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

What is a linear array, What is a linear array? An array is a way to re...

What is a linear array? An array is a way to reference a series of memory locations using the similar name. Every memory location is shown by an array element. An  array elemen

Determine the comparison of gouraud and phong shading, Comparison of Gourau...

Comparison of Gouraud and Phong Shading Phong shading requires more calculations, but produces better results for specular reflection than Gouraud shading in the form of more r

Linear node is given by means of pointer, A linear collection of data eleme...

A linear collection of data elements where the linear node is given by means of pointer is known as Linked list

Use a random number generator to create 10 numbers, Use a random number gen...

Use a random number generator to create 10 numbers between 1 and 1000 and store them in 2 different arrays.  The first array should contain the numbers as they are generated.  The

What is an algorithm, What is an algorithm?  What are the characteristics o...

What is an algorithm?  What are the characteristics of a good algorithm? An algorithm is "a step-by-step process for accomplishing some task'' An algorithm can be given in many

Primitive data structure, Primitive Data Structure These are the basic ...

Primitive Data Structure These are the basic structure and are directly operated upon by the machine instructions. These in general have dissimilar representations on different

Data structures, Aa) Come up with an ERD from the following scenario, clear...

Aa) Come up with an ERD from the following scenario, clearly stating all entities, attributes, relationships before final sketch of the ERD: [50 m

Explain backtracking, Explain Backtracking The  principal idea is to co...

Explain Backtracking The  principal idea is to construct solutions single component  at a time  and evaluate such  partially constructed candidates as follows. If a partiall

Explain expert system, 1. What is an expert system and where are they need...

1. What is an expert system and where are they needed? 2. What are the major issues involved in building an expert system?

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