this post was submitted on 19 Oct 2023
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As the volume of the room is finite, even "exponential" or worse search algorithms will complete in constant time.
<.<
Well, there's only finitely many atoms in the universe, do all algorithms therefore have constant time?
Although you could argue for very large amounts of clothes my method of throwing clothes on the floor starts performing worse due to clothes falling on the same spot and piling up again.
Unless you extend your room. Let's take a look at the ✨amortized✨time complexity.
Well landau notation only describes the behaviour as an input value tends to infinty, so yes, every real machine with constant finite memory will complete everything in constant time or loop forever, as it can only be in a finite amount of states.
Luckily, even if our computation models (RAM/TM/...) assume infinite memory, for most algorithms the asymptotic behaviour is describing small-case behaviour quite well.
But not always, e.g. InsertionSort is an O(n^2) algorithm, but IRL much faster than O(n log n) QuickSort/MergeSort, for n up to 7 or so. This is why in actual programs hybrid algorithms are used.