Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 6.4, Problem 2E
Program Plan Intro
To describe the correctness of the loop variant for the heap sort.
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Students have asked these similar questions
For starting array 25 22 24 28 26 29 21 23 27, tell, for each element: what is the
FIRST other element that it gets compared to during the sort? Assume, that when a
node is potentially moving down, that it gets compared to its left child first. (The first
line below asks you to tell me what the number 21 is compared to, the first time that
it is compared to anything within the heap sort algorithm. The second line asks what
22 is compared to for its first comparison, etc.)
21
22
23
24
25
26
27
28
29
25
27
23. You selected 27.
25
24
27
22
27
28
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ANSWER THE FULL QUESTION WITH A PROPER
EXPLANATION FOR EACH STEP FOR AN UPVOTE
PLEASE!
I WOULD LIKE TO LEARN RATHER THAN JUST KNOW
THE ANSWER
After the heap is built, and the first element deleted, value 22 takes its place, what
are the next two comparisons that happen? The first is between 22 and
24
The next is between that value and 26
What are they? The starting array is still 25 22 24 28 26 29 21 23 27. (Just enter
the number, no…
The following array is already a Heap. Illustrate how HeapSort works on this Heap.
You only have to show the first iteration of HeapSort - i.e., which element the root will be swapped with and the subsequent full FixHeap that follows.
You must clearly show the node and its children considered in each step.
A[1,...,n] = [ 23, 17, 14, 6, 13, 10, 1, 5, 4, 12 ]
You're given an array A[1...7]
Heap-Insert(A, 8), what is the resulting A?
(9, 7, 6, 4, 1, 5, 3). If you execute Max-
Chapter 6 Solutions
Introduction to Algorithms
Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3E
Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3P
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- 3. Sort the array A= [10, 15, 11, 12, 6, 28, 19] by using the operation (insertion and deletion) of Heapsort.arrow_forwardCould you help me the following questions? Sara and her friends said they have discovered a way to get O(1) category performance for both insert and remove in a priority queue. Their description of the data structure and algorithms is as follows: They use an array implementation for the priority queue The index of the array represents the rank of an element – e.g. an element whose rank is 50 will be placed at index 49 Each element is the head node to a linked list – if a new element is inserted into the priority queue with the same rank as another element already in the queue, the new element is added to the linked list at its head Example: If an element “X” with rank 25 exists at index 24, and a new element “Y” also has a rank of 25, the linked list at index 24 is “Y” then “X” When remove is performed, the element at the highest index is removed. If there is more than one node at that index, the node at the head of the linked list there is removed Based on this description of the…arrow_forwardJava: Implementing the remove(u) Method for a Meldable Heap Implement the remove(u) method in Java, which removes the node u from a MeldableHeap. This method should run in O(log n) expected time. First, add the nodes (with values ranging from 1 to 15) to the Meldable Heap without using a scanner. Then, demonstrate that the remove(x) method effectively removes the specified node by printing the number of nodes remaining in the heap and the value of the node being removed. Please provide comments in the program to enhance understanding of its functionality.arrow_forward
- Assume we have k heaps, each with a maximum of n items. These are to be combined into a single heap. Each of the following sub-parts provides a different method for merging the heaps, and you are required to calculate the large O running time for each method. We build a new linked list, L, that is empty. We continually remove the highest priority element from each of the k piles hi and insert it at the beginning of L, until hi is empty. The items of L are then transferred to an array and the array is heapified. What is the worst-case running time for a huge O?arrow_forwardmultiple choice: consider an array based implementation of a stack and its push operation. Beginning with an array of length 1 = (2^0), consider where the array’s length will be doubled whenever an insertion(via the push operation) is attempted when the array is full. What is the amortized complexity of performing a sequence of n push operations. a) Θ(log n) b) Θ(n) c) Θ(n^2) d) Θ(1)arrow_forward30. In the implementation for a breadth-first search we studied, a queue was used. The code below replaces the queue with a stack. List the pre-order enumeration that the vertices in the graph below are visited using this modified method, starting from vertex 0. } 3 /** stack-based search */ static void modSearch (Graph G, int start) { Stack S new AStack (G.n()); S.push(start); } 6 G.setMark (start, VISITED); while (S.length) > 0) { } modSearch: intv S.pop(); PreVisit (G, v); for (int w = G.first (v); w < G.n(); w = G.next(v, w)) if (G.getMark (w) == UNVISITED) { G.setMark (w, VISITED); S.push(w);arrow_forward
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