I'm curious if there's such a thing as an algorithm that has a runtime complexity of O(N^-1). If such an algorithm does exist, how would you go about implementing it?
1 Answer
Short answer: no, you can't have an algorithm that runs in O(N^-1). While a mathematical function can be O(N^-1), algorithms are made of discrete steps. Since an algorithm can only execute whole steps, it effectively means you can't achieve that complexity. The minimum time an algorithm takes is O(1) because it has to perform at least one step to be useful, and if it's set to 0 steps, it would effectively end up being not usable at all.
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