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.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {

	private int prim(int n, int[][] map) {
		int[] d = new int[n];
		int[] p = new int[n];
		boolean[] c = new boolean[n];
		Arrays.fill(d, Integer.MAX_VALUE);
		Arrays.fill(p, -1);
		d[0] = 0;
		while (true) {
			int min = Integer.MAX_VALUE;
			int u = -1;
			for (int i = 0; i < n; i++) {
				if (d[i] < min && c[i] == false) {
					min = d[i];
					u = i;
				}
			}
			if (u == -1) break;
			c[u] = true;
			for (int i = 0; i < n; i++) {
				if (!c[i] && map[u][i] != Integer.MAX_VALUE && map[u][i] < d[i]) {
					d[i] = map[u][i];
					p[i] = u;
				}
			}
		}
		int sum = 0;
		for (int i = 0; i < n; i++) {
			if (p[i] != -1) {
				sum += map[i][p[i]];
			}
		}
		return sum;
	}

	public void run() throws IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(reader.readLine());
		int[][] map = new int[n][n];
		for (int i = 0; i < n; i++) {
			StringTokenizer st = new StringTokenizer(reader.readLine());
			for (int j = 0; j < n; j++) {
				int v = Integer.parseInt(st.nextToken());
				map[i][j] = v == -1?Integer.MAX_VALUE:v;
			}
		}
		reader.close();
		System.out.println(prim(n, map));
	}

	public static void main(String[] args) throws IOException {
		new Main().run();
	}
}