Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Minimum Spanning Tree

For a given weighted graph $G = (V, E)$, find the minimum spanning tree (MST) of $G$ and print total weight of edges belong to the MST.

Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, a $n \times n$ adjacency matrix $A$ which represents $G$ is given.
$a_{ij}$ denotes the weight of edge connecting vertex $i$ and vertex $j$. If there is no edge between $i$ and $j$, $a_{ij}$ is given by -1.

Output

Print the total weight of the minimum spanning tree of $G$.

Constraints

$1 \leq n \leq 100$

$0 \leq a_{ij} \leq 2,000$ (if $a_{ij} \neq -1$)

$a_{ij} = a_{ji}$

$G$ is a connected graph

Sample Input 1

5
-1 2 3 1 -1
2 -1 -1 4 -1
3 -1 -1 1 1
1 4 1 -1 3
-1 -1 1 3 -1

Sample Output 1

5

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Haskell (judge verdict: Accepted)

import Control.Monad
import Data.Functor
import Data.List

main :: IO ()
main = do
  n <- readLn
  am <- replicateM n $ map read . words <$> getLine :: IO([[Int]])
  let filled = map (map (\w -> if w == -1 then maxBound else w)) am
  print . solve $ filled

solve :: [[Int]] -> Int
solve am = sum . map snd $ mst am [(0, 0)]

type Node = Int
type Weight = Int
type AdjMatrix = [[Weight]]
type SpanningTree = [(Node, Weight)]

mst :: AdjMatrix -> SpanningTree -> SpanningTree
mst am st
  | length am <= length st = st
  | otherwise = mst am (nearest:st)
  where
    spanned = map fst st
    neighbors = [(i, (am !! j) !! i)
      | i <- [0..(length am - 1)], j <- spanned, i `notElem` spanned]
    nearest = minimumBy (\x y -> compare (snd x) (snd y)) neighbors