Other Common Asymptotic Notations and Why Big O Trumps Them

Explore the definitions and roles of Big Omega, Big Theta, little o, and little omega asymptotic notations in algorithm analysis. Understand why Big O is commonly used for worst-case running time and space complexity evaluation, helping you assess algorithm efficiency more effectively.

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Big ‘Omega’ - Ω(.)
Why Big ‘O’ is preferred over other notations

Big ‘Omega’ - $\Omega(.)$

Mathematically, a function $f(n)$ is in $\Omega(g(n))$ if there exists a real constant $c > 0$ and there exists $n_o > 0$ such that $f(n) \geq cg(n)$ for $n \geq n_o$ . In other words, for sufficiently large values of $n$ , $f(n)$ will grow at least as fast as $g(n)$ .

It is a common misconception that Big O characterizes worst-case running time while Big Omega characterizes best-case running time of an algorithm. There is no one-to-one relationship between any of the cases and the asymptotic notations.

The following graph shows an example of functions $f(n)$ and $g$ ...

1.Introduction to Complexity Measures

2.Introduction to Lists

3.Introduction to Linked Lists

4.Introduction to Stacks and Queues

5.Introduction to Graphs

6.Introduction to Trees

7.Trie

8.Introduction to Heap

9.Introduction to Hashing

10.Summary of Data Structures

Mock Interview

Other Common Asymptotic Notations and Why Big O Trumps Them

Big ‘Omega’ - $\Omega(.)$

Other Common Asymptotic Notations and Why Big O Trumps Them

Big ‘Omega’ - Ω(.)\Omega(.)Ω(.)

Big ‘Omega’ - $\Omega(.)$