Dynamic Programming: Knapsack - Subset Sum
What is the time complexity of the space-optimized bottom-up subset sum algorithm given an input list of size n and target sum S?
What is the time complexity of the space-optimized bottom-up subset sum algorithm given an input list of size n and target sum S?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Solution:
Step 1: Identify loops in the algorithm
The algorithm has an outer loop over n elements and an inner loop over sums from S down to each num.Step 2: Calculate total operations
Each element causes up to S iterations, so total time is O(n * S). Recursive brute force is exponential, and linear or log factors are incorrect.Final Answer:
Option C -> Option CQuick Check:
Nested loops over n and S -> O(n * S) [OK]
Quick Trick: Nested loops over n and S -> multiply complexities [OK]
Common Mistakes:
MISTAKES- Confusing recursion stack space with time
- Assuming linear or exponential time incorrectly
Trap Explanation:
PITFALL- Some think time is O(n + S) because of initialization or confuse with brute force exponential time.
Interviewer Note:
CONTEXT- Checks understanding of DP complexity vs brute force and space optimization.
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