A simple recursive nested function, with short-circuiting for combinations whose sums are greater than N (this makes the whole thing viable for small values of N and give results as quickly as possible):
function C = temp4(N)
P = [250,500,500,1250,2500,5000,5000,15000,15000,15000,15000 8166,8926,9796,10800 11967,13333,14948,16875,16875,19200,22041,22041,25562];
C = {};
for ii = 1:numel(P)
nestfun(P(ii),P(ii+1:end))
end
function nestfun(t,V)
if sum(t)<N
for jj = 1:numel(V)
nestfun([t,V(jj)],V(jj+1:end))
end
elseif sum(t)==N
C{end+1} = t;
end
end
end
Tested (the repeated vectors are due to the repeated values in P):
>> temp4(3000)
ans = {
[500 2500]
[500 2500]}
>> temp4(30000) % a much more interesting example
ans = {
[250 500 500 1250 2500 5000 5000 15000]
[250 500 500 1250 2500 5000 5000 15000]
[250 500 500 1250 2500 5000 5000 15000]
[250 500 500 1250 2500 5000 5000 15000]
[15000 15000]
[15000 15000]
[15000 15000]
[15000 15000]
[15000 15000]
[15000 15000]
[10800 19200]}
Note that if N is large then you can expect to be waiting for some time... e.g. given all 620,448,401,733,239,000,000,000 combinations at a rate of 1 million checks per second, you would have to wait around
>> yrs = 620448401733239000000000/1e6/60/60/24/365 % years
yrs = 19674289755.62021
>> num2words(yrs,'sigfig',1,'type','money','unit','Year|')
ans = twenty billion years
