THIS QUESTION IS AN ALGORITHM PROBLEM, PLEASE USE CLEAR ENGLISH PSEUDOCODE AND GIVE A CORRECT SOLUTION!

There is a row of n items, numbered from 1 to n. Each item has an integer value: item i has value A[i], where A[1..n] is an array. You wish to pick some of the items but you cannot pick two adjacent items (that is, you cannot pick both items i and i + 1 for any j). Subject to this constraint, you wish to maximise the total sum of values of the items vou have picked (a) Provide a counterexample to show that it is not always optimal to pick the largest item. (b) Provide a counterexample to show that the optimal solution may require selecting a combination of odd and even numbered elements (c) Give an O(n) algorithm that determines this maximum total sum of values