Big o notation, Data Structure & Algorithms

Assignment Help:

This notation gives an upper bound for a function to within a constant factor. Given Figure illustrates the plot of f(n) = O(g(n)) depend on big O notation. We write f(n) = O(g(n)) if there are positive constants n0 & c such that to the right of n0, the value of f(n) always lies on or below cg(n).

2388_The o-Notation.png

Figure: Plot of  f(n) = O(g(n))

Mathematically specking, for a given function g(n), we specified a set of functions through O(g(n)) by the following notation:

O(g(n)) = {f(n) :  There exists a positive constant c and n0 such that 0 ≤  f(n) ≤ cg(n)

for all n ≥ n0 }

Obviously, we employ O-notation to describe the upper bound onto a function using a constant factor c.

We can view from the earlier definition of Θ that Θ is a tighter notation in comparison of big-O notation. f(n) = an + c is O(n) is also O(n2), but O (n) is asymptotically tight while O(n2) is notation.

While in terms of Θ notation, the above function f(n) is Θ (n). Because of the reason big-O notation is upper bound of function, it is frequently used to define the worst case running time of algorithms.


Related Discussions:- Big o notation

What do you mean by hash clash, What do you mean by hash clash? Hashing...

What do you mean by hash clash? Hashing is not perfect. Occasionally, a collision occurs when two different keys hash into the same hash value and are assigned to the same arra

What is called the basic operation of an algorithm, What is called the basi...

What is called the basic operation of an algorithm? The most significant operation of the algorithm is the operation contributing the most to the total running time is known as

Branch and bound algorithm, Suppose we have a set of N agents and a set of ...

Suppose we have a set of N agents and a set of N tasks.Each agent can only perform exactly one task and there is a cost associated with each assignment. We would like to find out a

Illumination of wire frame, Illumination of wire frame The colour or sh...

Illumination of wire frame The colour or shade that a surface appears to the human eye depends primarily on three  factors : Colour and strength of incoming illumination

Polynomials, Polynomials like  5x 4    +  2x 3    +  7x 2     +  10x  -  8...

Polynomials like  5x 4    +  2x 3    +  7x 2     +  10x  -  8  can  be  represented by using arrays. Arithmetic operations such as addition & multiplication of polynomials are com

Multidimensional array in one dimensional array, Q. By giving an example sh...

Q. By giving an example show how multidimensional array can be represented in one the dimensional array.

Graphs, In this unit, we will describe a data structure called Graph. Actua...

In this unit, we will describe a data structure called Graph. Actually, graph is a general tree along no parent-child relationship. In computer science, Graphs have several applica

Enumerate about the carrier set members, Enumerate about the carrier set me...

Enumerate about the carrier set members Ruby is written in C, so carrier set members (which is, individual symbols) are implemented as fixed-size arrays of characters (which is

Draw a flowchart to input start time and end time of vehicle, Speed cameras...

Speed cameras read the time a vehicle passes a point (A) on road and then reads time it passes a second point (B) on the same road (points A and B are 100 metres apart). Speed of t

Which is the most suitable data type, Problem 1. You are asked to store...

Problem 1. You are asked to store Names of all 100 students of class A in your Learning Centre. Which data type will you use? What is its syntax? Explaining the data typ

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