How many comparisons and swaps are required in insertion sort?

In the expected case, insertion sort requires 1/4(N2 – N) comparisons, and thus should require about 1/2 the comparisons needed by selection sort. This result is verified by the eight item list of Figure 5.11 and Figure 5.13.

How do you calculate the number of comparisons in merge sort?

Number of total comparison in merge sort = n*log2(n) – (n – 1).

How is recursion used in merge sort?

Recursion at work

1. a merge function, which actually combines two lists together and sorts them in the correct order.
2. and a mergeSort function, which will continue to split the input array again and again, recursively, and will also call merge again and again, recursively.

How do you count the number of comparisons in heap sort?

Heap sort makes at most 1.5*N calls on downHeap. DownHeap makes at most log(N) iterations, and each iteration makes two comparisons, so heap sort makes at most 3*N*log(N) comparisons. It can be shown than bottom up heap sort actually makes at most 2*N*log(N) comparisons.

How many times is merge sort called?

And in case of merge sort we are calling merge n-1 times and each time merge needs o(n) operations, so O(n*n).

Which of the following sorts do not use recursion in their algorithm for sorting?

Heapsort: Heap data structure is an array object that can be viewed as a nearly complete binary tree. To make the right element as the root is heap sorting. It does not use recursion.

What is non-recursive merge sort?

Bottom-up merge sort is a non-recursive variant of the merge sort, in which the array is sorted by a sequence of passes. During each pass, the array is divided into blocks of size m. (Initially, m = 1).

How many levels are there in a recursion tree?

The number of levels in the recursion tree is log2 (N). The cost at the last level where the size of the problem is 1 and the number of subproblems is N. The time complexity of the above recurrence relation is O (N logN).

How do you calculate recursion step by step?

Step 1: Identify the number of sub-problems and a parameter (or parameters) indicating an input’s size of each sub-problem (function call with smaller input size) Step 2: Add the time complexities of the sub-problems and the total number of basic operations performed at that stage of recursion.

What is the recurrence relation for quick sort?

A recurrence relation is an equation that defines a sequence where any term is defined in terms of its previous terms. The recurrence relation for the time complexity of some problems are given below: The time taken by quick sort depends upon the distribution of the input array and partition strategy.

How to calculate the cost of a sub-problem in a recursive tree?

This is illustrated through following recursion tree where each node represents the cost of the corresponding sub-problem- Cost of level-2 = n/4 + n/4 + n/4 + n/4 = n and so on. Suppose at level-x (last level), size of sub-problem becomes 1.