Subsets & Combinations - Count of Subsets With Sum K
What is the time complexity of the space-optimized dynamic programming solution to count subsets with sum K for an array of size n?
What is the time complexity of the space-optimized dynamic programming solution to count subsets with sum K for an array of size n?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand DP dimensions
The DP table has dimensions n (array size) and K (target sum).Step 2: Analyze nested loops
Outer loop runs n times, inner loop runs up to K times.Final Answer:
Option A → Option AQuick Check:
Exponential or quadratic complexities are incorrect here. [OK]
Quick Trick: DP subset sum runs in O(n*K) time [OK]
Common Mistakes:
MISTAKES- Confusing with exponential brute force
- Assuming linear time ignoring sum dimension
- Overestimating complexity as quadratic in n
Trap Explanation:
PITFALL- Mistaking exponential brute force for DP complexity.
Interviewer Note:
CONTEXT- Tests understanding of time complexity for DP subset sum solutions.
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