# Difference between revisions of "99 questions/Solutions/84"

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+ | [[Category:Programming exercise spoilers]] |

## Latest revision as of 03:50, 10 January 2017

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)
```