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 Kotlin (judge verdict: Wrong Answer)

import java.io.PrintWriter

data class Edge(val a: Int, val i: Int, val j: Int)

fun main(args: Array<String>) = with(PrintWriter(System.out)) {
    val n = readLine()!!.toInt()

    val a = mutableListOf<Edge>()
    for (i in 1..n) {
        readLine()!!.trim().split(' ').forEachIndexed { j, s ->
            val a_ij = s.toInt()
            if (a_ij != -1)
                a.add(Edge(a_ij, i, j))
        }
    }
    a.sortBy { it.a }

    var sum = 0
    val explored = mutableSetOf<Int>()
    a.forEach{ a_ij ->
        if (!explored.contains(a_ij.i) || !explored.contains(a_ij.j)) {
            sum += a_ij.a
            explored.add(a_ij.i)
            explored.add(a_ij.j)
        }
    }
    println(sum)
    flush()
}