Write predicates that will find solutions for the following colored-balls-in-a-r

Question

Write predicates that will find solutions for the following colored-balls-in-a-row problem with different sets of constraints.

You have six colored balls: 2 black, 2 red and 2 blue.

No balls of the same color may be adjacent to one another.

Write Prolog predicates to find all solutions for that situation (i.e. if you force recursion with “;”, Prolog will find the next solution, and the next, until it has found them all, and then it will fail).

Explanation / Answer

% a program that find solutions for each of the following colored ball problems with different sets of constraints. % to run, type either % sit1, sit2 or sit3. % select an element for use in permutation test % % If the element is the head of the list, then it is in the list, and the tail is left selectE(Element, [Element|Tail], Tail). % If the two lists have the same head, check for more elements in the rest of the lists selectE(Element, [Head|Tail1], [Head|Tail2]) :- selectE(Element, Tail1, Tail2). % generate permutations % % The empty list is a permutation of itself permutationQ([],[]). % List1 is a permutation of List2 if each element occurs in both lists % the same number of times permutationQ(List, [Head|Tail]) :- selectE(Head, List, Rest), permutationQ(Rest, Tail). % % There are 5 colors - 2 blues, 2 greens, 1 yellow % sit1 :- permutationQ([green,green,blue,blue,yellow],[A,B,C,D,E]), + A=B, + B=C, + C=D, + D=E, printout([A,B,C,D,E]). % print any solution you find % print solutions of sit1 printout([A,B,C,D,E]) :- nl, write('The order of colors from top to bottom is: '), nl, write(A),nl, write(B),nl, write(C),nl, write(D),nl, write(E),nl. % There are 6 colors - 1 red, 1 blue, 4 blacks, % sit2 :- permutationQ([black,black,black,black,red,blue],[A,B,C,D,E,F]), ((A==red -> D==blue); (A==blue -> D==red); (B==red -> E==blue); (B==blue -> E==red); (C==red -> F==blue); (C==blue -> F==red); (D==red -> C==blue); (D==blue -> C==red)), printout2([A,B,C,D,E,F]). % print any solution you find % print solutions of sit2 printout2([A,B,C,D,E,F]) :- nl, write('The order of colors from top to bottom is: '), nl, write(A),nl, write(B),nl, write(C),nl, write(D),nl, write(E),nl, write(F),nl. % There are 8 colors - 3 greens, 2 whites, 2 reds, 1 black sit3 :- permutationQ([black,white,white,red,red,green,green,green],[A,B,C,D,E,F,G,H]), % The colors in B and C are not green. + B=green, + C=green, % The colors in E and F are not green because the colors in F and G are not red. + E=green, + F=green, % Since red can't be in H, green can't be in G. + G=green, % The colors in D and H are the same color. D=H, % The colors in A and G are of different colors. + A=G, % The color in F and G are not red. + F=red, + G=red, % Red can't be in A because there isn't any other position on the left for the green. + A=red, % The colors in C and D are not red because the colors in B and C are not green. + C=red, + D=red, % Whites are neither A nor H. + A=white, + H=white, % White is not on D because white can't be on H. + D=white, printout3([A,B,C,D,E,F,G,H]). % print any solution you find % print solutions of sit3 printout3([A,B,C,D,E,F,G,H]) :- nl, write('The order of colors from top to bottom is: '), nl, write(A),nl, write(B),nl, write(C),nl, write(D),nl, write(E),nl, write(F),nl, write(G),nl, write(H),nl.

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