If the Target Sum problem is changed so that each number in the array can be chosen multiple times (unlimited reuse), which of the following statements correctly describes the impact on the dynamic programming approach?
hard🔁 Follow-up Q10 of Q15
Dynamic Programming: Knapsack - Target Sum
If the Target Sum problem is changed so that each number in the array can be chosen multiple times (unlimited reuse), which of the following statements correctly describes the impact on the dynamic programming approach?
AThe problem transforms into an unbounded subset sum variant requiring a change from 0/1 knapsack to unbounded knapsack DP.
BThe original 0/1 knapsack DP approach remains unchanged since sign assignments handle reuse inherently.
CA greedy algorithm can replace DP because unlimited reuse simplifies the problem.
DMemoization is no longer needed as unlimited reuse leads to a polynomial-time closed-form solution.
Step-by-Step Solution
Solution:
Step 1: Understand problem change
Allowing unlimited reuse means each number can be chosen multiple times, unlike the original 0/1 constraint.
Step 2: DP approach adjustment
This changes the problem to an unbounded knapsack variant, requiring DP that allows multiple counts per item.
Step 3: Sign assignment remains
Sign assignments still apply, but DP transitions must consider multiple uses of the same number.
Final Answer:
Option A -> Option A
Quick Check:
Unlimited reuse means unbounded knapsack DP needed [OK]
Quick Trick:Unlimited reuse means switch to unbounded knapsack DP [OK]
Common Mistakes:
MISTAKES
Assuming 0/1 knapsack DP still applies without changes.
Thinking greedy algorithms solve this variant optimally.
Believing memoization is unnecessary for unlimited reuse.
Trap Explanation:
PITFALL
Ignoring the need to change DP approach looks reasonable but leads to incorrect solutions.
Interviewer Note:
CONTEXT
Tests ability to adapt DP approach for problem variants with unlimited reuse.
Master "Target Sum" in Dynamic Programming: Knapsack
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