If you have not done so already, fork and clone the repository. Import it into Eclipse.
As you may recall, all of the MST algorithms rely on some sort of priority queue that allows you to find the smallest edge in a set of edges (the whole set of edges or the edges in Kruskal’s; those adjacent to the partial MST in Prim’s).
a. Identify an appropriate implementation of priority queues in Java.
b. Sketch how you will use that implementation to order edges by weight.
As you may recall, Prim’s algorithm is intended to work with undirected graphs, rather than directed graphs.
How will you accommodate that issue in your code?
As you may recall, Prim’s algorithm relies on two structures (beyond
the graph): a priority queue of edges left to process and a collection
of the edges already determined to be in the MST. We’ll call the
remaining and the second
The algorithm goes something like the following.
Pick a random vertex Add all of the edges from that vertex to remaining While edges remain Grab the remaining edge with the lowest weight If either vertex is not in the MST Add the edge to mst Add all the edges from that vertex to remaining (arguably, you should only add those that don't lead back to the MST)
How will you implement each of the following steps?
a. Represent the MST. (Remember it’s a collection of edges.)
b. Pick a random vertex.
c. Grab the remaining edge with lowest weight.
d. Determine if a vertex is in the MST.
e. Print out the MST.
Implement Prim’s algorithm. If you are unsure about any of the steps suggested above, you can discuss them with your instructor or mentor, review our suggestions at the end of this lab, or both.
If you find that you have extra time, implement Kruskal’s MST algorithm.
Edgeobjects to keep track of which edges remain. You’ll need to supply an edge comparator, which will look something like the following: (e1,e2) -> e1.weight().compareTo(e2.weight())
ArrayListto keep track of the edges in the MST.
Graphclass (or one of its descendants), you can randomly select a non-null element from
vertices. Alternately, you can choose the first (or last) non-null element.
ArrayLists have a
toStringmethod, you don’t need to do anything special to print out the MST.