Pardon me if the question is “silly”. I am new to algorithmic time complexity.
I understand that if I have n numbers and I want to sum them, it takes “n steps”, which means the algorithm is O(n) or linear time. i.e. Number of steps taken increases linearly with number of input, n.
If I write a new algorithm that does this summing 5 times, one after another, I understand that it is O(5n) = O(n) time, still linear (according to wikipedia).
Question
If I have say 10 different O(n) time algorithms (sum, linear time sort etc). And I run them one after another on the n inputs.
Does this mean that overall this runs in O(10n) = O(n), linear time?
Yep, O(kn) for any constant k, = O(n)
If you start growing your problem and decide that your 10 linear ops are actually k linear ops based on, say k being the length of a user input array, it would then be incorrect to drop that information from the big-oh