Question

The problem is simpler than knapsack (or a type of it, without values and only positive weights). The problem consists of checking whether a number can be a combination of others. The function should return true or false.

For example,

112 and a list with { 17, 100, 101 } should return false, 469 with the same list should return true, 35 should return false, 119 should return true, etc…

Edit: subset sum problem would be more accurate for this than knapsack.

Answer 1

An observation that will help you is that if your list is {a, b, c…} and the number you want to test is x, then x can be written as a sum of a sublist only if either x or x-a can be written as a sum of the sublist {b, c, …}. This lets you write a very simple recursive algorithm to solve the problem.

edit: here is some code, taking into account the comments below. Not tested so probably buggy; and not necessarily the fastest. But for a small dataset it will get the job done neatly.

bool is_subset_sum(int x, std::list::const_iterator start, std::list::const_iterator end)
{
  // for a 1-element list {a} we just need to test a|x
  if (start == end) return (x % *start == 0); 

  // if x is small enough  we don't need to bother testing x - a
  if (x<a) return is_subset_sum (x, start+1, end);

  // the default case. Note that the shortcut properties of || means the process ends as soon as we get a positive.
  return (is_subset_sum (x, start+1, end) || is_subset_sum (x-a, start, end));
}