Dynamic Programming: Knapsack - Last Stone Weight II
If stones can be split into fractional weights, which method best approximates the minimal last stone weight difference?
If stones can be split into fractional weights, which method best approximates the minimal last stone weight difference?
hard🔁 Follow Up Q10 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand fractional weights
Fractional weights allow splitting stones arbitrarilyStep 2: Recognize problem type
Discrete DP no longer applies; problem becomes continuous optimizationStep 3: Choose method
Linear programming can handle continuous variables and constraintsFinal Answer:
Option A -> Option AQuick Check:
Fractional weights -> continuous optimization [OK]
Quick Trick: Fractional weights -> use linear programming [OK]
Common Mistakes:
MISTAKES- Applying discrete DP to fractional weights
- Using greedy which may not minimize difference
- Ignoring continuous nature of problem
Trap Explanation:
PITFALL- Discrete DP looks familiar but fails with fractional inputs.
Interviewer Note:
CONTEXT- Tests ability to adapt algorithms to continuous problem variants.
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