Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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

import static java.lang.Integer.parseInt;

/**
 * Graph II - Minimum Spanning Tree
 */
public class Main {

	static final int INF = 1 << 29;

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line;

		int n = parseInt(br.readLine());

		int[][] a = new int[n][n];

		for (int i = 0; i < n; i++) {
			StringTokenizer st = new StringTokenizer(br.readLine());
			for (int j = 0; j < n; j++) {
				a[i][j] = parseInt(st.nextToken());
			}
		}

		//solve
		int cost = 0;
		int size = 0;
		boolean[] S = new boolean[n];

		S[0] = true;
		size++;

		while (size < n) {
			int min = INF;
			int v = -1;
			for (int i = 0; i < n; i++) {
				if (S[i]) {
					for (int j = 0; j < n; j++) {
						if (!S[j] && a[i][j] != -1 && a[i][j] < min) {
							min = a[i][j];
							v = j;
						}
					}
				}
			}
			S[v] = true;
			size++;
			cost += min;
		}

		System.out.println(cost);
	}
}