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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)