Dynamic Programming: Knapsack - Ones and Zeroes (2D Knapsack)
Suppose the problem is modified so that each string can be chosen multiple times (unbounded usage). Which change to the dynamic programming approach correctly adapts the solution?
Suppose the problem is modified so that each string can be chosen multiple times (unbounded usage). Which change to the dynamic programming approach correctly adapts the solution?
hard🎤 Interviewer Follow-up Q15 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand difference between 0/1 and unbounded knapsack
Unbounded knapsack allows multiple uses of the same item, so dp updates must allow reuse within the same iteration.Step 2: Adjust dp iteration order
Iterating dp forwards enables using updated states multiple times, correctly counting repeated strings.Step 3: Confirm correctness
Backward iteration prevents reuse in the same iteration, which is incorrect for unbounded usage.Final Answer:
Option A -> Option AQuick Check:
Forward iteration enables multiple item usage [OK]
Quick Trick: Unbounded knapsack uses forward dp iteration [OK]
Common Mistakes:
MISTAKES- Continuing backward iteration from 0/1 knapsack
- Adding extra dp dimensions unnecessarily
Trap Explanation:
PITFALL- Backward iteration is correct for 0/1 knapsack but breaks unbounded knapsack logic.
Interviewer Note:
CONTEXT- Tests candidate's understanding of knapsack variants and dp iteration order implications.
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