I recognized the weighted job scheduling shape pretty quickly, which felt good.
Recognize this as a weighted interval scheduling problem, solvable with dynamic programming after sorting deliveries by end time. Filter out deliveries that don't fit entirely within the shift window, then compute the maximum profit using binary search to find the latest non-overlapping delivery.
Pro tip: Clarify edge cases upfront, such as deliveries that start before the shift or end after it, and whether partial overlaps are allowed. Also, mention that if the number of deliveries is small, a simpler O(n^2) DP is acceptable, but for large n, the O(n log n) approach is preferred.
Ask about the input size, whether deliveries must fit entirely within the shift, and if overlapping is strictly prohibited. Confirm that the goal is to maximize total payout.
Remove any delivery that starts before the shift start or ends after the shift end. Sort the remaining deliveries by their end times.
Let dp[i] be the maximum profit using deliveries up to index i (sorted by end time). For each delivery i, find the latest non-overlapping delivery j using binary search, then dp[i] = max(dp[i-1], payout[i] + dp[j]).
Implement the DP with binary search for O(n log n) time. If n is small, a simpler O(n^2) approach is fine. Handle base cases and return dp[n].
Walk through a small example to verify correctness. Discuss time and space complexity, and mention alternative approaches like greedy (which fails) or graph-based methods.
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