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

Cohen sutherland algorithm, Using the cohen sutherland. Algorithm. Find the...

Using the cohen sutherland. Algorithm. Find the visible portion of the line P(40,80) Q(120,30) inside the window is defined as ABCD A(20,20),B(60,20),C(60,40)and D(20,40)

Process of accessing data stored in a serial access memory, The process of ...

The process of accessing data stored in a serial access memory is same to manipulating data on a By using stack  method.

Example of pre order traversal, Example of pre order traversal: Reading of...

Example of pre order traversal: Reading of a book, since we do not read next chapter unless we complete all sections of previous chapter & all its sections. Figure  : Rea

Degree of node, Q. The degree of a node is defined as the number of childre...

Q. The degree of a node is defined as the number of children it has. Shear show that in any binary tree, the total number of leaves is one more than the number of nodes of degree 2

Explain insertion sort, Q. Explain the insertion sort with a proper algorit...

Q. Explain the insertion sort with a proper algorithm. What is the complication of insertion sort in the worst case?

Define complete binary tree, Define Complete Binary Tree Complete Binar...

Define Complete Binary Tree Complete Binary Tree:- A whole binary tree of depth d is that strictly binary tree all of whose leaves are at level D.

2 Flow Charts, 1.Create a flowchart to show the process that will allow the...

1.Create a flowchart to show the process that will allow the implementation of Stack, Push, and Pop operations. 2.Create a flowchart to show the process that will allow the impleme

Explain critical path and chain, 1.  Using the traditional method of CPM: ...

1.  Using the traditional method of CPM: a.  What activities are on the critical path? b.  What is the expected total lead time of the project? 2.  Using CCPM: a.  What

Define order of growth, Define order of growth The  efficiency  analysi...

Define order of growth The  efficiency  analysis  framework  concentrates   on  the  order  of  growth  of  an  algorithm's   basic operation count as the principal indicator o

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