What is the space complexity of the top-down DP with memoization solution for the minimum cost tickets problem with n travel days?

medium🪤 Complexity Trap Q6 of Q15

Dynamic Programming: Knapsack - Minimum Cost for Tickets

AO(n)

BO(n^2)

CO(n) plus recursion stack up to O(n)

DO(1)

Step-by-Step Solution

Solution:

Step 1: Analyze memoization and recursion stack usage
Memo stores O(n) states, recursion stack can go as deep as O(n) in worst case.
Step 2: Combine space usage for total complexity
Total space is O(n) for memo plus O(n) for recursion stack, so O(n) + O(n) = O(n) but recursion stack is important.
Final Answer:
Option C -> Option C
Quick Check:
Memo + recursion stack both contribute to space [OK]

Quick Trick: Memo + recursion stack -> O(n) space [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

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

Interviewer Note:

CONTEXT

Master "Minimum Cost for Tickets" in Dynamic Programming: Knapsack

3 interactive learning modes - each teaches the same concept differently

Want More Practice?

15+ quiz questions · All difficulty levels · Free

More Dynamic Programming: Knapsack Quizzes