# 99 questions/80 to 89

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This is part of Ninety-Nine Haskell Problems, based on Ninety-Nine Prolog Problems.

If you want to work on one of these, put your name in the block so we know someone's working on it. Then, change n in your block to the appropriate problem number, and fill in the <Problem description>,<example in lisp>,<example in Haskell>,<solution in haskell> and <description of implementation> fields.

## 2 Problem 80

<Problem description>

```Example:
<example in lisp>

Example in Haskell:
<example in Haskell>
```

Solution:

`<solution in haskell>`

<description of implementation>

## 3 Problem 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.
```
```Example:
<example in lisp>

Example in Haskell:
paths 1 4 [(1,2),(2,3),(1,3),(3,4),(4,2),(5,6)]
[[1,2,3,4],[1,3,4]]
paths 2 6 [(1,2),(2,3),(1,3),(3,4),(4,2),(5,6)]
[]
```

Solution:

```import List (nub, elem)

data Graph a = [(a,a)]

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 c = paths2 a b g c [ y | (x,y) <- g, x == a ]

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

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

## 4 Problem 82

<Problem description>

```Example:
<example in lisp>

Example in Haskell:
<example in Haskell>
```

Solution:

`<solution in haskell>`

<description of implementation>

## 5 Problem 83

<Problem description>

```Example:
<example in lisp>

Example in Haskell:
<example in Haskell>
```

Solution:

`<solution in haskell>`

<description of implementation>

## 6 Problem 84

<Problem description>

```Example:
<example in lisp>

Example in Haskell:
<example in Haskell>
```

Solution:

`<solution in haskell>`

<description of implementation>

## 7 Problem 85

<Problem description>

```Example:
<example in lisp>

Example in Haskell:
<example in Haskell>
```

Solution:

`<solution in haskell>`

<description of implementation>

## 8 Problem 86

<Problem description>

```Example:
<example in lisp>

Example in Haskell:
<example in Haskell>
```

Solution:

`<solution in haskell>`

<description of implementation>

## 9 Problem 87

<Problem description>

```Example:
<example in lisp>

Example in Haskell:
<example in Haskell>
```

Solution:

`<solution in haskell>`

<description of implementation>

## 10 Problem 88

<Problem description>

```Example:
<example in lisp>

Example in Haskell:
<example in Haskell>
```

Solution:

`<solution in haskell>`

<description of implementation>

## 11 Problem 89

<Problem description>

```Example:
<example in lisp>

Example in Haskell:
<example in Haskell>
```

Solution:

`<solution in haskell>`

<description of implementation>