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What is the space complexity of the top-down memoized recursive solution for integer break with input n?

medium🪤 Complexity Trap Q6 of Q15
Dynamic Programming: Knapsack - Integer Break
What is the space complexity of the top-down memoized recursive solution for integer break with input n?
AO(1)
BO(n) plus recursion stack space O(n)
CO(n^2)
DO(n)
Step-by-Step Solution
Solution:

  1. Step 1: Analyze dp array space

    dp array size is n+1 -> O(n) space.

  2. Step 2: Analyze recursion stack depth

    Recursion depth can be up to n -> O(n) stack space.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Memo + recursion stack -> O(n) + O(n) = O(n) total [OK]
Quick Trick: Memo array + recursion stack both use O(n) space [OK]
Common Mistakes:
MISTAKES
  • Ignoring recursion stack space
  • Assuming constant space
Trap Explanation:
PITFALL
  • Candidates often forget recursion stack space, picking O(n) only for dp array.
Interviewer Note:
CONTEXT
  • Tests understanding of auxiliary space in recursive DP
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