what is the algorithm behind the solution below
<p>I encountered recursive exercises for improving my coding skills and found the following problem. </p>

<p>Given an array of ints, is it possible to choose a group of some of the ints, such that the group sums to the given target? Rather than looking at the whole array, our convention is to consider the part of the array starting at index start and continuing to the end of the array. The caller can specify the whole array simply by passing start as 0. No loops are needed -- the recursive calls progress down the array.</p>

<pre><code>groupSum(0, [2, 4, 8], 10) → true
groupSum(0, [2, 4, 8], 14) → true
groupSum(0, [2, 4, 8], 9) → false
</code></pre>

<p>After 2 days work and studying it i had nothing. i checked the given soluton and i still can not understand the solution after debugging it step by step. </p>

<pre><code>public boolean groupSum(int start, int[] nums, int target) {
  // Base case: if there are no numbers left, then there is a
  // solution only if target is 0.
  if (start &gt;= nums.length) return (target == 0);

  // Key idea: nums[start] is chosen or it is not.
  // Deal with nums[start], letting recursion
  // deal with all the rest of the array.

  // Recursive call trying the case that nums[start] is chosen --
  // subtract it from target in the call.
  if (groupSum(start + 1, nums, target - nums[start])) return true;

  // Recursive call trying the case that nums[start] is not chosen.
  if (groupSum(start + 1, nums, target)) return true;

  // If neither of the above worked, it's not possible.
  return false;
} 
</code></pre>

<p>The solution is quite short and its logic is combination based. What do you think about it? What is the explanation of the algorithm  behind it?</p>

<p>Regards</p>