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

Calculation of time complexity, Example: Assume the following of code: ...

Example: Assume the following of code: x = 4y + 3 z = z + 1 p = 1 As we have been seen, x, y, z and p are all scalar variables & the running time is constant irrespective

Entity relationship diagram, This question is based on the requirements of ...

This question is based on the requirements of a system to record band bookings at gigs. (A 'gig' is an event at which one or more bands are booked to play). You do not need to know

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-

A full binary tree with n leaves, A full binary tree with n leaves have:- ...

A full binary tree with n leaves have:- 2n -1 nodes.

Reverse order of elements on a slack, Q. Reverse the order of the elements ...

Q. Reverse the order of the elements on a stack S    (i) by using two additional stacks (ii) by using one additional queue. Ans :      L e t S be the stac

Recursion, i need help in java recursion assignment.

i need help in java recursion assignment.

Program insertion of a node into any circular linked list, Program Insertio...

Program Insertion of a node into any Circular Linked List Figure depicts a Circular linked list from which an element was deleted. ALGORITHM (Deletion of an element from a

ALGORITHM AND TRACING, WRITE AN ALGORITHM TO CONVERT PARENTHIZED INFIX TO P...

WRITE AN ALGORITHM TO CONVERT PARENTHIZED INFIX TO POSTFIX FORM ALSO TRACE ALG ON ((A+B)*C-(D-E)$F+G)

Values are automatically assigned to those array elements, What values a...

What values are automatically assigned to those array elements which are not explicitly initialized? Garbage values are automatically assigned to those array elements that

Linked list, write an algorithm for multiplication of two sparse matrices u...

write an algorithm for multiplication of two sparse matrices using Linked Lists

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