.1 marks Consider the element distinctness problem: Given an array A storing n inte- gers, determine whether all the elements in the array are distinct or not. That is, if all the elements in A are unique, return true; return false if there is at least one duplicate element in A. Below four different problem instances are provided; elements bolded are duplicate elements 0 1 2 3 4 5 6 23 1 2 34 false 0 1 2 3 4 5 4 1 22 68 false 0 1 2 3 true 0 1 2 3 4 5 6 7 true Design an algorithm that solves the element distinctness problem. a) [4 marks] Write pseudocode for the algorithm b) Pove your algorithm is correct, do this by proving the two following parts: i) marks] Show that the algorithm terminates in finite time ii) 12 marks) Show that the algorithm always produces correct output e) mark] Explain what the worst case for the algorithm is. d) 3 marks] Perform worst-case analysis to compute the time complexity of the algorithm. You must give the order of your complexity function using Big-Oh notation, and you must explain how you computed the time complexity