Dynamic Programming: Knapsack - Last Stone Weight II
What is the space complexity of the top-down memoized recursive solution for lastStoneWeightII, considering n stones and total sum W?
What is the space complexity of the top-down memoized recursive solution for lastStoneWeightII, considering n stones and total sum W?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze memoization cache size
Cache stores results for states (i, diff) where i up to n and diff up to W -> O(n * W)Step 2: Analyze recursion stack depth
Recursion depth is n, so stack space O(n)Step 3: Combine space usage
Total space = memo cache + recursion stack = O(n * W) + O(n) ≈ O(n * W)Final Answer:
Option B -> Option BQuick Check:
Memo cache dominates space -> O(n * W) [OK]
Quick Trick: Memo cache O(n*W), recursion stack O(n) -> total O(n*W) [OK]
Common Mistakes:
MISTAKES- Ignoring recursion stack
- Assuming only cache space
- Confusing time and space complexity
Trap Explanation:
PITFALL- Candidates forget recursion stack space, underestimating total space usage.
Interviewer Note:
CONTEXT- Tests understanding of auxiliary space in recursive DP
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