Finding all possible combinations of objects

I have 4 different obejcts with different weights each. I know the individual weights of the objects, the empty weight of the box and the total weight. Yet I do not know the number of objects. How can I find all the possible combinations of objects inside?

For example

Object1: 3 grams, Object2: 5 grams, Object3: 2 grams, Object4: 7 grams,

Empty weight of the box: 600 grams

What function may I use to find all the possible combination of objects within the box given the total weight is 850 grams?

Answer 1

[Steven Lord]

Implement one or more of the algorithms given on the Wikipedia page abour the knapsack problem.

[Torsten]

Usually, this gives one solution, not all.

Answer 2

[Matt J]

You can use the attached file,

w=850-600;
A=[3,5,2,7];
Nmax=ceil(w/min(A));

combinations=diophantine(A,w,0:Nmax)

combinations = 11174×4

77 2 1 1 72 5 1 1 67 8 1 1 62 11 1 1 57 14 1 1 52 17 1 1 47 20 1 1 42 23 1 1 37 26 1 1 32 29 1 1

[Torsten]

combinations=diophantine(A,w,0:Nmax)

instead of

combinations=diophantine(A,w,1:Nmax)

[Matt J]

Right!

Answer 3

[Torsten]

Brute force:

n1 = 83;
n2 = 50;
n3 = 125;
n4 = 35;

nsol = 0;
for i = 0:n1
    for j = 0:n2
        for k = 0:n3
            for l = 0:n4
                if 3*i + 5*j + 2*k + 7*l == 250
                    nsol = nsol+1;
                    sol(nsol,1) = i;
                    sol(nsol,2) = j;
                    sol(nsol,3) = k;
                    sol(nsol,4) = l;
                end
            end
        end
    end
end