Problem

1. Let G be a graph with n vertices and m edges such that all the edge weights in G are integers in the range [1,n]. Give an algorithm for finding a minimum spanning tree for G in O(mlog* n) time.

2. Write a class implementing a simplified graph ADT that has only methods relevant to undirected graphs and does not include update methods, using the adjacency matrix structure. Your class should include a constructor method that takes two collections (for example, sequences)-a collection V of vertex elements and a collection E of pairs of vertex elements-and produces the graph G that these two collections represent.