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 JAVA (judge verdict: Accepted)

import java.util.Scanner;

class Main {
  public static final int INF = 10000;
  public static int N;

  public static void main(String... args) {
    Scanner sc = new Scanner(System.in);
    N = sc.nextInt();
    int[][] roots = new int[N][N];
    Node[] nodes = new Node[N];

    for (int i = 0; i < N; i++) {
      nodes[i] = new Node();
      for (int j = 0; j < N; j++) {
        roots[i][j] = sc.nextInt();
      }
    }

    nodes[0].cost = 0;

    int min;
    int u = 0;
    while (true) {
      min = INF;

      for (int i = 0; i < N; i++) {
        if (!nodes[i].selected && nodes[i].cost < min) {
          min = nodes[i].cost;
          u = i;
        }
      }

      if (min == INF) {
        break;
      }

      nodes[u].selected = true;

      for (int v = 0; v < N; v++) {
        if (!nodes[v].selected && roots[u][v] != -1) {
          if (roots[u][v] < nodes[v].cost) {
            nodes[v].cost = roots[u][v];
          }
        }
      }
    }

    int result = 0;
    for (Node node : nodes) {
      result += node.cost;
    }

    System.out.println(result);
  }
}

class Node {
  public static final int INF = 10000;
  public int cost = INF;
  public boolean selected;

  public Node() { }
}