Task label order

Order the jobs of a repair crew so that the most urgent jobs finish as early as possible.

There are n jobs numbered 1 to n, and a lower number means a more urgent job. The crew does one job at a time. Each pair [a, b] in needs means that job a must be completed before job b starts. Pairs can repeat, and a pair like [3, 3] can never be satisfied.

Among all valid orders, the crew's boss wants this one: job 1 is done as early as possible; among the orders that achieve that, job 2 is done as early as possible; among those, job 3 as early as possible, and so on. (Putting the smallest *available* label first at each step does not do this.)

Input: n, the number of jobs, and needs, a list of [a, b] precedence pairs.

Output: that order as a list of the job numbers 1 to n, each exactly once, or an empty list if the precedence pairs cannot all be satisfied. The order is unique, so there are no ties to break.

There can be more than a thousand jobs, and trying all valid orders is hopeless.