Select all the statements below which are TRUE. The Heap sort algorithm uses div
ID: 3803085 • Letter: S
Question
Select all the statements below which are TRUE. The Heap sort algorithm uses divide-and-conquer approach. In a min-heap A, for every node i lessthanorequalto (n-1)/2 the value A[i] lessthanorequalto A[2i] and A[i] lessthanorequalto A[2i+1]. Counting sort is a comparison sort algorithm. Let L be a doubly -linked list with n elements. Then finding the successor of an element x takes Theta (n) in the worst-case The Heap sort algorithm is more efficient than the Insertion sort algorithm. Let A be a max-heap of height h. In the worst-case h = Theta (n).Explanation / Answer
Answer:
1. The heap sort algorithm uses DIVIDE AND CONQUER APPROACH.
There are only two sorting algorithms which works on this paradigm. They are heap sort and merge sort.
Divide and Conquer approach works as follows:
i) Divide the problem into a number of subproblems that are smaller instances of the same problem.
ii)Conquer the subproblems by solving them recursively. If they are small enough, solve the subproblems as base cases.
iii)Combine the solutions to the subproblems into the solution for the original problem.
2. Yes, in max heap the data at each node is less than or equal to data at node's children.
4. Yes, the time complexity of double linked list in worst case for finding the successor of an elemnet is O(n) as we have to traverse through whole list of n elements.
5. Heap sort is more effiecient than insertion sort because:
Heapsort is just like selection sort, but with a better way to get the largest element. Instead of scanning all the items to find the max,it pulls it from a heap.
Heaps have properties that allow heapsort to work in-place, without additional memory.
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