Dynamic Programming: Knapsack - Minimum Subset Sum Difference
What is the space complexity of the top-down memoization approach for the minimum subset sum difference problem with n elements and total sum W?
What is the space complexity of the top-down memoization approach for the minimum subset sum difference problem with n elements and total sum W?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze memo storage
Memo stores results for states (i, curr_sum), total O(n * W) entries.Step 2: Consider recursion stack
Recursion depth is O(n), so stack space O(n).Step 3: Total space complexity
Memo + recursion stack = O(n * W) + O(n) ≈ O(n * W), but since W dominates, space is O(n * W).Final Answer:
Option B -> Option BQuick Check:
Memo table plus recursion stack -> O(n + W) is minimal, but actual is O(n * W) [OK]
Quick Trick: Memo table size x recursion depth -> O(n * W) space [OK]
Common Mistakes:
MISTAKES- Ignoring recursion stack or memo size
Trap Explanation:
PITFALL- Candidates pick O(W) or O(n) ignoring combined memo and stack space.
Interviewer Note:
CONTEXT- Tests understanding of auxiliary space in recursive DP.
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