Compare and contrast various sorting techniques, Data Structure & Algorithms

Q. Compare and contrast various sorting techniques or methods with respect to the memory space and the computing time.                                                                                                    


Insertion sort:- Because of the presence of nested loops, each of which can take n iterations, insertion sort is O(n2). This bound is very tight, because the input in reverse order can actually achieve this bound. So complexity is equal to= (n(n-1))/2 = O(n2). Shellsort: - The running time of Shellsort depends on the option of increment sequence. The worst-case running time of the Shellsort, using the Shell's increments, is (n2).

Heapsort:- The basic approach is to build a binary heap of the n elements. This stage takes the O(n) time. We then perform n delete_min operations on it. The elements leave the heap smallest first, in the sorted order. By recording these elements in the second array and then copying the array back again, we sort the n elements. Since each delete_min takes O(log n) time, the total running time becoms O(n log n).

Mergesort:- Mergesort is a the example of the techniques which is used to analyze recursive routines. We may assume that n is a power of 2, so that we always divide into even halves. For n = 1, the time to mergesort is constant, to which we will

The two recursive mergesorts of size n/2,  in addition the time to merge, which is linear. The equations below say this exactly:

T(1) = 1

T(n) = 2T(n/2) + n

Quicksort:-  Similar to  mergesort,  quicksort  is  recursive,  and  hence,  its  analysis needs solving a recurrence formula. We will do the analysis for a quicksort, assuming a random pivot (no median-of-three partitioning) and no cutoff for such small files. We will take T(0) = T(1) = 1, as in mergesort. The running time of quicksort is equal to the running time of the two recursive calls an addition to the linear time spent in the partition (the pivot selection takes some constant time). This gives the basic quicksort relation as follows

T(n) = T(i) + T(n - i - 1) + cn

Posted Date: 7/11/2012 1:32:01 AM | Location : United States

Related Discussions:- Compare and contrast various sorting techniques, Assignment Help, Ask Question on Compare and contrast various sorting techniques, Get Answer, Expert's Help, Compare and contrast various sorting techniques Discussions

Write discussion on Compare and contrast various sorting techniques
Your posts are moderated
Related Questions
Ans: I nsertion into the B-tree: 1.  First search is made for the place where the new record must be positioned. As soon as the keys are inserted, they are sorted into th

Write the algorithm for compound interest

1. Start 2. Get h 3. If h T=288.15+(h*-0.0065) 4. else if h T=216.65 5. else if h T=216.65+(h*0.001) 6. else if h T=228.65+(h*0.0028) 7. else if h T=270.65 8.

The location of a node in a binary search tree is defined as a string such as LLRRL, which represents the node that you find by starting at the root, and traversing Left, traverse

The data structure needed to evaluate a postfix expression is  Stack

Example of Area Subdivision Method The procedure will be explained with respect to an illustrative problem, with the image consisting of five objects, namely a triangle (T), qu

Determine the number of character comparisons made by the brute-force algorithm in searching for the pattern GANDHI in the text

What is Efficiency of algorithm? Efficiency of an algorithm can be precisely explained and investigated with mathematical rigor.  There are two types of algorithm efficiency

Diffuse Illumination Diffuse illumination means light that comes from all directions not from one particular source. Think about the light of a grey cloudy day as compared to