What is the space complexity of the top-down memoized recursive solution for the coin change minimum coins problem with n coins and amount W?

medium🪤 Complexity Trap Q6 of Q15

Dynamic Programming: Knapsack - Coin Change (Minimum Coins)

AO(1)

BO(W)

CO(n * W)

DO(W) plus recursion stack depth O(W)

Step-by-Step Solution

Solution:

Step 1: Analyze memo dictionary size
Memo stores results for each amount up to W -> O(W) space.
Step 2: Analyze recursion stack depth
Recursion depth can be up to W in worst case -> O(W) stack space.
Final Answer:
Option D -> Option D
Quick Check:
Memo + recursion stack -> O(W) + O(W) = O(W) total [OK]

Quick Trick: Memo + recursion stack both use O(W) space [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Candidates often forget recursion stack space, underestimating total space complexity.

Interviewer Note:

CONTEXT

Tests understanding of auxiliary space including recursion stack in memoized DP.

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