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Stable Marriage Problem
import Data.List
import Data.Maybe
stableMatch :: (Eq m, Eq w) => [(m,[w])] -> [(w,[m])] -> [(m,w)]
stableMatch ms ws = stableMatch' []
stableMatch' ps = case unmarried ms ps of
Just unmarriedMan -> stableMatch' (findMatch unmarriedMan ws ps)
Nothing -> ps
-- Outcome - m is always married to someone
findMatch :: (Eq m,Eq w) => (m,[w]) -> [(w,[m])] -> [(m,w)] -> [(m,w)]
findMatch (m,w:rest) ws ps = case isEngaged w ps of
-- w is already engaged to m' - is there a better match?
Just m' -> if prefers (getPrefs ws w) m m'
then engage (breakup m' ps) m w
else findMatch (m,rest) ws ps
-- can match with first choice
Nothing -> engage ps m w
getPrefs :: Eq w => [(w,m)] -> w -> m
getPrefs ws w = fromJust $ lookup w ws
isEngaged :: Eq w => w -> [(m,w)] -> Maybe m
isEngaged w ps = fmap fst (find (\x -> snd x == w) ps)
engage :: [(m,w)] -> m -> w -> [(m,w)]
engage xs a b = (a,b) : xs
breakup :: Eq m => m -> [(m,w)] -> [(m,w)]
breakup m = filter (\x -> fst x /= m)
-- Returns the first man in in ms not in ps
unmarried :: Eq m => [(m,[w])] -> [(m,w)] -> Maybe (m,[w])
unmarried ms ps = find (\(m,_) -> m `notElem` engagedMen) ms
engagedMen = map fst ps
-- Returns true if w prefers first over second
prefers :: Eq m => [m] -> m -> m -> Bool
prefers ms m1 m2 = go ms
go [] = error "no match"
go (x:xs)
| x == m1 = True
| x == m2 = False
| otherwise = go xs
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