Prolog syntax - using function results

Question

Hi,

I am trying to perform a sum operation on every result of :

combination(0,_,[]).

combination(K,L,[X|Xs]) :- K > 0,

el(X,L,R), K1 is K-1, combination(K1,R,Xs).

el(X,[X|L],L).

el(X,[_|L],R) :- el(X,L,R).

For example, the user will enter is_sum_equal_10 ([1,2,3,4,5,6,7]) and the result will be true if the sum of any of the permutations equals 10.

I am struggling with putting it all together, can someone please help me define the is_sum_equal_10 rule that uses the combination rule for each permutation?

Thanks in advance!

Amy

Answer 1

OK, well it's pretty easy to write really, you just need a rule to say if a particular combination sums to 10, and then another extra one to count up through the different sizes of combination lists (which is required due to the way you wrote combination with the K that you need to decrease as you check the rule).

1 ?- [user].
|: combination(0,_,[]).
|: combination(K,L,[X|Xs]) :- K > 0,
|:    el(X,L,R), K1 is K-1, combination(K1,R,Xs).
|: el(X,[X|L],L).
|: el(X,[_|L],R) :- el(X,L,R).
|: 
|: totals_10([],10).
|: totals_10([X|Xs],T) :- N is T+X, totals_10(Xs,N).
|: 
|: is_comb_sum_equal_10(Numbers,_,R) :- combination(R,Numbers,C), totals_10(C,0).
|: is_comb_sum_equal_10(Numbers,N,R) :- Rnext is R+1, Rnext =< N,
|:    is_comb_sum_equal_10(Numbers,N,Rnext).
|: 
|: is_sum_equal_10(Numbers) :- length(Numbers,N), is_comb_sum_equal_10(Numbers,N,0).
|: 
% user://1 compiled 0.13 sec, 1,824 bytes
true.

2 ?- is_sum_equal_10([2,3,5]).
true .

3 ?- is_sum_equal_10([2,235,124,3,3347,5,2373]).
true .

4 ?- is_sum_equal_10([2,235,124,3,3347,6,2373]).
false.

5 ?- is_sum_equal_10([1,1,1,1,1,-1,1,1,1,1,12]).
false.

6 ?- is_sum_equal_10([1,1,1,1,1,-1,1,1,1,1,11]).
true ;
false.

Since you don't care about the actual list or how big it is in the is_sum_equal_10 thing, you can just sum the combinations as you go along, and even better, check the sum is correct as a rule for the base case. I think it's a bit neater if you subtract from the desired total to get to 0 at the base rather than adding up and checking at the end against the value you want. This gives you a very simple single ruleset to look for a certain sum.

7 ?- [user].
|: is_subset_sum(0,[]).
|: is_subset_sum(N,[_|Xs]) :- is_subset_sum(N,Xs).
|: is_subset_sum(N,[X|Xs]) :- R is N-X, is_subset_sum(R,Xs).
|: 
% user://2 compiled 0.03 sec, 540 bytes
true.

8 ?- is_subset_sum(10,[3,5,6]).
false.

9 ?- is_subset_sum(10,[123,4,1,77,3,2,34]).
true .

10 ?- is_subset_sum(11,[0,2,4,6,8,10,12,14,16,18,20,22]).
false.

This approach is of course both much easier to understand, and a lot more efficient.