Probably best illustrated with a small example.
Given the relations
A < B < C
A < P < Q
Correct outputs would be
ABCPQ or APQBC or APBCQ ... etc.
In other words, any ordering is valid in which the given relationships hold.
I am most interested in the solution that is easiest to implement, but the best O(n) in speed and time is interesting as well.
This is called topological sorting.
The standard algorithm is to output a minimal element, then remove it and repeat until done.