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 Scala (judge verdict: Accepted)

object Main extends App {
    val in = io.Source.stdin.getLines.map(_.trim.split(" ").map(_.toInt))
    val n = in.next.head
    val t = (0 to n-1).toArray
    val d = in.toSeq
    lazy val es = (for (i <- (0 to n-2); j <- (i+1 to n-1) if d(i)(j) != -1) yield (i, j, d(i)(j))).sortBy(_._3)
    var cost = 0

    def find(m: Int): Int = if(t(m) == m) m else {t(m) = find(t(m)); t(m)}
 
    def unite(x: Int, y: Int) = {
        val _x = find(x)
        val _y = find(y)
        if(_x != _y) t(_x) = _y
    }
 
    es.foreach(e => if (find(e._1) != find(e._2)) {unite(e._1, e._2); cost += e._3})
    println(cost)
}