# Find the length of the loop

One of the popular interivew tasks…

You are given a head of a linked list. Its known list contains cycle. The goal is to determine the length of the loop.

Here is straghtforward solution in haskell

{-
data Node a
instance Eq a => Eq (Node a)

next :: Node a -> Node a
-}

data Phase = TryFindLoop | FindLength deriving (Eq)

loopSize :: Eq a => Node a -> Int
loopSize a = slowAndFast a a 0 TryFindLoop
where slowAndFast :: (Eq node) =>
Node node -> Node node -> Int -> Phase -> Int
slowAndFast slow fast len phase =
let nextSlow = next slow
nextPreFast = next fast
nextFast = next nextPreFast in
if (slow == nextPreFast || slow == nextFast) then
if (phase == FindLength) then
if (nextPreFast == nextFast) then 1
else
2*(len+1) - len - (if slow == nextFast then 0 else 1)
else slowAndFast nextSlow nextSlow 0 FindLength
else
slowAndFast nextSlow nextFast (len + 1) phase



Complexity: time o(n), memory o(1)

The idea: consider two pointers ‘fast’ and ‘slow’. At each iteration ‘slow’ pointer makes one step, ‘fast’ - two steps. Somewhere ‘fast’ pointer touches ‘slow’ and you can find length of the loop.