Which modification to the optimal DP approach is correct?
hard🎤 Interviewer Follow-up Q15 of Q15
Dynamic Programming: Knapsack - Maximum Profit in Job Scheduling
Suppose the problem is modified so that jobs can be scheduled multiple times (i.e., unlimited reuse of the same job), still without overlapping. Which modification to the optimal DP approach is correct?
AReplace binary search with linear search to find compatible jobs and keep DP unchanged
BUse a 1D DP array indexed by time and for each time, consider all jobs that can start then, allowing reuse
CKeep the same DP with binary search but remove the skip option to always take the current job
DSort jobs by start time and use memoized recursion without binary search
Step-by-Step Solution
Step 1: Understand unlimited reuse impact
Allowing multiple uses of the same job means the problem resembles unbounded interval scheduling with no overlaps.
Step 2: Modify DP approach
Use a 1D DP array indexed by time (e.g., dp[t] = max profit up to time t). For each time, consider all jobs starting at or after t, allowing reuse by updating dp[end_i] = max(dp[end_i], dp[start_i] + profit_i).
Final Answer:
Option B -> Option B
Quick Check:
Binary search and skip logic do not handle reuse; time-indexed DP handles multiple scheduling [OK]
Quick Trick:Use time-indexed DP for unlimited job reuse [OK]
Common Mistakes:
MISTAKES
Trying to reuse binary search DP without changes
Removing skip option breaks correctness
Sorting by start time only
Trap Explanation:
PITFALL
Naively reusing the original DP fails because it assumes each job can be taken once; time-indexed DP is needed.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt DP to problem variants with reuse constraints.
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