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

Explain dijkstra''s algorithm, Explain Dijkstra's algorithm Dijkstra's ...

Explain Dijkstra's algorithm Dijkstra's algorithm: This problem is concerned with finding the least cost path from an originating node in a weighted graph to a destination node

Postfix expression, Ask question Write an algorithm for the evaluation of a...

Ask question Write an algorithm for the evaluation of a postfix expression using a stack#Minimum 100 words accepted#

Hw7, Handout 15 COMP 264: Introduction to Computer Systems (Section 001) Sp...

Handout 15 COMP 264: Introduction to Computer Systems (Section 001) Spring 2013 R. I. Greenberg Computer Science Department Loyola University Water TowerCampus, Lewis Towers 524 82

Need help with working out. I dont really get it, Suppose there are exactly...

Suppose there are exactly five packet switches (Figure 4) between a sending host and a receiving host connected by a virtual circuit line (shown as dotted line in figure 4). The tr

Red black tree, red black tree construction for 4,5,6,7,8,9

red black tree construction for 4,5,6,7,8,9

State the ways to construct container taxonomy, State the ways to construct...

State the ways to construct container taxonomy There are several ways that we could construct our container taxonomy from here; one way that works well is to make a fundamental

Dynamic programming., Count Scorecards(30 points) In a tournament, N playe...

Count Scorecards(30 points) In a tournament, N players play against each other exactly once. Each game results in either of the player winning. There are no ties. You have given a

What is quick sort, What is quick sort? Quick sort is a sorting algorit...

What is quick sort? Quick sort is a sorting algorithm that uses the idea if split and conquer. This algorithm chooses an element called as pivot element; search its position in

Lists, In the previous unit, we have discussed arrays. Arrays are data stru...

In the previous unit, we have discussed arrays. Arrays are data structures of fixed size. Insertion and deletion involves reshuffling of array elements. Thus, array manipulation

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