Problem 3. In this problem we focus on the BUILD-MAX-HEAP operation. 1. Illustrate the operation of BUILD-MAX-HEAP on the array A = [6,3,12,9,25,17,4,22,8,5]. 2. Prove that the running time of the BUILD-MAX-HEAP operation is O(n lg n). Note, this is not a tight bound.

Problem 3. In this problem we focus on the BUILD-MAX-HEAP operation. 1. Illustrate the operation of BUILD-MAX-HEAP on the array A = [6,3,12,9,25,17,4,22,8,5]. 2. Prove that the running time of the BUILD-MAX-HEAP operation is O(n lg n). Note, this is not a tight bound.

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

Problem 3. In this problem we focus on the BUILD-MAX-HEAP operation.
1. Illustrate the operation of BUILD-MAX-HEAP on the array
A = [6,3,12,9,25,17,4,22,8,5].
2. Prove that the running time of the BUILD-MAX-HEAP operation is O(n lg n).
Note, this is not a tight bound.

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Consider an unsorted array of n elements. Recall that the Heapsort Algorithm consists of two parts: first we run BUILD-MAX-HEAP to convert our input array into a max heap, and then we run MAX-HEAPIFY n times to generate the n elements of our sorted array. Demonstrate the Heapsort Algorithm on the input array [5, 2, 1, 7, 6, 3, 4]. Clearly show your steps.
use figure 6.5 to answer the question
Questions are attached
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Problem 4: Binomial heaps. Let H1 and H2 be two binomial heaps. We would like tomerge H1 and H2 to obtain the binomial heap H and also to find the minimum key in H.A standard approach would be to perform the following sequence of operationsH = Merge(H1, H2);m = Min(H).Alternatively, we may perform the following sequence of operationsm1 = Min(H1);m2 = Min(H2);m = min{m1, m2};H = Merge(H1, H2).(i) Give an example of heaps H1 and H2 in which the time complexity of all operations together in the standard approach is better than in the alternative approach.Note that the time complexity of finding the minimum element in the binomial heapdepends on the number of binomial trees in the heap. Justify your answer.(ii) Does there exist an example of heaps H1 and H2 in which the time complexity ofall operations together in the alternative approach is better than in the standardapproach. Again note that the time complexity of finding the minimum element inthe binomial heap depends on the number of…
use figure 6.5 to answer the question