Dynamic Programming: Knapsack - 0/1 Knapsack Problem
What is the space complexity of the top-down memoized 0/1 Knapsack solution with n items and capacity W?
What is the space complexity of the top-down memoized 0/1 Knapsack solution with n items and capacity W?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Memoization table size
Memo stores results for each (i, w) pair -> O(n * W) space.Step 2: Recursion stack depth
Maximum recursion depth is n, adding O(n) auxiliary space.Step 3: Total space
Sum of memo and recursion stack -> O(n * W + n).Final Answer:
Option B -> Option BQuick Check:
Memo + recursion stack space combined -> O(n*W + n) [OK]
Quick Trick: Memo table plus recursion stack -> O(n*W + n)
Common Mistakes:
MISTAKES- Ignoring recursion stack space
- Assuming only memo space counts
Trap Explanation:
PITFALL- Candidates forget recursion stack adds to total space complexity.
Interviewer Note:
CONTEXT- Tests understanding of auxiliary space in recursive DP
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