Given the following partial dp array after processing the first 3 items of nums = [3, 4, 5, 6] with target sum S=10: dp = [True, False, False, True, True, True, False, False, False, False, False] Which of the first three items was definitely included to achieve dp[3] = True?

hard🔄 Reverse Engineer Q9 of Q15

Dynamic Programming: Knapsack - Subset Sum

ANo item included yet

BItem with weight 4

CItem with weight 5

DItem with weight 3

Step-by-Step Solution

Solution:

Step 1: Interpret dp array meaning
dp[w] = True means sum w achievable with first 3 items.
Step 2: Check dp[3] = True
Sum 3 is achievable; since 3 is one of the first three items, it must be included or formed by others.
Step 3: Confirm item inclusion
Only item with weight 3 can directly form sum 3; 4 and 5 are larger than 3.
Final Answer:
Option D -> Option D
Quick Check:
Sum 3 requires item weight 3 included [OK]

Quick Trick: dp[w] True means sum w achievable; check item weights [OK]

Common Mistakes:

MISTAKES

Assuming sum 3 formed by 4 or 5
Ignoring direct weight matches

Trap Explanation:

PITFALL

Candidates confuse dp meaning or overlook direct item weights.

Interviewer Note:

CONTEXT

Tests deep understanding of DP state and subset reconstruction.

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More Dynamic Programming: Knapsack Quizzes

Given the following partial dp array after processing the first 3 items of nums = [3, 4, 5, 6] with target sum S=10: dp = [True, False, False, True, True, True, False, False, False, False, False] Which of the first three items was definitely included to achieve dp[3] = True?

Step 1: Interpret dp array meaning

Step 2: Check dp[3] = True

Step 3: Confirm item inclusion

Final Answer:

Quick Check:

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