Minimize Completion Time with Specialized Workers

There are n workers and m tasks. Each task has one designated proficient worker. That worker takes one hour to perform it; any other worker takes two hours. Workers operate in parallel but each handles only one task at a time. Assign all tasks to minimize the time when every task is complete, starting at time zero. ### Constraints and Clarifications The report identifies Codeforces 1701C, [Schedule Management](https://codeforces.com/problemset/problem/1701/C), and says the interview limits were much larger than the reference limits. Their exact values are not supplied, so do not assume the reference maximum applies. Use n>=1, m>=1 and valid worker IDs from 1 through n. Return the minimum integer completion time for one instance; no assignment witness is required. Use integer counts capable of representing the actual input size. ### Example With two workers and four tasks all assigned proficiently to worker 1, the minimum time is 3. Worker 1 performs three tasks while worker 2 performs one in two hours. ### What a Strong Answer Covers Aggregate tasks per proficient worker, derive a feasibility test for a candidate finishing time, prove its sufficiency and necessity, and use monotonicity to find the minimum efficiently. ### Follow-up Questions - Why is the spare capacity for unfamiliar tasks divided by two and rounded down? - Why can task identities be discarded after counting their proficient workers?