Compute a list of distinct odd numbers (if one exists), such that their sum is equal to a given number.

Question

:- use_module(library(clpfd)). % load constraint library

% [constraint] Compute a list of distinct odd numbers (if one exists), such that their sum is equal to a given number.

odd(Num) :- Num mod 2 #= 1.

sumOfList([],N,N) :- !.
sumOfList([H|T],Counter,N) :-
  NewN #= H + Counter,
  sumOfList(T,NewN,N).

buildOddList(N,InputList,L) :-
  %return list when sum of list is N
  V in 1..N,
  odd(V),
  append(InputList,[V],TempL),
  sumOfList(TempL,0,N)->
    L = TempL;
    buildOddList(N,TempL,L).

computeOddList(N) :-
  buildOddList(N,[],L),
  label(L).

This is my code, I can't seem to get the right output, any code critics? :)

Answer 1

:- use_module(library(clpfd)). % load constraint library

% [constraint] Compute a list of distinct odd numbers (if one exists), such that their sum is equal to a given number.

odd(Num) :- Num mod 2 #= 1.

sumOfList([],N,N) :- !.
sumOfList([H|T],Counter,N) :-
  NewN #= H + Counter,
  sumOfList(T,NewN,N).

oddList([]) :- !.
oddList([H|T]) :-
  odd(H),
  oddList(T).

computeOddList(N,L) :-
  (L = [];L=[_|_]),
  length(L,V),
  V in 1..N,
  L ins 1..N,
  all_different(L),
  oddList(L),
  sumOfList(L,0,N).

I managed to kinda solved it, however it doesn't end properly after it runs out of cases. Hmm.

Answer 2

Can suggest you this solution:

:- use_module(library(clpfd)).

all_odd([]) :-!.
all_odd([H | T]) :-
 H mod 2 #= 1,
 all_odd(T).

solve(N,L) :-
 N2 is floor(sqrt(N)),
 Len in 1..N2,
 label([Len]),

 length(L, Len),

 L ins 1..N,

 all_different(L),
 all_odd(L),

 sum(L,#=,N),

 label(L),

 % only show sorted sets
 sort(L,L).

Example:

?- solve(17,L).
L = [17] ;
L = [1, 3, 13] ;
L = [1, 5, 11] ;
L = [1, 7, 9] ;
L = [3, 5, 9] ;
false.

Answer 3

I see others have posted complete solutions already. Still, your code can be made to wok with only two slight modifications:

1. computeOddList only tests whether such a list exists. To know which list matches the constraints, just return it. Thus:

   computeOddList(N, L) :-
       ...
   

2. The list TempL may currently contain duplicates. Just place all_different(TempL) after append to fix that.

Now computeOddList will return at least one list of distinct odd numbers if it exists. Still, for e.g. computeOddList(17, L) it will not return all lists. I don't know clpFD myself, so other than suggesting you compare your code to Xonix' code I cannot really help you.