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.Scanner;

public class Main {

    private static final int MAX_N = 100;
    private static final int INF = 1 << 21;
    private static final int WHITE = 0;
    private static final int GRAY = 1;
    private static final int BLACK = 2;

    static int n;
    static int[][] M = new int[MAX_N][MAX_N];


    private static int prim() {
        // initialize
        int[] color = new int[MAX_N]; // visited or not
        int[] d = new int[MAX_N]; // min edge
        int[] p = new int[MAX_N]; // MST parent node

        for (int i = 0; i < n; i++) {
            color[i] = WHITE;
            d[i] = INF;
            p[i] = -1;
        }

        // start node
        d[0] = 0;

        while (true){
            int u = -1;
            int minv = INF;

            // find minimum value vertex
            for (int i = 0; i < n; i++) {
                if (color[i] != BLACK && d[i] < minv){
                    minv = d[i];
                    u = i;
                }
            }

            // didn't find any vertex
            if (u == -1)
                break;
            color[u] = BLACK;

            // add new edges
            for (int v = 0; v < n; v++) {
                if (color[v] != BLACK && M[v][u] != INF){
                    if (d[v] > M[v][u]) {
                        d[v] = M[v][u];
                        color[v] = GRAY;
                        p[v] = u;
                    }
                }

            }

        }

        int sum = 0;
        for (int i = 0; i < n; i++) {
            if (p[i] != -1)
                sum += M[p[i]][i];
        }

        return sum;
    }

    private static void input() {
        Scanner scanner = new Scanner(System.in);
        n = scanner.nextInt();
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                int e = scanner.nextInt();
                if (e == -1)
                    M[i][j] = INF;
                else
                    M[i][j] = e;
            }
        }
    }

    public static void main(String[] args){
        input();
        System.out.println(prim());
    }
}