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.Scanner;
import java.util.TreeSet;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[][] graph = new int[n][n];
		int[] keys = new int[n];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				graph[i][j] = in.nextInt();
			}
			keys[i] = 2001;
		}
		keys[0] = 0;
		TreeSet<Integer> spanSet = new TreeSet<Integer>();
		int u = 0;
		while (spanSet.size() < n) {
			u = minKey(keys, spanSet);
			spanSet.add(u);
			for (int i = 0; i < n; i++) {
				if (graph[u][i] != -1 && keys[i] > graph[u][i]) {
					keys[i] = graph[u][i];
				}
			}
		}
		int span = 0;
		for (int i = 0; i < n; i++) {
			span += keys[i];
		}
		System.out.println(span);
		in.close();
	}
	public static int minKey(int[] keys, TreeSet<Integer> spanSet) {
		int spot = 0;
		int value = 2001;
		for (int i = 0; i < keys.length; i++) {
			if (keys[i] < value && !spanSet.contains(i)) {
				spot = i;
				value = keys[i];
			}
		}
		return spot;
	}
}