CS 216 - Data Structures Homework #8

NOTE: This work is to be done in groups of 2-3.

Minimum Spanning Trees - Prim's Algorithm

Create a Java graphical minimum spanning tree demonstration MSTDemo that:

• gets a number of points as the first (optional) command line argument, or defaults to 1000 if none is given,
• generates the given number of random points with (x,y) each in the range [0,1),
• assumes an undirected edge between each distinct pair of points, weighted with the distance between the points,
• computes a minimum spanning tree using Prim's algorithm, and
• graphically displays this minimum spanning tree.

Your application may build on the Kruskal's algorithm demonstration code presented in class.

Note: A priority queue is necessary for Prim's algorithm.  Java's PriorityQueue class does not have the needed functionality of HEAP-INCREASE-KEY (Cormen et al, Introduction to Algorithms, 2nd ed, p. 140).  Note also that the HEAP-INCREASE-KEY procedure assumes that the index of the key is known by the caller.  A linear scan of the nodes to determine the index affects computational time complexity.  Maintaining a hash table to look up key indices provides a tradeoff of memory to keep this operation logarithmic.  Although your implementation need not be the most efficient, your computation for 1000 points should not require a significant wait.