# Floyd's cycle-finding algorithm

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Revision as of 15:11, 16 October 2011 by Csoroz (talk | contribs) (Add case for non-cyclic lists of odd length.)

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 _ [] = (xxs,[]) -- not cyclic
fCycle _ [_] = (xxs,[]) -- not cyclic
fCycle (x:xs) (_:y:ys)
| x == y = fStart xxs xs
| otherwise = fCycle xs ys
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 and both are finite, we have that

```
findCycle (xs ++ cycle ys) == (xs,ys)
```