Chapter 29.4, Problem 29.4.3CP

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) };

Prim’s Algorithm:

Prim’s Algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph by finding a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.