Problem

(a) List all structures that are both heaps and binary search trees. Assume that all elements of the structures have different values.

(b) Use the linear-time heap creation algorithm to create a heap out of the following keys: 10 12 1 14 6 5

(c) Consider that you have a class named Heap that preserves a heap of integers using an array of int - "elements" and an int variable named "count". Write a Heap method named isCorrect to check that the heap is correctly built.

(d) Write a Heap method named incrementPriority that, given the position of an element in the array just described, adds 1 to its value and reorganizes the heap if necessary. The reorganization should require no more than O(log n) operations, where n is the current number of heap elements.