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QUESTION 9 The index of the right child of a given node, X, in a binary...
1. In a heap, the upper bound on the number of leaves is: (A) O(n) (B)...
1. In a heap, the upper bound on the number of leaves is: (A) O(n) (B) O(1) (C) O(logn) (D) O(nlogn) 2. In a heap, the distance from the root to the furthest leaf is: (A) θ(nlogn) (B) θ(logn) (C) θ(1) (D) θ(n) 3. In a heap, let df be the distance of the furthest leaf from the root and let dc be the analogous distance of the closest leaf. What is df − dc, at most? (A) 1 (C)...
Computer Algorithm question 8) Give an algorithm for building a heap in O(n) 9) Prove the...
Computer Algorithm question
8) Give an algorithm for building a heap in O(n)
9) Prove the algorithm given in 8) runs in O(n) time.
10) What is the asymptotic runtime of an algorithm represented
by the following recurrence equation?
11) Suppose you have the following priority queue implemented as a (max) heap. What will the heap look like when the max node is removed and the heap is readjusted? Assume on each heapify operation the largest child node is selected...
C++ Question 5 5 pts In a min-heap of N elements, if we want to find...
C++
Question 5 5 pts In a min-heap of N elements, if we want to find the max element, we have to search all the leaves. What is the big-o running time of findMax? O(N^2) Oſlog N) O(N) OIN log N) Question 6 5 pts An AVL tree is a Binary Search Tree that has the following additional property for every node in the tree, the height of the left and right subtrees is the same none of the above...
C++ Question 9 5 pts Deleting the minimum element in a min-heap of N elements takes...
C++
Question 9 5 pts Deleting the minimum element in a min-heap of N elements takes in average case O(N log N) O(1) O(N) Oſlog N) D Question 10 5 pts The time taken to find an element in an AVL tree of depth d is Old) 02) Oſlog d) Old log d) Question 11 5 pts Secondary clustering in a hash table occurs when using Linear probing Separate chaining Quadratic probing Double hashing Question 12 5 pts When sorting...
THESE ARE TRUE/FALSE The best-time complexity for insertion sort is O(nlogn). The worst-time complexity for bubble...
THESE ARE TRUE/FALSE The best-time complexity for insertion sort is O(nlogn). The worst-time complexity for bubble sort is O(nlogn). A linked structure consists of nodes. Each node is dynamically created to hold an element. All the nodes are linked together to form a list. The time complexity for searching an element in a binary search tree is O(logn) The time complexity for inserting an element into a binary search tree is O(logn). In an AVL tree, the element just inserted...
SECTION B (4 QUESTIONS, 90 MARKS) Question 4. [32 marks in total] For this question, assume the definition of Java clas...
SECTION B (4 QUESTIONS, 90 MARKS) Question 4. [32 marks in total] For this question, assume the definition of Java class Heap given in the Appendix. The heaps referred to in this question are all maxHeaps. a. (5 marks) Insert into an empty (binary) heap the values 35, 4, 72, 36, 49, 50. Draw all intermediate steps b. (3 marks) Carry out one deletion operation on the final heap in (a.) above. c. (2 marks) Give the worst-case time complexity...
1. What is the worst case time complexity of insertion into a binary search tree with...
1. What is the worst case time complexity of insertion into a binary search tree with n elements? You should use the most accurate asymptotic notation for your answer. 2. A binary search tree is given in the following. Draw the resulting binary search tree (to the right of the given tree) after deleting the node with key value 8. 10 3. You have a sorted array B with n elements, where n is very large. Array C is obtained...
2. Suggest a structured plan (algorithm) for the bubble sort and selection sort, and perform running...
2. Suggest a structured plan (algorithm) for the bubble sort and selection sort, and perform running time analysis for both best and worst case. 3. Consider the age data of 12 children who are supposed to undergo for vaccination in ascending order of their age. Suggest and apply a sorting technique which can efficiently handle this data. Show all the intermediate steps clearly. Child ID 01 02 03 04 05 06 07 08 09 10 11 12 2. Age 1...
