Dynamic Programming: Knapsack - Maximum Profit in Job Scheduling
Suppose the job scheduling problem is extended to find the top K maximum profit schedules instead of just one. Which approach best adapts to this variant?
Suppose the job scheduling problem is extended to find the top K maximum profit schedules instead of just one. Which approach best adapts to this variant?
hard🎤 Interviewer Follow-up Q10 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand top K schedules requirement
We need multiple distinct schedules with top profits, not just one maximum.Step 2: Evaluate approaches
Brute force is exponential and impractical; memoization caches only max profit, insufficient; tabulation storing top K is complex and costly; greedy picking top K profitable jobs is a heuristic that can quickly produce top K candidates.Final Answer:
Option D -> Option DQuick Check:
Greedy heuristic best for top K approximate solutions [OK]
Quick Trick: Top K schedules require heuristic or complex DP [OK]
Common Mistakes:
MISTAKES- Assuming max profit DP suffices
- Ignoring complexity of top K enumeration
Trap Explanation:
PITFALL- Candidates often try to extend max profit DP directly without considering complexity.
Interviewer Note:
CONTEXT- Tests ability to handle complex variants and choose practical approaches.
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