# Difference between revisions of "Floyd's cycle-finding algorithm"

From HaskellWiki

(Add case for non-cyclic lists of odd length.) |
(Simplify pattern-matching equations.) |
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Line 3: | Line 3: | ||

findCycle :: Eq a => [a] -> ([a],[a]) |
findCycle :: Eq a => [a] -> ([a],[a]) |
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findCycle xxs = fCycle xxs xxs |
findCycle xxs = fCycle xxs xxs |
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− | where fCycle |
+ | where fCycle (x:xs) (_:y:ys) |

− | fCycle _ [_] = (xxs,[]) -- not cyclic |
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− | fCycle (x:xs) (_:y:ys) |
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| x == y = fStart xxs xs |
| x == y = fStart xxs xs |
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| otherwise = fCycle xs ys |
| otherwise = fCycle xs ys |
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+ | fCycle _ _ = (xxs,[]) -- not cyclic |
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fStart (x:xs) (y:ys) |
fStart (x:xs) (y:ys) |
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| x == y = ([], x:fLength x xs) |
| x == y = ([], x:fLength x xs) |

## Revision as of 15:24, 16 October 2011

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 and both are finite, we have that

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