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If candidates can include negative integers along with positive integers, and you want all unique combinations summing to a target with reuse allowed, which statement is correct about solving this variant?

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Subsets & Combinations - Combination Sum (Reuse Allowed)
If candidates can include negative integers along with positive integers, and you want all unique combinations summing to a target with reuse allowed, which statement is correct about solving this variant?
ASorting candidates and pruning negative numbers solves the problem.
BStandard backtracking works without modification since reuse is allowed.
CDynamic programming solves it in polynomial time regardless of negatives.
DBacktracking may not terminate without additional constraints due to infinite loops.
Step-by-Step Solution
Solution:

  1. Step 1: Consider negative numbers impact

    Negative numbers allow sums to oscillate, potentially causing infinite recursion.

  2. Step 2: Analyze backtracking termination

    Without constraints, backtracking can revisit states endlessly due to negative reuse.

  3. Step 3: Conclusion

    Additional constraints or memoization with cycle detection are needed to ensure termination.

  4. Final Answer:

    Option D -> Option D

  5. Quick Check:

    Negative reuse causes infinite recursion unless handled [OK]
Quick Trick: Negative candidates cause infinite recursion without safeguards [OK]
Common Mistakes:
MISTAKES
  • Assuming standard backtracking always terminates
  • Believing DP solves negatives in polynomial time without cycles
  • Ignoring infinite loops caused by negative reuse
Trap Explanation:
PITFALL
  • Ignoring infinite recursion risk from negative numbers makes other options seem plausible.
Interviewer Note:
CONTEXT
  • Tests understanding of algorithm limitations when problem constraints change.
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