Maximize profit from non-overlapping jobs

Q: Maximize profit from non-overlapping jobs

This question evaluates proficiency in weighted interval scheduling, dynamic programming concepts, and the use of efficient data structures for large-scale scheduling problems, including handling duplicate times, large reward values, and memory constraints.

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Question

You are given up to N = 200,000 jobs; each job i has a start time s_i, end time e_i (s_i < e_i), and reward w_i. Select a subset of non-overlapping jobs to maximize total reward. Return the maximum reward and one optimal set of job indices. Design an O(N log N) algorithm using sorting plus binary search or a balanced tree; explain how you reconstruct the chosen jobs and analyze time/space complexity. Handle duplicate start/end times, large rewards (up to 1e 9), and memory limits. Discuss alternatives (e.g., segment tree, coordinate compression) and how you would adapt the approach if jobs arrive online.

Maximize profit from non-overlapping jobs

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