Dynamic Programming: Knapsack - Maximum Profit in Job Scheduling
What is the space complexity of the memoized recursive job scheduling solution that caches results for each job index?
What is the space complexity of the memoized recursive job scheduling solution that caches results for each job index?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Memo dictionary stores results for each job index
Memo size is O(n).Step 2: Recursion stack depth is O(log n) due to binary search
Each recursive call reduces problem size via binary search, so max stack depth is O(log n).Step 3: Total space is memo + recursion stack = O(n + log n) ≈ O(n)
But binary search arrays and sorting add O(n log n) auxiliary space in some implementations.Final Answer:
Option D -> Option DQuick Check:
Memo + recursion stack + sorting -> O(n log n) [OK]
Quick Trick: Memo + recursion stack + sorting -> O(n log n) [OK]
Common Mistakes:
MISTAKES- Ignoring recursion stack space
- Assuming constant space for memo
Trap Explanation:
PITFALL- Candidates often forget recursion stack or auxiliary arrays in space calculation.
Interviewer Note:
CONTEXT- Tests understanding of space usage in recursive DP with memoization.
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