Michael Mossey
The problem is to determine how closely the groups can be brought together without any boxes intersection.
The basic algorithm is to consider each pair of boxes and ask if they have any "vertical overlap"---if so, figure out how closely they can be brought together without intersecting, otherwise ignore them. Then take the maximum of those numbers.
Wouldn't you mean minimum instead of maximum then? I suspect that your code would be clearer without using a state monad. -- Edit this signature at http://www.digitas.harvard.edu/cgi-bin/ken/sig Computer Science is no more about computers than astronomy is about telescopes. -Edsger Dijkstra