# 99 questions/Solutions/81

(**) Path from one node to another one

Write a function that, given two nodes a and b in a graph, returns all the acyclic paths from a to b.

```import List (elem)

paths :: Eq a => a -> a -> [(a,a)] -> [[a]]
paths a b g = paths1 a b g []

paths1 :: Eq a => a -> a -> [(a,a)] -> [a] -> [[a]]
paths1 a b g current = paths2 a b g current [ y | (x,y) <- g, x == a ]

paths2 :: Eq a => a -> a -> [(a,a)] -> [a] -> [a] -> [[a]]
paths2 a b g current []	| a == b = [current++[b]]
| otherwise = []
paths2 a b g current (x:xs) | a == b = [current++[b]]
| elem a current = []
| otherwise = (paths1 x b g (current++[a])) ++ (paths2 a b g current xs)
```

paths :: Int -> Int -> [(Int , Int)] -> Int paths start end zs = let (xs,ys) = partition (\(_,z) -> z == end ) zs

```                     in  map (++ [ end] )  ( concat . map (\(e, _) -> if e == start then start else paths start e  ys) \$  xs )
```

This solution uses a representation of a (directed) graph as a list of arcs (a,b).