(a) [3 points] Let A be an array with n distinct integer elements. Let ALGOA be an arbitrary algorithm that needs to find a pair of elements from A such that the elements sum to k. You may assume AlgoA can always find such a pair. Explain using the number of leaves in a decision tree why ALGOA must take N2(log n) time in the worst-case. Make sure that in your answer you explain how many leaves the decision tree has, how this affects the decision tree, and why AlgoA must have N(log n) worst-case time. (b) (3 points] Consider a sorted array B with n > 2 integers, where n mod 2 0. Let AlgoB be an arbitrary algorithm that checks whether every value in B occurs exactly twice. Prove that AlgoB needs to make at least a comparisons in the worst-case