Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
11th Edition
ISBN: 9780134670942
Author: Y. Daniel Liang
Publisher: PEARSON
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Chapter 29.5, Problem 29.5.4CP
Program Plan Intro

Weighted Graph:

A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists.

Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them.

Example of storing edge in a weighted graph:

Object[][] edges =

{new Integer(0), new Integer(1), new SomeTypeForWeight(8) };

 Spanning Tree:

In computer science, a Spanning Tree for a graph “G” is a subgraph of “G” that it is a free tree connecting all vertices in “V”.

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DJ and Mark are very lazy guys. These are not the guys from some game, these are the ones playing games all the time. Recently, they bought a new game named "Graph Vertices chooser". The rules of this game are pretty simple. It's a two-player game with each player taking alternating turns starting with DJ. You are given a weighed graph. All the vertices are initially unmarked. In each turn, a player chooses an unmarked vertex and mark it to red or black colour (DJ marks red whereas Mark marks black). The game ends when there is no any unmarked vertex left. After the end of the game, DJ's score will be weight of all the edges in graph such that both the end points of the edge are coloured red. Similarly, score of Mark is sum of weight of edges with both end points being black. DJ would like to maximize difference between his and Mark points, while Mark would like to minimize the difference between DJ's and his score. Both players optimally. Now, you are the one who decided to be the…
Identify the edges that compose the minimum spanning tree of the following graph. You can write a list of the edges, or just circle the weights in the graph of the edges in the MST. 1 6 (O 5 4 4 5 9 7 0 5 8 6 2 2 3 3 6
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