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> I cannot think of any algorithms with arbitrary sized inputs that have truly constant execution time.

With respect, I think you may misunderstand the meaning of "constant time" in the sense of complexity theory, i.e. O(1). Accessing an element in an array of size n is a constant time operation. See: https://stackoverflow.com/questions/7297916/why-does-accessi...

EDIT: Corrected "search" to "access"

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Wouldn’t searching for an element in an arbitrary array of size n happen in O(n) time, while only accessing it is considered O(1)? I could understand the search case for something like a hash table being O(1) but does that also apply to your standard array?

Ah, I misspoke. I meant "access", you're correct about searching. The original link I cited for explanation still applies.

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