Problem 1. (10 points) Show diagrammatically all stages of min-heap construction with the following keys stored in an array in that order: 26.9, 8, 22, 6, 14, l 115, 10, 7, I 3, 12, 25, 5, I 3 You should se the ellicient O(r) heapify algorithu. Problem 2. (20 points) Implement a function HEAP DELETE A,i) that deletes the item in location i from heap A and stll maintains the heap property. Your implementation should run in O(logn) time for an n-element min-heap. Prove the tine-complexily of your algorih Problem 3. (20 points) Given A , a sequence of n integers and k is an integer, l