Dynamic Programming: Knapsack - Subset Sum
What is the space complexity of the top-down memoized subset sum algorithm with n items and target sum S, considering recursion stack and memo storage?
What is the space complexity of the top-down memoized subset sum algorithm with n items and target sum S, considering recursion stack and memo storage?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze memo dictionary size
Memo stores results for up to n * S states.Step 2: Analyze recursion stack depth
Recursion depth is at most n, so stack space is O(n).Step 3: Combine space usage
Total space is dominated by memo storage O(n * S).Final Answer:
Option B -> Option BQuick Check:
Memo storage dominates space usage [OK]
Quick Trick: Memo storage dominates space -> O(n * S) [OK]
Common Mistakes:
MISTAKES- Ignoring memo size
- Assuming recursion stack dominates
Trap Explanation:
PITFALL- Candidates often underestimate memo storage space in top-down DP.
Interviewer Note:
CONTEXT- Tests understanding of space usage in recursive memoized DP.
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