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

State about the pre- and post conditions, State about the pre- and post con...

State about the pre- and post conditions Programmers can easily document other pre- and post conditions and class invariants, though, and insert code to check most value preco

Sparse matrices, SPARSE MATRICES Matrices along with good number of zer...

SPARSE MATRICES Matrices along with good number of zero entries are called sparse matrices. Refer the following matrices of Figure (a)

State warnock algorithm, Warnock's Algorithm An interesting approach to...

Warnock's Algorithm An interesting approach to the hidden-surface problem was presented by Warnock. His method does not try to decide exactly what is happening in the scene but

Binary search, Explain binary search with an example

Explain binary search with an example

Data Structure, Ask consider the file name cars.text each line in the file ...

Ask consider the file name cars.text each line in the file contains information about a car ( year,company,manufacture,model name,type) 1-read the file 2-add each car which is repr

Data structures, 1.  You are required to hand in both a hard copy and an el...

1.  You are required to hand in both a hard copy and an electronic copy of the written report on the project described in A, including all the diagrams you have drawn.  2.  You

Stack, how we will make projects on stack in c?

how we will make projects on stack in c?

Total weight of minimum spanning tree, a) Run your program for α = 0.05, 0...

a) Run your program for α = 0.05, 0.5, and 0.95. You can use n = 30, and W = 10. What is impact of increasing value of α on connectivity of G'? To answer this question, for each v

Linked lists - implementation, The Linked list is a chain of structures whe...

The Linked list is a chain of structures wherein each structure contains data in addition to pointer, which stores the address (link) of the next logical structure in the list.

Data flow diagrams, How to construct a data flow diagram for a college assi...

How to construct a data flow diagram for a college assignment and marking systemA

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