99 questions/Solutions/84

<Example in Haskell> Create an undirected-graph: graph = mkGraph False (1,5) [(1,2,12),(1,3,34),(1,5,78),(2,4,55),(2,5,32),(3,4,61),(3,5,44),(4,5,93)]

False means undirected

Use prim algorithm to find the minimal spanning tree: prim graph

Output: [(55,2,4),(34,1,3),(32,2,5),(12,1,2)]

module Prim where

import Data.List import Array

type Graph n w = Array n [(n,w)]

mkGraph dir bnds es =

   accumArray (\xs x -> x:xs) [] bnds
              ([(x1,(x2,w)) | (x1,x2,w) <- es] ++
              if dir then []
              else [(x2,(x1,w)) | (x1,x2,w) <- es, x1 /= x2])
              

adjacent g v = map fst (g!v)

nodes g = indices g

edgeIn g (x,y) = elem y (adjacent g x)

weight x y g = head [c | (a,c) <- g!x, a == y]

edgesD g = [(v1,v2,w) | v1 <- nodes g, (v2,w) <- g!v1] edgesU g = [(v1,v2,w) | v1 <- nodes g, (v2,w) <- g!v1, v1 < v2]

prim g = prim' [n] ns []

   where (n:ns) = nodes g
         es = edgesU g
         prim' t [] mst = mst
         prim' t r mst = let e@(c,u',v') = minimum[(c,u,v) | (u,v,c) <- es, elem u t,elem v r]
                         in  prim' (v':t) (delete v' r) (e:mst)