I think this should be categorized as "Recursive" rather than "Backtracking". One definition ofBacktracking is:

Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, andabandons a candidate as soon as it determines that the candidate cannot possibly be completed to a valid solution.

I don't see the emphasized part here. To me, this is just a recursive algorithm which tries all possible ways to partition the set into two subsets, evaluating them and picking the best, solving anoptimization problem.

Ah, I see the issue now. This does not solve the "tug of war" problem; you are missing the side condition that both sets should have size n/2.

This does solve the "partition" problem (which can be reduced to the 0-1-knapsack problem) however.

I suggest either renaming this topartition - and removing the GfG reference - or fixing the implementation s.t. the subsets each have size n/2 (note: if n is odd, the sizes may differ by one).

(Note: Calculating the sum of nums in each recursive call is wasteful. But the implementation is correct, and really "efficiently" solving the problem isn't possible anyways (unless P = NP), so I don't mind terribly much. Ideally you should have an outer function, which takes justnums as a parameter, and an inner function, which takes justindex andtarget.)