[Haskell-beginners] Graham Scan exercise from Chapter 3 RWH -Spoilers. Don't read if you want to do this exercise.

Jürgen Doser jurgen.doser at gmail.com
Fri Sep 3 06:57:38 EDT 2010

```El jue, 02-09-2010 a las 17:21 -0700, Michael Litchard escribió:
> Below is my solution for the Graham Scan Algorithm.
> I tried to limit myself to information in the first three chapters
> while completing this problem.
> Now, I want to remove the explicit recursion and use more idiomatic
> Haskell. I'd like to get some advice on which functions/modules would
>
>
> <code>
> data Direction = DStraight
>                | DLeft
>                | DRight
>                  deriving (Eq,Show)
>
> type PointXY = (Double,Double)
>
> calcTurn :: PointXY -> PointXY -> PointXY -> Direction
> calcTurn a b c
>         | crossProduct == 0 = DStraight
>         | crossProduct > 0  = DLeft
>         | otherwise         = DRight
>        where crossProduct = ((fst b - fst a) * (snd c - snd a)) -
> ((snd b - snd a) * (fst c - fst a))

Instead of using fst, snd, I usually use pattern matching:

calcTurn (x1,y1) (x2,y2) (x3,y3) = ...
where crossProduct = (x2-x1)*(y3-y1)-...

> calcDirectionList :: [PointXY] -> [Direction]
> calcDirectionList (x:y:z:zs) = (calcTurn x y z) : (calcDirectionList (y:z:zs))
> calcDirectionList _ = []

It is tempting to use some kind of map or foldr for this. Unfortunately,
there isn't a really nice way. Such a "sliding window" map is
occasionally useful, but there is no pre-defined function for it in the
libraries. One way to avoid the explicit recursion is to first create a
list of all the triples, and then map calcTurn over it:

calcDirectionList points = map (\(x,y,z) -> calcTurn x y z)
(zip3 points (tail points) (tail (tail points)))

Unless one has seen this idiom before, I don't think this is any clearer
than the explicit recursion. Not having a curry3 doesn't help either.

> sortListByY :: [PointXY] -> [PointXY]
> sortListByY [] = []
> sortListByY [a] = [a]
> sortListByY (a:as) = insert (sortListByY as)
>            where insert [] = [a]
>                  insert (b:bs) | snd a <= snd b = a : b : bs
>                                | otherwise      = b : insert bs

You can use Data.List.sortBy and Data.Ord.comparing for this.

> sortListByCoTangent :: [PointXY] -> [PointXY]
> sortListByCoTangent [] = []
> sortListByCoTangent [a] = [a]
> sortListByCoTangent (a:as) = a : insert (sortListByCoTangent as)
>                  where insert :: [PointXY] -> [PointXY]
>                        insert [b] = [b]
>                        insert (b:c:cs) | (myCoTan a b) >= (myCoTan a
> c) =  b : insert (c:cs)
>                                        | otherwise
>  =  c : insert (b:cs)
>                              where myCoTan :: PointXY -> PointXY -> Double
>                                    myCoTan p1 p2 = (fst p2 - fst p1) /
> (snd p2 - snd p1)

This doesn't look like a straightforward sort, because of the special
handling of the first element. After that, it seems to be a sort where
the comparing function takes the first element as an argument. So you
can again use sortBy and comparing.

Next, I try to avoid nesting where to save on horizontal space. And
again, I would use pattern matching instead of fst and snd.

> createHull :: [PointXY] -> [PointXY]
> createHull (a:b:c:cs) = a : filterPoint (createHull (b:c:cs))
>         where filterPoint :: [PointXY] -> [PointXY]
>               filterPoint (x:y:z:zs)
>                         | calcTurn x y z == (DLeft)     = [x] ++ [y]
> ++ [z] ++ filterPoint (zs)
>                         | otherwise                     = [x] ++ [z]
> ++ filterPoint (zs)
>               filterPoint [x] = a:[x]
>               filterPoint _ = []
> createHull _ = []

You pattern match on b,c, but never use them. why not:

createHull (a:as) = a : filterPoint (createHull as)

and handle the case of not enough points in filterPoint itself.

then:

[x]++[y]++[z]++ ... = [x,y,z]++ ...
a:[x] = [a,x]

Again, there is no really nice way to avoid the explicit recursion here.
Are you sure this is the right way to do it, though? There seem to be a
lot of redundant calls to filterPoint.

Jürgen

```