Assignment 3 -- Programming Project Design and Analysis of Algorithms (CS 4071) -- Fall 2016 Diameter and Connected Components of a Network ###Electronic copy of source code due Sunday, Nov. 6 at 12:00 midnight. Hard copy due at beginning of class on Monday, Nov. 7. Include your group number and members of the group as a comment at the beginning of the program and submit only ONE hard copy and ONE electronic copy (have ONE group member upload electronic copy).
Topics covered: Graphs, BFS, distance matrix, diameter, connected components. The topology of a network is modeled with a graph. Write a C++ program that inputs a graph G by first inputting the number of vertices n followed by a sequence of pairs i j where i and j are integers between 0 and n, inclusive, representing the edges of the graph, and ending with a negative integer sentinel to indicate the end of the input. For example, 5 0 1 1 4 2 3 1 3 3 4 -1 represents the graph G = (V,E) given by: V = {0,1,2,3,4} E = {{0,1},{1,4},{2,3},{1,3},{3,4}}. Your program will compute the distance matrix of G, which you will use to compute the diameter of G in the case when G is connected and the connected components of G, otherwise. You can proceed as follows: Implement the graph G with its adjacency matrix Implement the function BFS(G,v) for performing a breadth-first search where the visit operation involves computing the distance from v to the vertex being visited. This will require a queue, which you can get from the Standard Template Library (STL). Implement a function DistanceMatrix(G), which computes the distance matrix of G, where entry ij is assigned the distance from i to j if i and j are connected and -1 otherwise. Have DistanceMatrix() also returns a Boolean value that is true if G is connected and false, otherwise. DistanceMatrix() will call BFS(). Implement a function Diameter(G)that returns the diameter of G if G is connected and -1, otherwise. Diameter(G)will call DistanceMatrix(). Implement a function Components(G)for computing the vertex sets of the connected components of G. Components()will call DistanceMatrix(). Store the entire source code for your program in a single file. Your program should run using g++ on a UNIX platform. Have your program output the adjacency matrix of the graph as well as the distance matrix, the diameter in the case when G is connected and the connected components, otherwise. Output the connected components by outputting the vertex set of each connected component. Your program should be user-friendly, well-commented, with the output welldocumented. Submit the source code for your program on-line by uploading to Blackboard (have ONE member of your group upload. Make sure to include a comment in your program with your Group Number and Group Members). Also submit a hard copy of your program with output for two sample runs, one with a connected graph G and one with a disconnected graph G (ONE hard copy per group submitted at the beginning of class on the due date).