Suppose the problem is modified so that each number in the input array can be used multiple times to form the subsets. Which change to the DP approach correctly solves this variant?

hard🎤 Interviewer Follow-up Q15 of Q15

Dynamic Programming: Knapsack - Equal Partition (Partition Equal Subset Sum)

AKeep the same code but iterate the dp array backwards to avoid reuse of elements

BChange the inner loop to iterate forwards from num to target to allow multiple uses of the same element

CUse recursion without memoization to explore all combinations with repeats

DDouble the dp array size to track counts of each element used

Step-by-Step Solution

Solution:

Step 1: Understand the difference between 0/1 and unbounded knapsack
Allowing multiple uses means the problem becomes unbounded knapsack, which requires forward iteration over dp array.
Step 2: Identify correct dp iteration direction
Iterating forwards from num to target allows dp[w] to build upon dp[w - num] updated in the same iteration, enabling multiple uses.
Final Answer:
Option B -> Option B
Quick Check:
Backward iteration prevents multiple uses; forward iteration enables them [OK]

Quick Trick: Forward dp iteration enables multiple uses of elements [OK]

Common Mistakes:

MISTAKES

Using backward iteration from 0/1 knapsack
Ignoring iteration direction for repeats

Trap Explanation:

PITFALL

Backward iteration is correct for 0/1 knapsack but breaks unbounded knapsack logic

Interviewer Note:

CONTEXT

Tests if candidate understands how iteration direction encodes element reuse in DP

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More Dynamic Programming: Knapsack Quizzes

Suppose the problem is modified so that each number in the input array can be used multiple times to form the subsets. Which change to the DP approach correctly solves this variant?

Step 1: Understand the difference between 0/1 and unbounded knapsack

Step 2: Identify correct dp iteration direction

Final Answer:

Quick Check:

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