Sorry to sound stupid, but how is that exponential? Isn't it O(mn) where m = number of floors and n = number of shafts?
EDIT: Unless there's some dependence between m and n, like if taller buildings always need more shafts or something.
EDIT: Unless there's some dependence between m and n, like if taller buildings always need more shafts or something.
The dependence is on keeping wait times reasonable. Taller buildings mean each shaft's elevator spends more time travelling, i.e. less time being available.
It's really rough in convention center hotels when a huge convention comes to town a lot of the time it's practically impossible to get an elevator down from the middle floors because it's already full from the floors above you.