# Room assignments - Algorithm

The lottery algorithm that is used here at Ashdown is designed in a way to give higher preference to those with greater seniority in Ashdown, as well as assign the best possible room to you based on your preferences. Your best strategy is to simply preference rooms/suites in decreasing order from most to least desired.

If you are interested in the gory details, the algorithm is given below:

Each resident submits to us a list of rooms, in order, that they are interested in living in, above their own, ranked in order of preference, from most preferrerd to least preferred. Residents should NOT list rooms that they are not willing to live in.

First, all residents are ranked by the number of seniority points they have. A seniority point is earned for every term of residence at Ashdown and additional points are earned for every term successfully served (as decided by AHEC) as an officer at Ashdown. Residents with equal seniority points are ranked in a random computer-generated order. For the sake of discussion, we will label the entire list of ranked residents {r0,r1>, ... rN-1} for N residents.

To execute the lottery, we begin with r0 and assign them the first room on their list that is vacant (a lottery is never run if there are no vacancies) and keep them in their current room if no room on their list is vacant. If moved, their old room becomes vacant and they occupy their new room. Similarly, we then move on to r1, r2, ..., in order, assigning each to the first room on their list that is vacant. If any rn gets moved, we mark rn's old room as vacant and evaluate again from r0, in case rn's old room (now vacant) happens to be more highly preferred for any of r0...rn-1. Each time a move occurs, the lottery re-runs all preferences from the beginning. When, at some iteration, the lottery is run through from r0 to rN-1 without moving anyone, we consider the situation optimal, the lottery stops, and the final state is reached.

The running time is typically O(N2) but has the features that (1) it will necessarily converge, (2) is efficient in assigning based on seniority point ranks, and (3) makes your best strategy very simple: to rank rooms in the order you prefer them.

Stapled groups are treated as a virtual person with seniority equal to the sum of the constituents' seniority points. When the virtual person's turn is reached, the first suite on the group's preference list that can accomodate all group members is chosen, with one exception: staple groups of size 2 are not assigned to 3-bedroom accomodations if all 3 bedrooms are vacant. If any staple request is successful (i.e. a move occurred), all staple group members' individual forms, if any, are discarded. If the staple request is unsuccessful, any individual forms that were submitted by the constituents will be processed normally as the lottery proceeds down the seniority point rankings.

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