5) | 0 | S (6) | 0 | (1) | (2) | (3) | (4) | (5) | (6) 0 | 1 | 0 0 101 10 |0 |1 |0 | 0 |1 |0 | 0 |0 10 | 0 |1|0 11 10 |0 |1 10 10 |1 10 10 10 10 | 1 |0|0 0 10 10

2)Initialise the 2D matrix for reversed graph adjacency matrix of exactly same size as original matrix.

3)Now we have to traverse the whole Matrix using 2 'for' Nested Loop or any method of your choice.

4)In the Inner loop we will be checking for the value 1 and as we get the value 1 then we just have to exchange the x and y coordinates with each other and store 1 on that coordinates in Matrix that we have made for Reverse graph. Like this we will get the adjacency matrix for reversed graph.

G-Original Graph Matrix

RG-Reversed Graph Matrix - Initially RG will have all 0 values

suppose in this example we will get 1 at G[1][0] So we have to store 1 at RG[0][1].

G[0][2] is 1 therefore we to store 1 at GR[2][0]

5)After the nested are done traversing each matrix address, we will have our adjacency matrix for reversed graph done.

6)Now we just have to return this reversed Grap Matrix.

A (0) A(O)O B(1) 0 C(2) 1 D(3) 0 G(4) 0 H(5) O (6) 0 B C D G H (1) (2) (3) (4) (5) 1 OOO 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 O O O 1 0 0 0 0 0 1

7) End of function

So Now we got our adjacency Matrix for reversed Graph so now we can easily fill the table for Reversed graph

E{A}={B}

E{B}={C,S}

E{C}={A,D,G}

E{D}={B}

E{G}={D}

E{H}={G}

E{S}={H}

Here is the Reversed Graph:-

$1585781770418_image.png$

I have also added Programming in JAVA it will help you to understand it better.

CODE:-

public class ReverseGraph { public static int[][] reverse(int[][] G) int[][] RG=new int[G.length][G.length]; for(int i=0;i<G.length;i++) for(int j=0; j<G.length;j++) if(G[i][j]==1) RG[j][i]=1; return RG; //DRIVER MAIN METHOD JUST TO CHECK THE PROGRAM OUTPUT public static void main(String[] args) { // TODO Auto-generated method stub int[][] G= {{0,0,1,0,0,0,0},{1,0,0,1,0,0,0},{0,1,0,0,0,0,0},{0,0,1,0,1,0,0},{0,0,1,0,0,1,0},{0,0,0,0,0,0,1},{0,1,0,0,0,0,0}}; int[][] RG=reverse(); for(int i=0;i<G.length; i++) for(int j=0; j<G.length;j++) System.out.print(RG[i][j]+" "); System.out.println();

OUTPUT:- Adjacency Matrix for reversed Graph

<terminated> ReverseGraph [Java Appl 100 000 0 0 1 0 0 0 1 1 0 0 1 1 0 0 01 00000 0001000 0000100 OOO0010