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

class Graph2 {
    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 Graph2() { 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 ++) {
                adjMatrix[i][j] = adjWeight[i][j] = 0;
            }
        }
        int w;
        for(i = 0; i < totalVertex; i ++) {
            for(j = 0; j < totalVertex; j ++) {
                w = in.nextInt();
                if(w > -1) {
                    adjMatrix[i][j] = 1;
                }
                adjWeight[i][j] = w;
            }
        }
        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 MinSpan(int s) {
        // create array to store distances
        // initialize source node to 0 and rest to max value
        int[] dist = new int[totalVertex];
        int[] prev = new int[totalVertex];


        for(int i = 0; i < totalVertex; i++) {
            dist[i] = Integer.MAX_VALUE;
            prev[i] = -1;
        }

        dist[s] = 0;
        LinkedList<Integer> q = new LinkedList<Integer>();
        while(q.size()!=totalVertex) {
            int nearest = getUnsettledNearest(dist);
            if(dist[nearest] == Integer.MAX_VALUE) break;
            ifSettled[nearest] = true;
            q.add(nearest);
            for(int neighbor : getUnsettledNeighbors(nearest)) {
                if(getWeight(nearest, neighbor) < dist[neighbor]) {
                    dist[neighbor] = getWeight(nearest, neighbor);
                    //prev[neighbor] = nearest;
                }
            }
        }


        int totalWeight = 0;
        for(int i = 0; i < totalVertex; i ++) {

            if(dist[i]!=Integer.MAX_VALUE) totalWeight += dist[i];

        }
        return totalWeight;
    }
}
public class Main {
    public static void main(String[] argv) {
        Graph2 g = new Graph2();
        g.loadAdjMatrix();
        System.out.println(g.MinSpan(0));
    }
}