# [Haskell-cafe] Newb: List of nodes in a graph - is there a prettier way?

Dan Weston westondan at imageworks.com
Fri Sep 28 19:15:57 EDT 2007

```If I haven't mistaken what you're asking for, how about:

import Data.Set as S
nodes = foldr (\(a,b) -> S.insert a . S.insert b) S.empty

Torsten Otto wrote:
> Howdy,
>
> I'm working towards Dijkstra's algorithm here and I have a feeling that
> I could do without the helper function nodesInternal in the following
> code, if I only could figure out how. Any hints would be appreciated.
>
> nodes::Graph->[Id] should (and actually does) return a list of all nodes
> in the graph.
>
> Thanks a bunch in advance.
> Regards,
> Torsten Otto
>
>
>  >module Route where
>
> Datatypes for the representation of the graph:
>
>  >type Id = Int
>  >type Weight = Int
>  >type Edge = (Id,Id)
>  >type Graph = [ (Edge, Weight) ]
>
>  >graph::Graph
>  >graph =  [ ((0,1),1),
>  >            ((0,2),3),
>  >            ((0,4),6),
>  >            ((1,2),1),
>  >            ((1,3),3),
>  >            ((2,0),1),
>  >            ((2,1),2),
>  >            ((2,3),1),
>  >            ((3,0),3),
>  >            ((3,4),2),
>  >            ((4,3),1),
>  >            ((5,2),9)]
>
>  >data Cost = Finite Weight | Infinity
>  >            deriving (Eq, Ord, Show)
>
>  >type PathCost = (Cost, Id)
>
> Return the number of edges in the graph:
>
>  >edges :: Graph -> Int
>  >edges graph = length graph
>
> Calculate the sum of all weights:
>
>  >weightTotal::Graph -> Weight
>  >weightTotal ((edge, weight):xs)| xs == []     = weight
>  >                                | otherwise    = weight + (weightTotal
> xs)
>
> List all the nodes in the graph:
>
>  >nodes::Graph -> [Id]
>  >nodes graph = nodesInternal [] graph
>
>  >nodesInternal::[Id]->Graph->[Id]
>  >nodesInternal list (((id1,id2),weight):xs)
>  >        | (elem id1 list) && (elem id2 list)        = nodesInternal
> list xs
>  >        | (elem id1 list) && (not (elem id2 list))    = nodesInternal
> (id2:list) xs
>  >        | (not (elem id1 list)) && (elem id2 list)    = nodesInternal
> (id1:list) xs
>  >        | (not (elem id1 list)) && (not (elem id2 list))    =
> nodesInternal (id1:id2:list) xs
>  >nodesInternal list []    = list
>
> Function for adding costs so that we can make use of Infinity for
> impossible routes:
>
>  >addCosts::Cost -> Cost -> Cost
>  >addCosts Infinity Infinity        = Infinity
>  >addCosts Infinity (Finite x)     = Infinity
>  >addCosts (Finite x) Infinity    = Infinity
>  >addCosts (Finite x) (Finite y) = Finite (x + y)
>
> Return the cost of a given edge:
>
>  >lookUp::Edge -> Graph -> Cost
>  >lookUp (id1,id2) (((id1x,id2x),weightx):xs)
>  >        | (id1==id1x && id2==id2x)    = Finite weightx
>  >        | xs==[]                    = Infinity
>  >        | otherwise                    = lookUp (id1,id2) xs
>
>
>
>
>
>
>
> _______________________________________________