Note that this is the "stable roommates problem" and does not necessarily have an "optimal" solution (where "optimal" means "no unmatched pair of people would'v

Note that this is the "stable roommates problem" and does not necessarily have an "optimal" solution (where "optimal" means "no unmatched pair of people would've rather been matched together". Eg, if Albert prefers Bob over Charles, Bob prefers Charles over Albert, and Charles prefers Albert over Bob, and all three prefer being matched with the last person over anyone else).