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.util.LinkedList;
import java.util.Scanner;
import java.util.Iterator;

class Graph {
	int totalDist;
	private int totalVertex;
	//adjMatrix[u][v] = 1 if there is an edge from u to v, otherwise 0
	private int[][] adjMatrix;
	//adjWeight[u][v] -- the weight of the edge from u to v if there is one
	private int[][] adjWeight;
	//if a node is settled (e.g., processed in the Dijkstra's algorithm)
	private Boolean[] ifSettled;
	public Graph() { totalVertex = 0; }
	public int getTotalVertex() { return totalVertex; }
	//load graph from standard input
	public void loadAdjMatrix() {
		Scanner in = new Scanner(System.in);
		totalVertex = in.nextInt();
		adjMatrix = new int[totalVertex][totalVertex];
		adjWeight = new int[totalVertex][totalVertex];
		ifSettled = new Boolean[totalVertex];
		int i, j;
		for(i = 0; i < totalVertex; i ++) {
			ifSettled[i] = false;
			for(j = 0; j < totalVertex; j ++) {
				adjWeight[i][j] = in.nextInt();
				if (adjWeight[i][j] != -1) {
					adjMatrix[i][j] = 1;
				}
			}
		}
		in.close();
	}
	//return weight of the edge from u to v if there is one
	public int getWeight(int u, int v) {
		return adjWeight[u][v];
	}
	//return neighbors of u as a LinkedList
	public LinkedList<Integer> getNeighbors(int u) {
		LinkedList<Integer> tmp = new LinkedList<Integer>();
		for(int v = 0; v < totalVertex; v ++) {
			if(adjMatrix[u][v] == 1) tmp.add(v);
		}
		return tmp;
	}
	//return unsettled neighbors of u as a LinkedList
	public LinkedList<Integer> getUnsettledNeighbors(int u) {
		LinkedList<Integer> tmp = new LinkedList<Integer>();
		for(int v = 0; v < totalVertex; v ++) {
			if((adjMatrix[u][v] == 1) && (ifSettled[v] == false)) tmp.add(v);
		}
		return tmp;
	}
	//return the unsettled node that has the smallest dist
	public int getUnsettledNearest(int[] dist) {
		int md = Integer.MAX_VALUE;
		int mv = -1;
		int v;
		for(v = 0; v < totalVertex; v ++) {
			if((ifSettled[v] == false) && (dist[v] < md)) {
				md = dist[v];
				mv = v;
			}
		}
		return mv;
	}
	//implement the following	
	public int Dijkstra(int s) {
		int[] dist = new int[totalVertex];
		LinkedList<Integer> unsettled = new LinkedList<Integer>();
		for(int i = 0; i < totalVertex; i++) {
			unsettled.add(i);
			dist[i] = Integer.MAX_VALUE;
			ifSettled[i] = false;
		}
		dist[0] = 0;
		
		while(!unsettled.isEmpty()) {
			Integer shortestNeighbor = getUnsettledNearest(dist);
			
			ifSettled[shortestNeighbor] = true;
			unsettled.remove(shortestNeighbor); 
			
			LinkedList<Integer> neighbors = getUnsettledNeighbors(shortestNeighbor);
			Iterator<Integer> iterateneighbors = neighbors.iterator();
			
			while(iterateneighbors.hasNext()){
				int curr = iterateneighbors.next();
				if(dist[curr] > adjWeight[shortestNeighbor][curr]) {
					dist[curr] = adjWeight[shortestNeighbor][curr];
				}
			}
			
		}
		for(int i = 0; i < dist.length; i++) {
			totalDist = totalDist + dist[i];
		}
		
		return totalDist;
	}
}


public class Main {
	public static void main(String[] argv) {
		Graph g = new Graph();
		g.loadAdjMatrix();
		int dist = g.Dijkstra(0);
		System.out.println(dist);
	}
}