Algorithm to find possible combinations in Matlab with one constraint?

Question

A very simple example :

A=[100 250 300]

How do I find all possible combinations as long as each combination has a sum of less than 500 ?

Answer 1

This code should work. The result will be stored in the cell array C :

A = [100 250 300];
B = 500;
C = cell(0);

for i = 1:size(A,2)
    D = nchoosek(A,i);
    for j = 1:size(D,1)
        if (sum(D(j,:)) < B)
            C{end+1} = D(j,:);
        end
    end
end

or more compact:

A = [100 250 300];
B = 500;
C = cell(0);

for i = 1:size(A,2)
    C = [C; num2cell(nchoosek(A,i),2)];
end
C = C(cellfun(@(x) sum(x), C) < B);

Answer 2

This simple code

A=[100 250 300];
p = perms(A);

for nn = 1:numel(A)    
    p(sum(p(:,1:nn), 2) < 500, 1:nn)
end

Gives the following output

ans =

   300
   300
   250
   250
   100
   100

ans =
   300   100
   250   100
   100   250
   100   300

If you want to remove duplicates, like [300 100] and [100 300], simply use the sort command to sort the values and then you can remove duplicates using unique