1. (a). [2 mark] What is the lower bound on the runtime of any comparison based sorting algorithm on n elements? (b). [2 mark] What is the worst-case runtime of quicksort on n elements? (c). [2 mark] Below is a tree that is the result of four Union-Find operations, with weighted-union and path compression. The first two operations are union(D,A) and union(B,C), what are the last two operations? A (B (d).12 Marks] Give the definition of little-oh. That is, f(n) is o(g(n)) if and only if... (NOTE: you cannot use the limit definition.) (e). [2 Marks] What is the maximum number of internal nodes in a 2-3 tree with height 4 (Recall, height of a leaf is 0 and leaves are emptyull)