The Pattern That Matters
LeetCode 2187 (Minimum Time to Complete Trips) isn't just another coding exercise. It's a canonical example of binary search on answer, a pattern that applies directly to enterprise scheduling, resource allocation, and capacity planning problems.
The problem: Given buses with different trip durations running in parallel, find the minimum time to complete a target number of trips. Brute force (checking each time unit) hits O(10^14) operations for large inputs. Binary search cuts this to O(n log(min(time) × totalTrips)).
Why This Translates to Production
The core insight applies wherever you're optimizing on a monotonic dimension:
- Batch job scheduling: Minimum time to process N tasks across M workers with varying speeds
- Resource provisioning: Minimum capacity to meet SLA targets
- Load balancing: Optimal request distribution across heterogeneous servers
The pattern exploits a simple property: if you can meet a target in time T, you can meet it in T+1. This transforms an unbounded linear search into a bounded binary search.
The Implementation
The feasibility check is straightforward: for time T, each resource completes T/duration[i] units of work. Sum these. If sum ≥ target, T works. Binary search finds the smallest such T.
Bounds matter: lower bound is 1, upper bound is min(duration) × target (worst case: fastest resource does all work alone). Constraints from the problem: up to 10^5 resources, durations and targets up to 10^7.
What We're Not Seeing
No enterprise scheduling frameworks are advertising this pattern explicitly, though it's embedded in capacity planning algorithms across AWS, GCP, and Azure autoscalers. The LeetCode problem dates to August 2022 (Weekly Contest 282). No updates since.
The technique requires careful handling of integer overflow (use long/int64) and off-by-one errors in binary search termination. The pattern appears across LeetCode problems 875 (Koko Eating Bananas), 1011 (Capacity to Ship Packages), and others, all modeling similar resource-time tradeoffs.
The Practical Takeaway
When you're staring at a scheduling problem that feels like it needs expensive simulation, ask: is the answer space monotonic? If yes, binary search probably works. The pattern ships in production schedulers daily. LeetCode 2187 just makes it explicit.