To show that an n-element heap has height [lg n].
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A: Answer: I have done code and also I have attached code and code screenshot as well as output
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Q: Ollogn) O Ollogn)
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- In a min-heap, the next largest element of any element can be found in O(log n) time. True FalsePython code please thank you!!Suppose we have an ArrayHeap that uses the array representation from class (also called "tree representation 3B" in lecture). Recall that in this representation that the leftmost item is unused. Consider a heap with the following underlying array: | •| | 2|•| • | •| | -8 5 1 10 | 10 | 12 --- Suppose we are using our heap to represent a priority queue. If we call removeSmallest on the heap above, where will the 12 end up after removeSmallest has completed execution? Assume removeSmallest works as described in the lecture. By "completed execution", we mean the entire operation is done and the array again obeys our heap properties. O 12 will not move. O 12 will not be present in the heap. O In the root position previously occupied by a -8. O In a position previously occupied by a 5. O In a position previously occupied by a -2. O In a position previously occupied by a 9. O In a position previously occupied by a 8. O In a position previously occupied by a 0. O In a position previously…
- You are given a list of numbers for which you need to construct a min-heap. (A min-heap is a complete binary tree in which every key is less than or equal to the keys in its children.) How would you use an algorithm for constructing a max-heap (a heap as defined in Section 6.4) to construct a min-heap? You need to describe your algorithm in pseudo code.Determine the height of an n-element heap. Show all work necessary! Also, you must prove its correctness.Given the following list of integers: 12,15,20,25 (a) Apply the BUILDHEAP procedure to this list, in a right-to-left scan. Draw appropriate trees each time the addition of a new element causes changes in the tree structure. (b) Now, sort the list obtained in part(a) in a series of exchange and heapify steps. Once again, draw appropriate trees to illustrate each exchange-heapify step.