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

Mcs-021, #questWrite an algorithm for multiplication of two sparse matrices...

#questWrite an algorithm for multiplication of two sparse matrices using Linked Lists.ion..

Define merge sort, Define Merge Sort  Merge sort is a perfect example ...

Define Merge Sort  Merge sort is a perfect example of a successful application of the divide and conquer method. It sorts a given array A[0...n-l] by separating it into two ha

Preorder traversal of a binary tree, Preorder traversal of a binary tree ...

Preorder traversal of a binary tree struct NODE { struct NODE *left; int value;     /* can take any data type */ struct NODE *right; };   preorder(struct N

What are the objectives of visual realism applications, What are the Object...

What are the Objectives of visual realism applications After studying this unit, you should be able to know specific needs of realism, add realism to pictures by el

Whether the infix expression has balanced parenthesis or not, Using stacks,...

Using stacks, write an algorithm to determine whether the infix expression has balanced parenthesis or not Algorithm parseparens This algorithm reads a source program and

Explain in detail about the abstract data type, Abstract data type The ...

Abstract data type The thing which makes an abstract data type abstract is that its carrier set and its operations are mathematical entities, like geometric objects or numbers;

Explain cam software, Explain CAM software CAD/CAM software has been re...

Explain CAM software CAD/CAM software has been recognized as an essential tool in the designing and manufacturing of a product due to its ability to depict the designs and tool

If, 1. Start 2. Get h 3. If h T=288.15+(h*-0.0065) 4. else if h T=2...

1. Start 2. Get h 3. If h T=288.15+(h*-0.0065) 4. else if h T=216.65 5. else if h T=216.65+(h*0.001) 6. else if h T=228.65+(h*0.0028) 7. else if h T=270.65 8.

Define strictly binary tree, Define Strictly Binary Tree Strictly Bina...

Define Strictly Binary Tree Strictly Binary Tree: - If each non leaf node in binary tree has non empty left and right sub-trees , then the tree is known as a strictly binary t

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