Dynamic Programming: Knapsack - Maximum Profit in Job Scheduling
What is the time complexity of the optimal job scheduling algorithm that sorts jobs by end time and uses binary search with a DP array of size n?
What is the time complexity of the optimal job scheduling algorithm that sorts jobs by end time and uses binary search with a DP array of size n?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Identify sorting cost
Sorting n jobs by end time costs O(n log n).Step 2: Analyze DP loop with binary search
For each job, binary search among ends array costs O(log n), repeated n times -> O(n log n).Final Answer:
Option D -> Option DQuick Check:
Sorting + n binary searches dominate; no nested O(n^2) loops [OK]
Quick Trick: Sorting + binary search per job -> O(n log n) [OK]
Common Mistakes:
MISTAKES- Assuming O(n^2) due to DP
- Ignoring binary search cost
- Confusing max end time W with input size n
Trap Explanation:
PITFALL- O(n^2) looks plausible since DP often involves nested loops, but binary search reduces inner loop to log n.
Interviewer Note:
CONTEXT- Checks if candidate understands how binary search optimizes DP and distinguishes input size from value range.
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