Consider the following max-heap: i 0 1 2 3 4 5 6 7 8 pq[i] -...
Consider the following max-heap:
| i | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| pq[i] | - | 30 | 18 | 28 | 17 | 6 | 20 | 2 | 9 |
Show the resulting heap as array after performing delmax().
Homework Answers
Given heap:
In order to delete 30, we replace 9 i.e. the last node with it and then delete 30:
Then we swap the value 9 with the immediate maximum child:
Further we again swap 9 with the immediate child 20 as:
This results in the final heap!
Please find the required resulting heap as an array as the following:
| 28 | 18 | 20 | 17 | 6 | 9 | 2 |
A max-heap with 10 elements is given in the following array format. The following three sub-questions...
A max-heap with 10 elements is given in the following array format. The following three sub-questions all refer to this max heap. i 1 2 3 4 5 6 7 8 9 10 A[i] 99 90 80 70 60 50 40 30 20 10 Show the result after applying heap-increase-key(A, 9, 95) to the max-heap at the top of this page: i 1 2 3 4 5 6 7 8 9 10 A[i] Show the result after applying heap-extract-max(A) to...
Consider the following max-heap stored as an array: <7, 6, 4, 2, 5, 1, 3>. Draw...
Consider the following max-heap stored as an array: <7, 6, 4, 2, 5, 1, 3>. Draw this max-heap as an (undirected) binary tree and give both adjacency-list representation and adjacency-matrix representation of the binary tree
braw the binary min heap that results from inserting 8, 7, 3, 2, 4, 6, 9,...
braw the binary min heap that results from inserting 8, 7, 3, 2, 4, 6, 9, 5, 1 in that order into an initially empty binary min hea p. Show final tree and the array representation of the heap. No need to show the intermediate work. 0 5 6 8 10 12 9. Consi der the binary heap shown below. What would the heap look like after deleteMin operation is performed? Show your work. 13 28 44 61 60 68...
Consider the min-priority queue implemented by a binary heap. (The max-priority queue is treated in §6.5...
Consider the min-priority queue implemented by a binary heap. (The max-priority queue is treated in §6.5 Priority queues in the textbook.) Show the binary tree implemented by the array A = 〈5, 8, 9, 11, 10, 12, 10, 12, 15, 11, 14, 13, 16, 15〉. Show the binary tree resulting from Heap-Insert(A, 6) where A is the array in (a). Show the binary tree resulting from Extract-Min(A) where A is the array in (a). Show the binary tree resulting from...
NOTE: Completing the Third Chart is the most important. This is one question with three parts. (4 pts) Is the following array-based tree a min-heap or a max-heap or not a heap at all? 85 91 S8 95 1...
NOTE: Completing the Third Chart is the most
important. This is one question with three parts.
(4 pts) Is the following array-based tree a min-heap or a max-heap or not a heap at all? 85 91 S8 95 100 92 a. Min-heap b. Max-heap c. Not a heap 5 pts) Turn the following array-based binary tree into a max-heap. Show your work step by step. (You will not need all the columns) 34 7 12 47 19 5 pts) Show...
Please ignore red marks. Thanks 6. (8 pts) Illustrate the algorithmic operations on the maximum binary...
Please ignore red marks. Thanks
6. (8 pts) Illustrate the algorithmic operations on the maximum binary heap data sti 'perations on the maximum binary heap data structure as directed. BUILD-MAX-HEAP(A) MAX-HEAPIFY (A. i) 1 A heap-size = A.length 11 = LEFT() 2 for i = A.length/2) downto 1 2 r = RIGHT() 3 MAX-HEAPIFY (A,i) 3 if / S 4.heap-size and All > A[i] HEAP-EXTRACT-MAX (A) 4 largest = 1 5 else largest = 1 1 if A.heap-size <1 6...
Given the following array of integers (of capacity 20) with 12 items: 0 1 2 3...
Given the following array of integers (of capacity 20) with 12 items: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 8 4 10 15 5 7 11 3 9 13 1 6 Index of last element = 11 Does this array represent a min heap? If not, convert it to a min heap (i.e., “heapify” it). Please show all steps.
(c) Draw the binary heap structure that is equivalent to the following list (the root is...
(c) Draw the binary heap structure that is equivalent to the following list (the root is first element). [5, 9, 8, 12, 15, 11, 19, 14, 20, 18, 17, 13] [4 marks] (d) Show the resulting tree after the value 6 is added to the heap in the part (c). Note that the binary heap properties must be restored after insertion. Show your working; you may show the data structure in tree or array form. [3 marks]
This question is about the min-heap. A min-heap with 10 elements is given in the following...
This question is about the min-heap. A min-heap with 10 elements is given in the following array format. The following three sub-questions all refer to this min-heap i 1 2 3 4 5 6 7 8 9 10 A[i] 11 22 33 44 55 66 77 88 99 100 Show the result after applying heap-decrease-key(A, 6, 12) to the min-heap at the top of this page: i 1 2 3 4 5 6 7 8 9 10 A[i] Show the...
in c++ please. thank you! Page 4 of 4 5. Heap and heapsort: answer the following...
in c++ please. thank you!
Page 4 of 4 5. Heap and heapsort: answer the following three questions. a) (1 pt) What is the definition of a max heap? | 0 b) (2 pts) When we insert an element, 5, to the following max heap, what would be the resulting max heap? Give the detailed procedure. (14) (10) c) (2 pts) Based on b), when we remove the root element in the max heap, what would be the resulting max...
braw the binary min heap that results from inserting 8, 7, 3, 2, 4, 6, 9, 5, 1 in that order into an initially empty binary min hea p. Show final tree and the array representation of the heap. No need to show the intermediate work. 0 5 6 8 10 12 9. Consi der the binary heap shown below. What would the heap look like after deleteMin operation is performed? Show your work. 13 28 44 61 60 68...
NOTE: Completing the Third Chart is the most
important. This is one question with three parts.
(4 pts) Is the following array-based tree a min-heap or a max-heap or not a heap at all? 85 91 S8 95 100 92 a. Min-heap b. Max-heap c. Not a heap 5 pts) Turn the following array-based binary tree into a max-heap. Show your work step by step. (You will not need all the columns) 34 7 12 47 19 5 pts) Show...
Please ignore red marks. Thanks
6. (8 pts) Illustrate the algorithmic operations on the maximum binary heap data sti 'perations on the maximum binary heap data structure as directed. BUILD-MAX-HEAP(A) MAX-HEAPIFY (A. i) 1 A heap-size = A.length 11 = LEFT() 2 for i = A.length/2) downto 1 2 r = RIGHT() 3 MAX-HEAPIFY (A,i) 3 if / S 4.heap-size and All > A[i] HEAP-EXTRACT-MAX (A) 4 largest = 1 5 else largest = 1 1 if A.heap-size <1 6...
(c) Draw the binary heap structure that is equivalent to the following list (the root is first element). [5, 9, 8, 12, 15, 11, 19, 14, 20, 18, 17, 13] [4 marks] (d) Show the resulting tree after the value 6 is added to the heap in the part (c). Note that the binary heap properties must be restored after insertion. Show your working; you may show the data structure in tree or array form. [3 marks]
in c++ please. thank you!
Page 4 of 4 5. Heap and heapsort: answer the following three questions. a) (1 pt) What is the definition of a max heap? | 0 b) (2 pts) When we insert an element, 5, to the following max heap, what would be the resulting max heap? Give the detailed procedure. (14) (10) c) (2 pts) Based on b), when we remove the root element in the max heap, what would be the resulting max...
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