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Suppose the problem is modified so that each element in the array can be chosen multiple times (unbounded). Which modification to the DP approach correctly solves this variant?

hard🎤 Interviewer Follow-up Q15 of Q15
Dynamic Programming: Knapsack - Minimum Subset Sum Difference
Suppose the problem is modified so that each element in the array can be chosen multiple times (unbounded). Which modification to the DP approach correctly solves this variant?
AChange inner loop to iterate forwards from num to total_sum to allow reuse
BKeep inner loop iterating backwards from total_sum to num as in original code
CUse recursion without memoization to handle multiple uses
DSort array and greedily pick largest elements repeatedly
Step-by-Step Solution

  1. Step 1: Understand reuse impact on DP iteration

    For unbounded knapsack variants, inner loop must iterate forwards to allow multiple counts of the same element.

  2. Step 2: Contrast with original code

    Original code iterates backwards to avoid counting elements multiple times; forward iteration enables reuse.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Forward iteration in inner loop enables multiple uses of elements [OK]
Quick Trick: Forward iteration allows multiple element reuse in DP [OK]
Common Mistakes:
MISTAKES
  • Using backward iteration causing single use only
  • Assuming recursion without memo is efficient
Trap Explanation:
PITFALL
  • Backward iteration looks correct but forbids reuse, a subtle but critical difference.
Interviewer Note:
CONTEXT
  • Tests candidate's understanding of knapsack variants and DP iteration direction.
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