Suppose that we would like to verify if the elements in array A satisfy the heap property, assuming the usual heap implementation shown in class. Write the pseudo-code for a recursive algorithm called VerifyHeap(A), which returns true if A is indeed a valid max-heap, and false otherwise. You may use the attribute A:heapsize. Write the recurrence for the runtime of your algorithm, and justify the worst-case runtime of O(n) and the best-case of O(1).

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Heap Sort

A Heap is a type of data structure that is built on trees. It's a binary tree that's virtually complete. Except for the very bottom level, all levels of the tree must be filled in a heap. The last (bottom) level should be filled from left to right. The heap data structure is used for the efficient implementation of priority queues.Heap can be of two types: