Due: Wednesday, April 24th in class Late assignments will be penalized 20% per day.

Book Questions from Introduction to Algorithms - 3rd ed.

23.1-2, 23.2-4, 23.2-5, 24.1-1, 24.3-1

Hints:

23.1-2 - Consider the following graph

23.2-4 - Note that the running time of Kruskal’s algorithm is given by

But since |E| < |V²|, O(lg E) = O(lg V²) = O(2 lg V) = O(lg V) and hence O(E lg E) = O(E lg V). Which parts can be improved if we know the range of edge weights?

23.2-5 - Note that the running time of Prim’s algorithm is given by

Consider using an array rather than a heap. How does this affect the above parts when the range of weights in known?