Dynamic Programming: Knapsack - Maximum Profit in Job Scheduling
Given the dp array after processing 5 jobs sorted by end time: dp = [20, 50, 50, 120, 150], which job was most likely included last to achieve dp[4] = 150?
Given the dp array after processing 5 jobs sorted by end time: dp = [20, 50, 50, 120, 150], which job was most likely included last to achieve dp[4] = 150?
hard🔄 Reverse Engineer Q9 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze dp progression
dp[4]=150 is max profit including jobs up to index 4.Step 2: Identify last job contributing to dp[4]
Since dp[3]=120 and dp[4]=150, last job likely adds 30 profit (150-120=30) or more if combined with compatible jobs.Step 3: Match profit and end time
Job with profit 60 ending latest fits last job increasing total profit to 150.Final Answer:
Option A -> Option AQuick Check:
Last job with profit 60 raises dp from 120 to 150 [OK]
Quick Trick: Last dp increment matches last job profit [OK]
Common Mistakes:
MISTAKES- Picking earliest job
- Ignoring dp incremental differences
Trap Explanation:
PITFALL- Candidates confuse dp indices with job profits or order.
Interviewer Note:
CONTEXT- Tests ability to reason backwards from DP table to input jobs.
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