1. Prove that the time efficiency of find(x) is in O(log n) for the union-by-size version of quick union.
2. Find at least twoWeb sites with animations of Kruskal's and Prim's algorithms. Discuss their merits and demerits.
3. Design and conduct an experiment to empirically compare the efficiencies of Prim's and Kruskal's algorithms on random graphs of different sizes and densities.