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If the Matchsticks to Square problem is changed so that each matchstick can be used infinitely many times, which algorithmic approach is most efficient to determine if a square can be formed?

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Subsets & Combinations - Matchsticks to Square
If the Matchsticks to Square problem is changed so that each matchstick can be used infinitely many times, which algorithmic approach is most efficient to determine if a square can be formed?
ABacktracking with bitmask and memoization
BDynamic programming with unlimited item usage (unbounded knapsack style)
CGreedy algorithm sorting matchsticks descending
DDivide and conquer splitting matchsticks into halves
Step-by-Step Solution
Solution:

  1. Step 1: Recognize unlimited usage

    Unlimited reuse means bitmask is not applicable as states can't track usage.

  2. Step 2: Use unbounded knapsack DP

    Dynamic programming allowing unlimited usage of items fits this variant.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Unlimited usage problems map to unbounded knapsack DP [OK]
Quick Trick: Unlimited usage -> unbounded knapsack DP approach [OK]
Common Mistakes:
MISTAKES
  • Trying to use bitmask which tracks single usage
  • Assuming greedy can solve all unlimited usage problems
  • Ignoring the change in problem constraints
Trap Explanation:
PITFALL
  • Bitmask memoization fails with unlimited usage due to state explosion
Interviewer Note:
CONTEXT
  • Tests ability to adapt algorithmic approach to problem variants
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