5. (10 points) Given an array A[1, 2,..., n] of numbers (some or all of which may be negative), we want to design a divide-and-conquer algorithm to find the sub array Ai, i +1,..., k] such that L-i A[j] is maximum. We want our algorithm to be as eficient as possible as regards its worst case complexity. Show all work including the recurrence relation that arises and its solution by master theprem. (Your score will depend on the worst case complexity of your valid algorithm!]