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

Ruby implements range of t abstract data type, Ruby implements Range of T A...

Ruby implements Range of T Abstract data type Ruby implements Range of T ADT in its Range class. Elements of carrier set are represented in Range instances by recording interna

Array implementation of a multiqueue, Program gives the program segment by ...

Program gives the program segment by using arrays for the insertion of an element to a queue into the multiqueue. Program: Program segment for the insertion of any element to t

Explain the array and linked list implementation of stack, Question 1. ...

Question 1. How can you find out the end of a String? Write an algorithm to find out the substring of a string. 2. Explain the insertion and deletion operation of linked lis

Avl tree rotations, AVL trees and the nodes it contains must meet strict ba...

AVL trees and the nodes it contains must meet strict balance requirements to maintain O(log n) search time. These balance restrictions are kept maintained via various rotation func

Merge sort, Merge sort is a sorting algorithm which uses the basic idea of ...

Merge sort is a sorting algorithm which uses the basic idea of divide and conquers. This algorithm initially divides the array into two halves, sorts them separately and then merge

Determine in brief the painter algorithm, Determine in brief the Painter A...

Determine in brief the Painter Algorithm a) The farthest polygon, namely the rectangle PQRS, is stored first. (b) The next farthest, the quadrilateral ABCD, is superpo

The space - time trade off, The best algorithm to solve a given problem is ...

The best algorithm to solve a given problem is one that requires less space in memory and takes less time to complete its execution. But in practice it is not always possible to

STACK, 5. Implement a stack (write pseudo-code for STACK-EMPTY, PUSH, and P...

5. Implement a stack (write pseudo-code for STACK-EMPTY, PUSH, and POP) using a singly linked list L. The operations PUSH and POP should still take O(1) time.

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

ERM, Hi, can you give me a quote for an E-R diagram

Hi, can you give me a quote for an E-R diagram

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