In Prolog, problems are solved using backtracking. It s a declarative paradigm rather than an imperative one (like in C, PHP or Python). In this kind of languages is it worth to think in terms of complexity?
The natural way you think problems seems to be O(N^2) as someone pointed in this question.
Its important to analyze Complexity in any Language be it prolog or any imperative language. However I can give you some tips to speed up your prolog programs
You can definitely analyze the complexity of Prolog programs, just like any other language. That particular problem you linked might be O(n^2). But not all Prolog programs will have this complexity. For example, you can easily write a SAT solver in Prolog, and that problem is NP-Complete.
It entirely depends on the problem.
e.g. summing a list of numbers is O(N), as far as I can tell.
sum([],0).
sum(List,Total) :-
sum(List,0,Total).
sum([],Total,Total).
sum([Head|Rest],Accumulator,Total) :-
SoFar is Head + Accumulator,
sum(Rest,SoFar,Total).
The only actions are the addition ("is") and the recursive call, which should both be worth 1 each. They ll both be performed ~ once per item in the list, so the total actions should be ~ 2N, which is O(N).
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