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Voeg bottom-up implementatie toe #21

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Voeg bottom-up implementatie toe #21

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23 changes: 23 additions & 0 deletions semester1/DT/oefenzittingen/Prolog/oefenzitting 2/Oefening 3.pl
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Original file line number Diff line number Diff line change
Expand Up @@ -12,8 +12,14 @@
% voor positie 5 wordt de som berekend van 3 en 4
% Het cijfer dat op positie 3 staat wordt dus meer dan 2 keer berekend, ook positie 4 wordt opnieuw berekend,
% terwijl we deze al weten.
%
% time(fib(25,R)). :
% 300,097 inferences, 1.476 CPU in 1.476 seconds (100% CPU, 203329 Lips)

% Betere methode is door een lijst op te stellen tot het benodigde nummer:
%
% time(fib2(50000,R)). :
% 99,999 inferences, 0.300 CPU in 0.300 seconds (100% CPU, 333319 Lips)
fib2(X,Y) :- fib2(X,Y,[1,0]).

fib2(1,0,_):- !.
Expand All @@ -22,3 +28,20 @@
X1 is X - 1,
R1 is A + B,
fib2(X1,Y,[R1,A,B|Rest]).

% Bottom-up implementatie (bron: "Prolog programming for artificial intelligence", Ivan Bratko, 1e editie - p. 196)
%
% time(fib3(50000,R)). :
% 199,995 inferences, 0.198 CPU in 0.198 seconds (100% CPU, 1010524 Lips)
fib3(1,0).
fib3(N,R) :-
forwardfib(2,N,0,1,R).

forwardfib(M,N,_,F2,F2) :-
M >= N.

forwardfib(M,N,F1,F2,F) :-
M < N,
MM is M + 1,
FF is F1 + F2,
forwardfib(MM,N,F2,FF,F).