Prolog: Distance between cities - prolog

Question

I'm new to Prolog. I'm trying to make a simple program that find the distance between cities using recursive structure. The problem occurs when I try to find sum distance between cities that are not directly connected (e.g. london to sydney).
distance(london,newyork,3.2).
distance(london,capetown,5.8).
distance(london,rome,0.8).
distance(london,panama,4.5).
distance(panama,sydney,7.7).
distance(newyork,sanfrancisco,2.5).
distance(newyork,panama,1.9).
distance(sanfrancisco,sydney,6.2).
distance(sanfrancisco,tokyo,4.5).
distance(tokyo,calcutta,2.5).
distance(tokyo,sydney,4.1).
distance(sydney,calcutta,4.4).
distance(sydney,capetown,6.0).
distance(capetowm,rome,5.1).
distance(calcutta,cairo,2.2).
distance(cairo,rome,0.9).
connected(X,Y,Distance):-
distance(X,Y,Distance).
connected(X,Y,Distance):-
distance(X,Z,NewDistance),
connected(Z,Y,NewDistance),
Distance is Distance+NewDistance.

Answer 1

You can modify your last rule like this:
connected(X,Y,Distance):- distance(X,Z,Distance1),
distance(Z,Y,Distance2),
SumDistance is Distance1+Distance2,
write(SumDistance).
Here is my result:
1 ?- connected(london,sydney,X).
12.2
true .
The route is London -> Panama -> Sydney. I used trace. to see how it works:
2 ?- trace.
true.
[trace] 2 ?- connected(london,sydney,X)
....
Redo: (7) distance(london, _G1945, _G1946) ? creep
Exit: (7) distance(london, panama, 4.5) ? creep
Call: (7) distance(panama, sydney, _G1950) ? creep
Exit: (7) distance(panama, sydney, 7.7) ? creep
Call: (7) _G1955 is 4.5+7.7 ? creep
Exit: (7) 12.2 is 4.5+7.7 ? creep
Call: (7) write(12.2) ? creep
12.2
Exit: (7) write(12.2) ? creep
Exit: (6) connected(london, sydney, _G1871) ? creep
(I have removed some of the tracing because it was too long).