Find the highest subset of an integer array whose sums add up to a given target

Question

I am trying to find a subset of values within an array which add up to a given number and return an array of that subset. I need the return array to contain the highest poss

Answer 1

The basic pattern for recursion is:

1. Return known value for simple case(s). For this problem, the simple cases are (a) a target of 0 (solution is the empty array) and (b) a negative target (failure).
2. Recurse and return some calculation based on the answer. For this problem, we look at each candidate value, and recurse with a target reduced by that value, returning an array composed of the result of the recursion with the addition of the current element.

So:

// Find subset of a that sums to n.
function subset_sum(n, a) {
  // SIMPLE CASES
  if (n < 0)   return null;       // Nothing adds up to a negative number
  if (n === 0) return [];         // Empty list is the solution for a target of 0

  // RECURSIVE CASE
  a = a.slice();
  while (a.length) {              // Try remaining values
    var v = a.shift();            // Take next value
    var s = subset_sum(n - v, a); // Find solution recursively
    if (s) return s.concat(v);    // If solution, return
  }
}

To enforce the rule that you want to prefer higher values first, pass this function an array of values that is pre-sorted in descending order.

> subset_sum(19, [11, 9, 7, 5, 3, 2, 1])
< [1, 7, 11]