Canvas →XC 6 D Question 10 5 pts When sorting n records, Quicksort has worst-case cost...
Canvas →XC 6 D Question 10 5 pts When sorting n records, Quicksort has worst-case cost On) On 2) On logn) Olm Question 11 5 pts In the worst case, the very best that a comparison based sorting algorithm can do when sorting n records is On 2) Allog in! (n) (login) Question 12 5 pts An AVL tree is a Binary Search Tree that has the following additional property none of the above for every node in the tree....
Discrete Math Max Heap After you build your heap, you then compare the values of the vertices, in the following way: If a child of a parent node is larger than the parent node, switch their posit...
Discrete Math
Max Heap After you build your heap, you then compare the values of the vertices, in the following way: If a child of a parent node is larger than the parent node, switch their positions. Using the list above, the following operations would take place: The parent of value 4 would swap with child of value 8. 1. 8 4 Now the parent value of 4 would swap places with the child value of 6. 2. 6 2...
Computer Algorithm question
8) Give an algorithm for building a heap in O(n)
9) Prove the algorithm given in 8) runs in O(n) time.
10) What is the asymptotic runtime of an algorithm represented
by the following recurrence equation?
11) Suppose you have the following priority queue implemented as a (max) heap. What will the heap look like when the max node is removed and the heap is readjusted? Assume on each heapify operation the largest child node is selected...
C++
Question 5 5 pts In a min-heap of N elements, if we want to find the max element, we have to search all the leaves. What is the big-o running time of findMax? O(N^2) Oſlog N) O(N) OIN log N) Question 6 5 pts An AVL tree is a Binary Search Tree that has the following additional property for every node in the tree, the height of the left and right subtrees is the same none of the above...
C++
Question 9 5 pts Deleting the minimum element in a min-heap of N elements takes in average case O(N log N) O(1) O(N) Oſlog N) D Question 10 5 pts The time taken to find an element in an AVL tree of depth d is Old) 02) Oſlog d) Old log d) Question 11 5 pts Secondary clustering in a hash table occurs when using Linear probing Separate chaining Quadratic probing Double hashing Question 12 5 pts When sorting...
SECTION B (4 QUESTIONS, 90 MARKS) Question 4. [32 marks in total] For this question, assume the definition of Java class Heap given in the Appendix. The heaps referred to in this question are all maxHeaps. a. (5 marks) Insert into an empty (binary) heap the values 35, 4, 72, 36, 49, 50. Draw all intermediate steps b. (3 marks) Carry out one deletion operation on the final heap in (a.) above. c. (2 marks) Give the worst-case time complexity...
1. What is the worst case time complexity of insertion into a binary search tree with n elements? You should use the most accurate asymptotic notation for your answer. 2. A binary search tree is given in the following. Draw the resulting binary search tree (to the right of the given tree) after deleting the node with key value 8. 10 3. You have a sorted array B with n elements, where n is very large. Array C is obtained...
2. Suggest a structured plan (algorithm) for the bubble sort and selection sort, and perform running time analysis for both best and worst case. 3. Consider the age data of 12 children who are supposed to undergo for vaccination in ascending order of their age. Suggest and apply a sorting technique which can efficiently handle this data. Show all the intermediate steps clearly. Child ID 01 02 03 04 05 06 07 08 09 10 11 12 2. Age 1...
Canvas →XC 6 D Question 10 5 pts When sorting n records, Quicksort has worst-case cost On) On 2) On logn) Olm Question 11 5 pts In the worst case, the very best that a comparison based sorting algorithm can do when sorting n records is On 2) Allog in! (n) (login) Question 12 5 pts An AVL tree is a Binary Search Tree that has the following additional property none of the above for every node in the tree....
Discrete Math
Max Heap After you build your heap, you then compare the values of the vertices, in the following way: If a child of a parent node is larger than the parent node, switch their positions. Using the list above, the following operations would take place: The parent of value 4 would swap with child of value 8. 1. 8 4 Now the parent value of 4 would swap places with the child value of 6. 2. 6 2...
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