Floyd's cycle-finding algorithm
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This is a Haskell impelementation of Floyd's cycle-finding algorithm for finding cycles in lists.
findCycle :: Eq a => [a] -> ([a],[a])
findCycle xxs = fCycle xxs xxs
where fCycle (x:xs) (_:y:ys)
| x == y = fStart xxs xs
| otherwise = fCycle xs ys
fCycle _ _ = (xxs,[]) -- not cyclic
fStart (x:xs) (y:ys)
| x == y = ([], x:fLength x xs)
| otherwise = let (as,bs) = fStart xs ys in (x:as,bs)
fLength x (y:ys)
| x == y = []
| otherwise = y:fLength x ys
This function is essentially the inverse of cycle. I.e. if xs and ys don't have a common suffix, their elements are unique and both are finite, we have that
findCycle (xs ++ cycle ys) == (xs,ys)