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Suppose the subset sum problem is extended to allow negative integers in the input list. Which of the following statements is true about solving this variant efficiently?

hard🎤 Interviewer Follow-up Q10 of Q15

Dynamic Programming: Knapsack - Subset Sum

Suppose the subset sum problem is extended to allow negative integers in the input list. Which of the following statements is true about solving this variant efficiently?

AGreedy approach can solve it optimally

BDP must be modified to handle negative sums, often requiring offsetting indices

CThe problem becomes trivial since negative numbers can cancel positives

DThe standard 0/1 subset sum DP approach works without modification

Step-by-Step Solution

Solution:

Step 1: Understand impact of negative numbers
Negative numbers allow sums to decrease, making subset sums unbounded in negative direction.
Step 2: Analyze DP applicability
Standard DP uses non-negative indices; negative sums require complex offsetting or infinite DP states.
Step 3: Recognize problem complexity
DP must be modified to handle negative sums, often by offsetting indices to keep them non-negative.
Final Answer:
Option B -> Option B
Quick Check:
Negative numbers break standard DP assumptions [OK]

Quick Trick: Negative numbers require DP modifications with offset indices [OK]

Common Mistakes:

MISTAKES

Assuming DP works unchanged
Thinking greedy suffices

Trap Explanation:

PITFALL

Candidates underestimate complexity introduced by negative numbers.

Interviewer Note:

CONTEXT

Tests candidate's ability to adapt or recognize limits of DP patterns.

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