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 to find compatible jobs?
What is the time complexity of the optimal job scheduling algorithm that sorts jobs by end time and uses binary search to find compatible jobs?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Sorting jobs by end time
Sorting takes O(n log n) time.Step 2: For each job, binary search for compatible job
Binary search per job takes O(log n), total O(n log n).Final Answer:
Option C -> Option CQuick Check:
Sorting + binary search per job -> O(n log n) [OK]
Quick Trick: Sorting + binary search per job -> O(n log n) [OK]
Common Mistakes:
MISTAKES- Assuming O(n^2) due to nested loops
- Confusing with knapsack weight W
Trap Explanation:
PITFALL- Candidates often mistake binary search as linear scan causing O(n^2).
Interviewer Note:
CONTEXT- Tests understanding of binary search impact on DP time complexity.
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