This is a good video but it gets the definition of omega and theta wrong, or at least their definition is very non-standard. By default, O, omega and theta all

This is a good video but it gets the definition of omega and theta wrong, or at least their definition is very non-standard. By default, O, omega and theta all refer to the worst case running time. - O(n) means worst_case_run_time <= C n - omega(n) means worst_case_run_time >= C n - theta(n) means C1 n <= worst_case_run_time <= C2 n If you want to talk about something other than worst case, you usually just say it in words, like "the average complexity of this algorithm is O(n^2)". (I can't remember when someone has ever looked at "best case".) To rephrase - "This algorithm is O(something)" means I have an upper bound on the running time on the worst inputs. - "This algorithm is omega(something)" means I have a lower bound on the running time on the worst inputs. - "This algorithm is theta(something)" means I have both an upper and lower bound on the running time on the worst inputs (that differ only by a constant multiple. In particular, a lower bound does not mean "best case" (they aren't even in the same part of the sentence). (There's also some other detail from the video like the bit representation of string length that needs a footnote but that's much less important, I think.)