Other Common Asymptotic Notations and Why Big O Trumps Them

Discover the key asymptotic notations beyond Big O, including Big Omega, Big Theta, little o, and little omega. Understand their definitions, differences, and practical uses. Learn why Big O notation is commonly preferred for analyzing worst-case time and space complexity in algorithms, helping you grasp complexity measures essential for efficient coding and interview success.

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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 the 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 $g(n)$ with a Big Omega relationship.

1.Introduction to Complexity Measures

2.Introduction to Arrays

3.Introduction to Linked Lists

4.Introduction to Stack/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’ - $\Omega(.)$

Big ‘Theta’ - $\Theta(.)$

Other Common Asymptotic Notations and Why Big O Trumps Them

Big ‘Omega’ - Ω(.)\Omega(.)Ω(.)

Big ‘Theta’ - Θ(.)\Theta(.)Θ(.)

Big ‘Omega’ - $\Omega(.)$

Big ‘Theta’ - $\Theta(.)$