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

A min-max heap is a data structure that supports both deleteMin and deleteMax in O(log N) per operation. The structure is identical to a binary heap, but the heap-order 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.

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(log N) time.

Figure Min-max heap