What is meaning of Algorithmic Notations

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Hi,

As Big O notation, its shows worst case possibility.

What Theta Notation like, Theta Notation,Little-O Notation ,Little Omega Notation means.

If possible please give question in simple English rather that Mathematics.

Thanks

Posted 26-Mar-12 19:29pm

Pranit Kothari

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OriginalGriff · Answer 1 · 2012-03-26T21:16:00

Solution 1

You can't really define these notations in "simple English" - they are complicated mathematical concepts which need precise definitions to show the significant differences.

Google: Look at Wiki, and a Wolfram Alpha - they both explain them, but not in simple English!

Posted 26-Mar-12 21:16pm

OriginalGriff

CPallini · Answer 2 · 2012-03-26T21:42:00

Solution 2

Simple English Answer: "Get a Math book and study it" (or, with other, more authoritative words: "There is no Royal Road to geometry").

Posted 26-Mar-12 21:42pm

CPallini

YvesDaoust · Answer 3 · 2012-04-23T05:50:00

First note that Big O is not specifically related to the worst-case behavior of an algorithm, but to the so called asymptotic behavior of any function, i.e. how the function compares to another one in the limit when N goes to infinity.

f(N) = O(g(N)) means that f grows like g or faster.

f(N) = uppercase omega(g(N)) means that f grows like g or slower.

f(N) = lowercase theta(g(N)) means that f grows like g.

f(N) = o(g(N)) means that f / g goes to zero.

f(N) = lowercase omega(g(N)) means that f / g goes to infinity.

Example: the sum of the N first integers is lowercase theta(N^2); sorting N numbers certainly takes time O(N) because you need to look at every number at least once; N.log(N) is uppercase omega(N.sqrt(N))...

This notation can apply to the worst-case/best-case/average-case running time of algorithms, or to known upper/lower bounds of these.