Complexity of an algorithm, Data Structure & Algorithms

Assignment Help:

Q. Explain the complexity of an algorithm?  What are the worst case analysis and best case analysis explain with an example.                                                                                                                

Ans:

The complexity of the algorithm M is the function f(n) which gives the running time or storage space requirement of the algorithm in terms of the size n of the input data. Frequently, the storage space needed by an algorithm is just a multiple of the data size n. Therefore, the term "complexity" should be referring to the running time of the algorithm.

We find the complexity function f(n) for the certain number of cases. The two cases to which one usually investigates in complexity theory are as follows:-
i. The worst case:-  the maximum value of f(n) for any input possible
ii. The best case:-  the least possible value of f(n)

For example:-

Hear if we take an example of linear search in which an integer Item is to searched or found in an array Data. The complexity if the search algorithm is given by number C of comparisons between Item and Data[k].

Worst case:-

The worst case occurs when the Item is last element in the array Data or is it not there at all. In both of these cases, we get

C(n)=n

In the average case, we presume that the Item is present is the array and is likely to be present in any position in the array. Hence the number of comparisons can be any of the numbers 1, 2, 3........n and each number occurs with probability

p = 1/n.

C(n) = 1. 1/n + 2.1/n + ... + n.1/n

= (n+1) / 2

hence the average number of comparisons needed to locate the Item in to array Data is approximately the same to half the number of elements in the Data list.


Related Discussions:- Complexity of an algorithm

Elaborate the symbols of abstract data type, Elaborate the symbols of abstr...

Elaborate the symbols of abstract data type length(a)-returns the number of characters in symbol a. capitalize(a)-returns the symbol generated from a by making its first cha

Hash tables, Q. Explain the Hash Tables, Hash function and Hashing Techniqu...

Q. Explain the Hash Tables, Hash function and Hashing Techniques properly?             A n s . H as h Table is explained as follows : A hash table is a data struc

Deletion of any element from the queue, Program segment for the deletion of...

Program segment for the deletion of any element from the queue delmq(i)  /* Delete any element from queue i */ { int i,x; if ( front[i] == rear[i]) printf("Queue is

B-tree, Unlike a binary-tree, each node of a B-tree may have a number of ke...

Unlike a binary-tree, each node of a B-tree may have a number of keys and children. The keys are stored or saved in non-decreasing order. Each key has an related child that is the

Prefix and Postfix Expressions, Q.   Draw the expression tree of the infix ...

Q.   Draw the expression tree of the infix expression written below and then  convert it intoPrefix and Postfix expressions. ((a + b) + c * (d + e) + f )* (g + h )

Basic organization of computer system, what happen''s in my computer when ...

what happen''s in my computer when i input any passage

Write the algorithm to find input and output value, This algorithm inputs 5...

This algorithm inputs 5 values and outputs how many input numbers were positive and how many were negative. Data to be used: N = 1, -5, 2, -8, -7

Explain in detail about the abstract data type, Abstract data type The ...

Abstract data type The thing which makes an abstract data type abstract is that its carrier set and its operations are mathematical entities, like geometric objects or numbers;

Applications in file systems of avl trees, 1. In computer science, a classi...

1. In computer science, a classic problem is how to dynamically store information so as to let for quick look up. This searching problem arises frequently in dictionaries, symbol t

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