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: Wrong Answer)

import java.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int amount = input.nextInt();
		int[][] matrix = new int[amount][amount];
		int[] visited = new int[amount];
		int weight = 0;
		visited[0] = 0;
		
		for(int i = 1; i < amount; i++) {
			visited[i] = -1;
		}
		for(int i = 0; i < amount; i++) {
			for(int j = 0; j < amount; j++) {
				int num = input.nextInt();
				matrix[i][j] = num;
			}
		}
		for(int i = 0; i < amount; i++) {
			matrix[i][0] = -1;
		}
		input.close();
		int vertex = 0;
		int min = 2001;
		int x = 0;
		for(int i = 1; i < amount; i++) {
			while(visited[x] != -1) {
				for(int j = 0; j < amount; j++) {
					int compare = matrix[visited[x]][j];
					if(compare < min && compare != -1) {
						min = compare;
						vertex = j;
					}
				}
				x++;
			}
			weight += min;
			visited[i] = vertex;
			for(int k = 0; k < amount; k++) {
				matrix[k][vertex] = -1;
			}
		}
		System.out.println(weight);
	}
}