Dynamic Programming: Knapsack - Minimum Subset Sum Difference
What is the time complexity of the space-optimized bottom-up dynamic programming solution for the minimum subset sum difference problem, given an input array of size n and total sum S?
What is the time complexity of the space-optimized bottom-up dynamic programming solution for the minimum subset sum difference problem, given an input array of size n and total sum S?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Identify loops in the code
Outer loop runs n times (for each element), inner loop runs up to total_sum S times.Step 2: Calculate total complexity
Time complexity is O(n * S) because each element updates dp array of size S.Final Answer:
Option C -> Option CQuick Check:
DP iterates over n elements and sums up to S [OK]
Quick Trick: Time depends on n and total sum, not n squared [OK]
Common Mistakes:
MISTAKES- Confusing n with S or assuming quadratic n^2
- Ignoring dp array size impact
Trap Explanation:
PITFALL- O(n^2) looks plausible if candidate thinks only about n loops, ignoring sum dimension.
Interviewer Note:
CONTEXT- Checks if candidate understands DP complexity depends on sum range, not just input size.
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