MATLAB - Recursive Dynamic Programming - matlab

Question

I seem to have a problem with my knapsack algoritm on MATLAB. I have several files to add to the storage and they have certain values. I would like to maximize the total value under a certain capacity restriction.
The values are 10, 40, 30, 50.
The sizes are 6, 4, 5, 3.
The capacity is 10.
When I run the code, I get the optimal total value but I cannot specify which files have been added to the storage. Is there a way to do this? I tried adding the file numbers into an array but it wouldn't work. The array is emptied every time the function is run.
The code I have is as follows:
function maxim=addfiles(v,w,cap,n)
maxim=0;
stored=[];
if (cap==0)||(n==0)
return
else
if w(n)>cap
maxim=addfiles(v,w,cap,n-1);
else
if addfiles(v,w,cap,n-1)<v(n)+addfiles(v,w,cap-w(n),n-1)
maxim=v(n)+addfiles(v,w,cap-w(n),n-1);
stored(n)=n;
else maxim=addfiles(v,w,cap,n-1);
end
end
end
What I want from the algorithm is to return something like:
Optimal value: 90
Files added: 2,4
Thank you in advance.

Answer 1

I rewrote your code so it will return the maximum value and the selection; not sure if it's more MATLABish than you're used to, but it does the same thing, and is better commented :-D
%// Knapsack problem
%// v = values (non-negative, vector)
%// w = weights (positive, vector)
%// cap = available capacity (non-negative, scalar)
%// n = the remaining number of objects (non-negative, scalar)
%//
%// maxim = max accumulated value (non-negative, scalar)
%// stored = index of stored objects (integer, vector)
function [maxim, stored] = addfiles(v,w,cap,n)
%// End of recursion
if (cap==0)||(n==0)
maxim = 0;
stored = [];
return;
end;
%// Above capacity
if w(n) > cap
[maxim, stored] = addfiles(v,w,cap,n-1);
return;
end;
%// Alternatives 1/2
[maxim1, stored1] = addfiles(v,w,cap,n-1);
[maxim2, stored2] = addfiles(v,w,cap-w(n),n-1);
if maxim1 < v(n) + maxim2
%// Adding is good
maxim = v(n) + maxim2;
stored = [stored2, n];
else
%// Adding is bad
maxim = maxim1;
stored = stored1;
end;
end
Save in addfiles.m, then call with:
[maxim,stored] = addfiles([10, 40, 30, 50], [6, 4, 5, 3], 10, 4)