Problem:
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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)

{-# LANGUAGE BangPatterns #-}

import           Control.Applicative
import           Control.Monad
import qualified Data.ByteString.Char8 as B

import           Data.Array.IArray
import           Data.Array.IO
import           Data.Array.MArray
import           Data.Array.Unboxed
import           Data.Array.Unsafe

readi :: B.ByteString -> Int
readi b | Just (n, _) <- B.readInt b = n

prim :: Int -> UArray (Int, Int) Int -> [Int]
prim n g = go [1] []
  where
    go :: [Int] -> [Int] -> [Int]
    go !as !bs
        | null xs   = bs
        | otherwise = let (v, i) = minimum xs
                       in go (i:as) (v:bs)
      where
        xs =
            [ (g ! (a, i), i)
            | i <- filter (`notElem` as) [1 .. n]
            , a <- as
            , (g ! (a, i)) /= -1
            ]

main :: IO ()
main = do
    n <- readLn
    xss <- fmap (fmap readi . B.words) <$> replicateM n B.getLine
    a <- newArray ((1, 1), (n, n)) (-1) :: IO (IOUArray (Int, Int) Int)
    forM_ (zip [1 ..] xss) $ \(i, xs) -> do
        forM_ (zip [1 ..] xs) $ \(j, x) -> do
            writeArray a (i, j) x
    a <- unsafeFreeze a :: IO (UArray (Int, Int) Int)

    print . sum $ prim n a