[Solved] Suppose the Target Sum problem is modified so that each number in the array can be used multiple times (unlimited... Which of the following changes correctly adapts the DP solution to this variant? | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Target Sum

Suppose the Target Sum problem is modified so that each number in the array can be used multiple times (unlimited reuse). Which of the following changes correctly adapts the DP solution to this variant?

AUse a 1D dp array and update dp in forward order for each num to allow reuse

BKeep the same DP with offset and update dp in reverse order to avoid double counting

CUse a 2D dp array with dimensions n and sum, but only update dp[i][s] from dp[i-1][s-num]

DSwitch to a brute force recursion since DP cannot handle reuse

Step-by-Step Solution

Step 1: Understand reuse impact on DP iteration
Allowing unlimited reuse means for each num, dp must be updated in forward order so that dp[s-num] includes ways using current num multiple times.
Step 2: Identify correct DP update order
Backward iteration prevents reuse by only using previous states. Forward iteration accumulates counts correctly for unlimited usage.
Step 3: Evaluate options
Use a 1D dp array and update dp in forward order for each num to allow reuse correctly updates dp forward. Keep the same DP with offset and update dp in reverse order to avoid double counting backward iteration is for no reuse. Use a 2D dp array with dimensions n and sum, but only update dp[i][s] from dp[i-1][s-num] restricts to previous items only. Switch to a brute force recursion since DP cannot handle reuse is inefficient.
Final Answer:
Option A -> Option A
Quick Check:
Forward dp update enables multiple usage of same number [OK]

Quick Trick: Forward dp iteration enables unlimited reuse [OK]

Common Mistakes:

MISTAKES

Using backward iteration which forbids reuse

Trap Explanation:

PITFALL

Backward iteration looks safer but disallows multiple usage, a subtle but critical difference.

Interviewer Note:

CONTEXT

Checks candidate's understanding of DP iteration order for reuse variants.

Master "Target Sum" in Dynamic Programming: Knapsack

3 interactive learning modes - each teaches the same concept differently

Try It Solution Trace

More Dynamic Programming: Knapsack Quizzes

Which of the following changes correctly adapts the DP solution to this variant?

Step 1: Understand reuse impact on DP iteration

Step 2: Identify correct DP update order

Step 3: Evaluate options

Final Answer:

Quick Check:

Want More Practice?