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Consider the following Python function implementing the space-optimized subset sum algorithm. Given nums = [2, 3, 7] and S = 5, what is the value of dp[5] after processing all elements?

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Dynamic Programming: Knapsack - Subset Sum

Consider the following Python function implementing the space-optimized subset sum algorithm. Given nums = [2, 3, 7] and S = 5, what is the value of dp[5] after processing all elements?

ATrue

BFalse

CIndexError due to out-of-range access

DNone (function does not return a boolean)

Step-by-Step Solution

Solution:

Step 1: Trace dp array after processing num=2
Initially dp=[True, False, False, False, False, False]. After num=2, dp[2]=True because dp[0] was True.
Step 2: Trace dp array after processing num=3
From w=5 down to 3, dp[5]=dp[5] or dp[2]=False or True -> True, dp[3]=dp[3] or dp[0]=False or True -> True.
Final Answer:
Option A -> Option A
Quick Check:
Subset {2,3} sums to 5 -> dp[5] is True [OK]

Quick Trick: Trace dp updates backward to avoid double counting [OK]

Common Mistakes:

MISTAKES

Iterating dp forward causing overcounting
Off-by-one errors in dp indices

Trap Explanation:

PITFALL

Forward iteration would incorrectly update dp and produce wrong results.

Interviewer Note:

CONTEXT

Tests ability to mentally execute space-optimized DP and boundary conditions.

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