Dynamic Programming: Knapsack - Coin Change II (Count Ways)
What is the space complexity of the top-down memoized solution for Coin Change II with n coins and amount W?
What is the space complexity of the top-down memoized solution for Coin Change II with n coins and amount W?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze memo dictionary size
Memo stores results for states (i, amt), total up to n * W entries.Step 2: Consider recursion stack depth
Recursion stack depth is at most n + W in worst case.Step 3: Total space complexity
Memoization table plus recursion stack leads to O(n * W) space complexity.Final Answer:
Option D -> Option DQuick Check:
Memo table dominates space usage, O(n * W) [OK]
Quick Trick: Memo table size dominates space -> O(n * W) [OK]
Common Mistakes:
MISTAKES- Ignoring recursion stack space
- Assuming only memo space counts
Trap Explanation:
PITFALL- Candidates forget recursion stack space adds to total space complexity.
Interviewer Note:
CONTEXT- Tests understanding of space usage in recursive memoized DP.
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