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

Decision tree, . Create a decision table that describes the movement of inv...

. Create a decision table that describes the movement of inventory

Execute algorithm to convert infix into post fix expression, Q. Execute you...

Q. Execute your algorithm to convert the infix expression to the post fix expression with the given infix expression as input Q = [(A + B)/(C + D) ↑ (E / F)]+ (G + H)/ I

Define binary tree, Define Binary Tree  A binary tree T is explained as...

Define Binary Tree  A binary tree T is explained as a finite set of nodes that is either empty or having of root and two disjoint binary trees TL, and TR known as, respectively

Logic circuits, the voltage wave forms are applied at the inputs of an EX-O...

the voltage wave forms are applied at the inputs of an EX-OR gate. determine the output wave form

Explain the concept of colouring, Colouring The use of colours in CAD/C...

Colouring The use of colours in CAD/CAM has two main objectives : facilitate creating geometry and display images. Colours can be used in geometric construction. In this case,

Search on a heap file, Consider the file " search_2013 ". This is a text fi...

Consider the file " search_2013 ". This is a text file containingsearch key values; each entry is a particular ID (in the schema given above). You are tosimulate searching over a h

Binary tree traversals, We have discussed already about three tree traversa...

We have discussed already about three tree traversal methods in the earlier section on general tree. The similar three different ways to do the traversal -inorder , preorder, and p

If-then-else statements, In this example, suppose the statements are simple...

In this example, suppose the statements are simple unless illustrious otherwise. if-then-else statements if (cond) { sequence of statements 1 } else { sequence of st

Define the term ''complexity of an algorithm, Define the term 'complexity o...

Define the term 'complexity of an algorithm; Complexity of an algorithm is the calculate of analysis of algorithm. Analyzing an algorithm means predicting the resources that th

Explain binary search tree, Binary search tree. A binary search tree is...

Binary search tree. A binary search tree is a binary tree that is either empty or in which every node having a key that satisfies the following conditions: - All keys (if an

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