# 99 questions/Solutions/84

### From HaskellWiki

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)