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

Acyclic graphs, Acyclic Graphs In a directed graph a path is said to fo...

Acyclic Graphs In a directed graph a path is said to form a cycle is there exists a path (A,B,C,.....P) such that A = P. A graph is called acyclic graph if there is no cycle in

Find strongly connected components - dfs, A striking application of DFS is ...

A striking application of DFS is determine a strongly connected component of a graph. Definition: For graph G = (V, E) , where V refer to the set of vertices and E refer to the

State in brief about assertion, State  in brief about assertion Asser...

State  in brief about assertion Assertion: A statement which should be true at a designated point in a program.

Dijkstras algorithm, Djikstra's algorithm (named after it is discovered by ...

Djikstra's algorithm (named after it is discovered by Dutch computer scientist E.W. Dijkstra) resolves the problem of finding the shortest path through a point in a graph (the sour

Draws a rectangular grid algorithms, Prepare a GUI called Hotplate GUI that...

Prepare a GUI called Hotplate GUI that holds a central panel that draws a rectangular grid that represents Element objects which should be held in a 2-dimensional array. The applic

Abstract data type- queue, A significant aspect of Abstract Data Types is t...

A significant aspect of Abstract Data Types is that they explain the properties of a data structure without specifying the details of its implementation. The properties might be im

Total impedent of the circuit, an electrical student designed a circuit in...

an electrical student designed a circuit in which the impedence in one part of a series circuit is 2+j8 ohms and the impedent is another part of the circuit is 4-j60 ohm mm program

Write an algorithm to illustrate this repeated calculation, The below formu...

The below formula is used to calculate n: n = (x * x)/ (1 - x). Value x = 0 is used to stop the algorithm. Calculation is repeated using values of x until value x = 0 is input. The

What is complexity, Complexity is the rate at which the needed storage or c...

Complexity is the rate at which the needed storage or consumed time rise as a function of the problem size. The absolute growth based on the machine utilized to execute the program

Algorithm, write an algorithm given each students name and grade points for...

write an algorithm given each students name and grade points for six courses.find his grade point average and group students into the gpa groups 3.5

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