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Given the final dp array for target=5 as dp = [True, False, True, False, True, False], which of the following input arrays could produce this dp state after processing all elements?

hard🔄 Reverse Engineer Q9 of Q15

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

Given the final dp array for target=5 as dp = [True, False, True, False, True, False], which of the following input arrays could produce this dp state after processing all elements?

A[1, 3, 4]

B[1, 2, 4]

C[2, 3, 5]

D[1, 2, 3]

Step-by-Step Solution

Solution:

Step 1: Interpret dp array meaning
dp[w] = True means sum w achievable. Here sums 0,2,4 achievable, sums 1,3,5 not.
Step 2: Check which input matches achievable sums
Input [1, 2, 4] can form sums 0,2,4 but not 1,3,5 after processing all elements.
Final Answer:
Option B -> Option B
Quick Check:
Only [1,2,4] matches dp pattern [OK]

Quick Trick: dp array shows achievable sums after all elements [OK]

Common Mistakes:

MISTAKES

Not interpreting dp meaning correctly
Assuming dp true means sum not achievable

Trap Explanation:

PITFALL

Candidates confuse dp meaning or do not simulate sums carefully.

Interviewer Note:

CONTEXT

Tests deep understanding of DP state and input relation

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