- Can it be assumed that they have eual distaste for all unrated sections?
Correct. They are supposed to rank all of the sections they are capable of attending. If they can't attend it, they don't rank it ... and anything they can't attend is equally worthless
- Can a student be in more than one section?
no. (sorry, i should have considered that varient)
- Do all sections have to have students? ... Do the numbers of places per section, total to the number of students?
Excellent question: No, and "not neccessarily"
I initially tried to simplify the description of the problem a little bit. A previous placement process has already partially filled these sections, the data I'll be starting with is the maximum number of additional students each section can accomidate and the list of students not yet placed in a section with their prefrences for a section.
It's completely possible that a section might allready be full (ie: have 0 room) and I believe it's possible that there may be more total students then their are spaces left.
- What are the orders of magnitude you are dealing with?
I believe I need to deal with roughly 750 students, 10-15 sections, and anywhere from 0 to 20 spots in each section.
I'm not adverse to using a brute force approach and letting it churn for a few hours. I'm just not sure what the best brute force approach is, or how to decide when one solution is "better" then another.