# Floyd's cycle-finding algorithm

From HaskellWiki

This is a Haskell implementation 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)
```