# Big O, Big Theta, Big Omega

Is it right

• Big O - Worst case

• Big Theta - Averge Case

• Big Omega - Best Case

Hi @Azizbek_Khushvakov,
Yes, This is the right representation of notations.
Happy learning!

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Not quite. All three notations can be used for best-case, worst-case, or for average-case as these notations give asymptotic bounds on a function that may correspond to the best-case, the worst-case, or the average-case running time. These notations may often be used in the sense you mention, but they donâ€™t have to be. Letâ€™s take an example.

The best case running time of insertion sort is linear. A linear polynomial is Big-O(n) but it is also Big-Omega (n), and therefore it is also Big-Theta(n). So it would be perfectly legitimate to say â€śThe best-case running time of insertion sort is Big-O(n)â€ť. We donâ€™t typically use the Big-O notation with the best case because thatâ€™s not very useful for us. For the best case, a Big-Omega lower bound is more useful for expressing that we canâ€™t do better than this. For the worst case, Big-O is useful because it tells us we canâ€™t do worse than this.

When using these notations to express a fact about a running time (best, worse, average), think about whether you want to say bounded from above (Big-O), bounded from below (Big-Omega), or bounded from both above and below (Big-Theta).