A min-max heap is a data structure that supports both deleteMin and deleteMax in O(logN) p...

A min-max heap is a data structure that supports both deleteMin and deleteMax in O(logN) per operation. The structure is identical to a binary heap, but the heaporder property is that for any node, X, at even depth, the element stored at X is smaller than the parent but larger than the grandparent (where this makes sense), and for any node, X, at odd depth, the element stored at X is larger than the parent but smaller than the grandparent. See Figure 1.

a. How do we find the minimum and maximum elements?

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b. Give an algorithm to insert a new node into the min-max heap.

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c. Give an algorithm to perform deleteMin and deleteMax.

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d. Can you build a min-max heap in linear time?

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e. Suppose we would like to support deleteMin, deleteMax, and merge. Propose a data structure to support all operations in O(logN) time.

Figure 1: Min-max heap