CMPS 101
Abstract Data Types
Spring 2003
Programming Assignment 5
Due Wednesday June 4, 12:00 midnight
In the assignment you will extend your Graph module in C to implement Kruskal’s algorithm for finding
a minimum weight spanning tree in a weighted (undirected) graph. It is recommended that you use your
graph module from pa4 as a starting point for this project. However, since extensive changes to the
design will be necessary, you may choose to start from scratch. In any case it is not required that your
graph module in this project be backward compatible with pa4, or that the functionality from that project
be maintained.
One significant difference between this project and pa4 is that you will be working with undirected
graphs. Thus it will be necessary to create a function called AddEdge(u, v) (instead of AddDirectedEdge)
which establishes an undirected edge joining vertices u and v. AddEdge(u, v) will add v to the adjacency
list of u, and u to the adjacency list of v. Another difference is that each edge will posses a label as well
as a weight. It will therefore be worthwhile to include a private Edge struct (analogous to Node in List) in
your Graph module which encapsulates label, and weight, together with any other data associated with an
edge, such as it’s end vertices. The struct GraphStruct should then include a (dynamically allocated) array
of pointers to these Edges.
Kruskal’s algorithm requires that edges be processed in non-decreasing order by weight. Your Graph
module should therefore include a (private) function which will sort the Edge array. You may use any
sorting algorithm you like to implement this function. Kruskal’s algorithm also utilizes a disjoint set data
structure. Your project will implement this structure as a separate ADT module called DisjointSet. Your
DisjointSet module may use the linked list representation with weighted union heuristic, or the disjoint set
forest representation with union-by-rank and path compression heuristics. Design decisions such as these
should of course be carefully documented in your README file.
Your DisjointSet module will export the following functions.
/* Constructors-Destructors */
DisjointSetHndl NewDisjointSet(int n);
void FreeDisjointSet(DisjointSetHndl *pS);
/* Access functions */
int getNumElements(DisjointSetHndl S);
int getNumSets(DisjointSetHndl S);
int FindSet(DisjointSetHndl S, int x);
/* Manipulation procedures */
void Union(DisjointSetHndl S, int x, int y);
The elements of each member of a collection of disjoint sets will be integers. Function NewDisjointSet
returns a handle to a new DisjointSet object representing the collection {{1}, {2}, {3}, ..., { n}}. Thus
there is no need for a MakeSet function, since NewDisjointSet does essentially n MakeSet operations at
once. Function FreeDisjointSet frees all heap memory associated with a DisjointSet object, and sets its
DisjointSetHndl to Null. Functions getNumElements and getNumSets return the number of underlying
elements, and the number of sets in the collection, respectively. Function FindSet returns the
