Dynamic Programming: Knapsack - Perfect Squares
What is the space complexity of the top-down memoization solution for the Perfect Squares problem, considering both memo storage and recursion stack?
What is the space complexity of the top-down memoization solution for the Perfect Squares problem, considering both memo storage and recursion stack?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Memo dictionary size
Memo stores results for all k from 0 to n -> O(n) space.Step 2: Recursion stack depth
Worst-case recursion depth can be up to n (subtracting 1 each call) -> O(n) stack space.Step 3: Total space complexity
Sum of memo and recursion stack space is O(n) + O(n) = O(n).Final Answer:
Option C -> Option CQuick Check:
Memo + recursion stack both O(n), combined O(n) total space [OK]
Quick Trick: Memo O(n) + recursion stack O(n) -> combined O(n) [OK]
Common Mistakes:
MISTAKES- Ignoring recursion stack space
- Assuming only memo space counts
- Underestimating stack depth
Trap Explanation:
PITFALL- Candidates often forget recursion stack space, underestimating total space.
Interviewer Note:
CONTEXT- Tests understanding of auxiliary space including recursion stack in memoized DP
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