Question

I am learning recursion and having hard time in tracing recursion.
Here is my problem and I have the solution which is working perfectly fine.
I am stuck at some point and not able to proceed with tracing.

problem:
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.

Solution:

public static boolean groupSum1(int start, int[] nums, int target)
      {
          if (start >= nums.length) return (target == 0);             
          if (groupSum1(start + 1, nums, target - nums[start])) return true;              
          if (groupSum1(start + 1, nums, target)) return true;            
          return false;
        }

start = 0 (where we have to start the array)

nums[]={10,8,6} target = 16

Please help me with tracing of the problem?

Answer 1

Start by numbering the lines

  public static boolean groupSum1(int start, int[] nums, int target)
  {
  1.    if (start >= nums.length) return (target == 0);             
  2.    if (groupSum1(start + 1, nums, target - nums[start])) return true;              
  3.    if (groupSum1(start + 1, nums, target)) return true;            
  4.    return false;
  }

Here’s the execution (assuming this is what you are asking for):

1 call groupSum1(0, {10, 8, 6}, 16)
    1. 0 < 3 next
2 call groupSum1(1, {10, 8, 6}, 6)
    1. 1 < 3 next
3 call groupSum1(2, {10, 8, 6}, -2)
    1. 2 < 3 next
4 call groupSum1(3, {10, 8, 6}, -8)
    1. 3 == 3 return false to call 3      
back to call 3 in line 2.
5 call groupSum1(3, {10, 8, 6}, -2)
    1. 3 == 3 return false to call 3
back to call 3 in line 3.
    return false to call 2
back to call 2 in line 2.
6 call groupSum1(2, {10, 8, 6}, 6)
    2 < 3 next
7 call groupSum1(3, {10, 8, 6}, 0)
    3 == 3 return true to call 6
back to call 6 in line 2.
    return true to call 2
back to call 2 in line 3.
    return true to call 1
back to call 1 in line 2.
    return true

The number in front of the recursive call is just an index I’m using to keep track of depth. I hope it’s understandable.