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

Pre-order and post order traversal of a binary tree, The pre-order and post...

The pre-order and post order traversal of a Binary Tree generates the same output. The tree can have maximum One node

Tic Tac Toe game , Book to refer: Introduction to Algorithms, 3rd Ed, by Cl...

Book to refer: Introduction to Algorithms, 3rd Ed, by Clifford Stein, Thomas H. Cormen, Ronald Rivest, Charles E. Leiserson Question: Tic Tac Toe game -Design a GUI and implement

Analysis of algorithms, A common person's faith is that a computer can do a...

A common person's faith is that a computer can do anything. It is far from truth. In realism computer can carry out only definite predefined instructions. The formal illustration o

Explain about franklin algorithm, Explain about Franklin Algorithm We m...

Explain about Franklin Algorithm We mentioned how the number of possible comparisons of polygons grows as the square of the number of polygons in the scene. Many of the hidden-

Binary tree with depth 3, Q. Construct a complete binary tree with depth 3 ...

Q. Construct a complete binary tree with depth 3 for this tree which is maintained in the memory using the linked representation. Make the adjacency list and adjacency matrix for t

Define the carrier set of the symbol abstract data type, Define the Carrier...

Define the Carrier set of the Symbol ADT Carrier set of the Symbol ADT is the set of all finite sequences of characters over Unicode characters set (Unicode is a standard char

Algorithm for stack using array, write an algorithm for stack using array p...

write an algorithm for stack using array performing the operations as insertion ,deletion , display,isempty,isfull.

Find the adjacency matrix, Consider the digraph G with three vertices P1,P2...

Consider the digraph G with three vertices P1,P2 and P3 and four directed edges, one each from P1 to P2, P1 to P3, P2 to P3 and P3 to P1. a. Sketch the digraph. b. Find the a

Explain the linked list implementation of stack, Question 1 Explain the fo...

Question 1 Explain the following? Arrays Stack Trees Question 2 Explain the Linked list implementation of stack Question 3 What is a binary tree? Expla

Asymptotic notation.., important points on asymptotic notation to remember

important points on asymptotic notation to remember

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