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What is the time complexity of the space-optimized bottom-up DP solution for the minimum subset sum difference problem with n elements and total sum W?

medium🪤 Complexity Trap Q5 of Q15

Dynamic Programming: Knapsack - Minimum Subset Sum Difference

What is the time complexity of the space-optimized bottom-up DP solution for the minimum subset sum difference problem with n elements and total sum W?

AO(n^2)

BO(n + W)

CO(W^2)

DO(n * W)

Step-by-Step Solution

Solution:

Step 1: Analyze loops
Outer loop runs n times, inner loop runs up to W times (total sum).
Step 2: Calculate total complexity
Overall complexity is O(n * W) due to nested loops.
Final Answer:
Option D -> Option D
Quick Check:
DP over n items and sum W -> O(n * W) [OK]

Quick Trick: Nested loops over n and total sum W -> O(n * W) [OK]

Common Mistakes:

MISTAKES

Confusing n with W, assuming quadratic in n only

Trap Explanation:

PITFALL

Candidates often pick O(n^2) ignoring that inner loop depends on W, not n.

Interviewer Note:

CONTEXT

Tests understanding of DP time complexity with sum dimension.

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