List combination start

Question

I copied this code from this page:

% combination(K,L,C) :- C is a list of K distinct elements 
%    chosen from the list L
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, if you enter combination(2,[1,2,3,4],L), the result is:

L = [1, 2] ;
L = [1, 3] ;
L = [1, 4] ;
L = [2, 3] ;
L = [2, 4] ;
L = [3, 4] ;

Now I would like to enter something that allows you to start at a determined point of the combination. For example, something like: combination(2,[1,2,3,4],[1,4],L), and the result:

L = [1, 4] ;
L = [2, 3] ;
L = [2, 4] ;
L = [3, 4] ;

Starting the combination at [1,4] and skipping the "steps" [1,2] and [1,3].

Thanks for you help!

Answer 1

try this

combination(0,_,[]).
combination(K,L,[X|Xs]) :- 
    K > 0,
    el(X,L,R), 
    K1 is K-1, 
    combination(K1,R,Xs).

generate(K, L, X, Pivot, Resault) :-
    bagof(X, L^combination(K, L, X), Bag),
    iterate(Bag, Pivot, Resault).

iterate([], _, []).
iterate([P|T], P, [P|T]):-!.
iterate([H|T], P, Res) :-
    iterate(T, P, Res).

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

use generate/5 like this:

| ?- generate(2, [1,2,3,4], X, [1,4], Res).

Res = [[1,4],[2,3],[2,4],[3,4]]
yes.

first I gather all the solutions in a bag, then I iterate through the bag to find a pivot member, if I find it the resault is a list with the pivot as head, and rest of solutions as tail. and if I don't the resault is an empty list.

not a very wise solution, but works.