Complexity of quick sort, Data Structure & Algorithms

Assignment Help:

Q. What do you mean by the best case complexity of quick sort and outline why it is so. How would its worst case behaviour arise?                                                                                                 

Ans:

In the best case complexity, pivot is in the middle. To simplify the calculation, we assume that the two sub-files are both  exactly half  of the size of the original file, and although this gives a minor overestimate, this is except able because we are only interested in a Big-Oh answer.

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

which yields

T(n) = cn log n + n = O(n log n)

In the worst case the pivot is the smallest element, all the time. Then i = 0 and if we ignore  T(0) = 1, which is not important, the recurrence is T(n) = T(n - 1) + cn, n > 1 which yields

1908_Quick Sort1.png


Related Discussions:- Complexity of quick sort

COBOL, write a COBOL program to find the biggest of two numbers

write a COBOL program to find the biggest of two numbers

Explain thread, Thread By changing the NULL lines in a binary tree to ...

Thread By changing the NULL lines in a binary tree to special links known as threads, it is possible to perform traversal, insertion and deletion without using either a stack

Determine the disjoint of division method, Determine the Disjoint of divisi...

Determine the Disjoint of division method A polygon is disjoint from the viewport if the x- and y-extents of the polygon do not overlap the viewport anywhere. In this case; reg

Define midsquare method, Midsquare Method :- this operates in 2 steps. In t...

Midsquare Method :- this operates in 2 steps. In the first step the square of the key value K is taken. In the 2nd step, the hash value is obtained by deleting digits from ends of

Define algorithm, What is an Algorithm? An algorithm is a sequence of u...

What is an Algorithm? An algorithm is a sequence of unambiguous instructions for solving a problem, i.e., for getting a needed output for any legitimate input in a finite amoun

Conversion of forest into tree, Conversion of Forest into Tree A binary...

Conversion of Forest into Tree A binary tree may be used to show an entire forest, since the next pointer in the root of a tree can be used to point to the next tree of the for

Define ordinary variable, Ordinary variable An ordinary variable of a e...

Ordinary variable An ordinary variable of a easy data type can store a one element only

Queues, what is queues? how it work? and why it used? i want an assignment...

what is queues? how it work? and why it used? i want an assignment on queue .....

Algorithsm, What are the properties of an algorithsm?

What are the properties of an algorithsm?

Define a sparse metrics, Define a sparse metrics. A matrix in which num...

Define a sparse metrics. A matrix in which number of zero entries are much higher than the number of non zero entries is known as sparse matrix. The natural method of showing m

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd