Dynamic Programming: Knapsack - Subset Sum
What is the time complexity of the bottom-up subset sum dynamic programming algorithm given n items and target sum S?
What is the time complexity of the bottom-up subset sum dynamic programming algorithm given n items and target sum S?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze nested loops
Outer loop runs n times; inner loop runs up to S times.Step 2: Multiply loops for total complexity
Total time is O(n * S) due to nested iteration over items and sums.Final Answer:
Option D -> Option DQuick Check:
DP table size is n by S [OK]
Quick Trick: Nested loops over n and S -> O(n * S) [OK]
Common Mistakes:
MISTAKES- Confusing with O(n + S)
- Assuming exponential due to subsets
Trap Explanation:
PITFALL- Candidates often forget S factor or confuse with brute force exponential time.
Interviewer Note:
CONTEXT- Tests understanding of DP time complexity and nested loops.
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