1. (a). [2 mark] If a free tree has n nodes, then how many edges does it have? (b). [2 mark] Given a graph G (V,E) where IVIn and |El m, what is the worst-case running time of Prim's algorithm for finding a minimum spanning tree? (c). [2 mark] Suppose that logn f (n)/g(n)0. Is f (n) E o(g(n)) or is g(n) E o(f (n)? (d). [2 Marks] Consider the following id] array which is the result of a sequence of quick-unions. Draw the corresponding disjoint set trees idli] 9779376 759 e). 12 Marks) What is the least number of internal nodes in a left-leaning red-black tree with 2 red edges