This is a variant of the Gale/Shapley algorithm in python designed to address the Stable Marriage Problem. The variant here is that certain marriages are forbidden.
Given a set of men and women to be paired for marriage, each man ranks all the women in order of his preference and each women ranks all the men in order of her preference. A randomized list of forbidden marriages is provided.
A stable set of engagements for marriage is one where no man prefers a women over the one he is engaged to, where that other woman also prefers that man over the one she is engaged to. I.e. with consulting marriages, there would be no reason for the engagements between the people to change.
Gale and Shapley proved that there is a stable set of engagements for any set of preferences and their algorithm finds a set of stable engagements with a worst case running time of n^2 iterations through the main loop.
We’re provided with a list of men (M) and women (W), indicating each mans (and womans) spousal preferences ranked from highest to lowest.
We’re also provided with a randomized list of forbidden marriages (actually, a dict that lists for each man the women they are forbidden to marry). Forbidden marriages are not permitted, so the algorithm should never marry forbidden pairs of men and women.
The task is to implement the Gale-Shapley algorithm for finding a stable set of engagements.
We want to use this algorithm to produce a matching, which we can then test for stability by the criteria indicated above.
We’re also asked to perturb the resulting matching (swapping the spouses of two couples) and re-test for stability. The perturbed matching should be found to be unstable.