Prolog write n as sum of consecutive numbers - prolog

Question

I'm studying prolog and I want to determine all decomposition of n (n given, positive), as sum of consecutive natural numbers but I don't know how to approach this.
Any ideas ?

Answer 1

The key here is between/3, which relates numbers and ranges. Prolog is not going to conjure up numbers from thin air, you have to give it some clues. In this case, you can assume a range of numbers between 1 and the n which you are given:
decomp2(N, X, Y) :-
between(1, N, X),
between(1, N, Y),
N =:= X + Y.
This will give you the sum of two numbers that yields N:
?- decomp2(5, X, Y).
X = 1,
Y = 4 ;
X = 2,
Y = 3 ;
X = 3,
Y = 2 ;
X = 4,
Y = 1 ;
Once you can get two, you can get a longer list by tearing one value off with decomp2/2 and getting the rest through induction. You just need to come up with a base case, such as, the singleton list of N:
decomp(N, [N]).
decomp(N, [X|L]) :- decomp2(N, X, Y), decomp(Y, L).
Be warned that this is going to produce a lot of repetition!
?- decomp(5, L).
L = [5] ;
L = [1, 4] ;
L = [1, 1, 3] ;
L = [1, 1, 1, 2] ;
L = [1, 1, 1, 1, 1] ;
L = [1, 1, 2, 1] ;
L = [1, 2, 2] ;
L = [1, 2, 1, 1] ;
L = [1, 3, 1] ;
L = [2, 3] ;
L = [2, 1, 2] ;
L = [2, 1, 1, 1] ;
L = [2, 2, 1] ;
L = [3, 2] ;
L = [3, 1, 1] ;
L = [4, 1] ;
You could probably clamp down on the repetition by introducing an ordering requirement, such as that X be greater than Y.

Answer 2

I have reached the solution and it looks something like this:
Remark: in isConsecutive i get rid of the "solution" when the list is the number itself
% equal with the given parameter N.
% generatePair(N - integer, X - integer, Y - integer)
% generatePair(i,o,o)
% generatePair(N) = { (X,Y), X<Y && X+Y=N
generatePair(N, X, Y) :-
my_between(1, N, Y),
my_between(1, N, X),
X < Y,
N =:= X + Y.
% This predicate decomposes the given number N into a list of integers
% such that their sum is equal to N.
% decomposeNumber(N - integer, L - list)
% decomposeNumber(i,o)
% decomposeNumber(N) = { [X|L]
decomposeNumber(N, [N]).
decomposeNumber(N, [X|L]) :- generatePair(N, X, Y), decomposeNumber(Y, L).
% This predicate checks it the that elements in the given list have
% consecutive value.
% isConsecutive(L - list)
% isConsecutive(i)
% isConsecutive([l1,l2,..,ln]) = { true, L=[l1,l2] && l1+1=l2
% { isConsecutive(l2..ln), l1+1=l2 && n>2
% { false, otherwise
isConsecutive([X,Y]):-X+1=:=Y.
isConsecutive([H1,H2|T]):-H2=:=H1+1, isConsecutive([H2|T]).
nAsSumOfConsecutives(N,L):-decomposeNumber(N,X), isConsecutive(X), L=X.
main(N,L):-findall(R,nAsSumOfConsecutives(N,R),L).