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;

class Main{
    final static int LEN = 105;
    public static void main(String args[]){
	int[][] graph = new int[LEN][LEN];
	int[] minCost = new int[LEN];
	int count=0;
	int v;
	Boolean[] used = new Boolean[LEN];

	Scanner in = new Scanner(System.in);

	//read
	int n = in.nextInt();
	for(int i=0; i<n; i++){
	    for(int j=0; j<n; j++){
		int k = in.nextInt();
		graph[i][j]=(k==-1? Integer.MAX_VALUE : k);
	    }
	}

	//make prim
	for(int i=0; i<n; i++){
	    minCost[i]=Integer.MAX_VALUE;
	    used[i]=false;
	}

	minCost[0]=0;

	while(true){
	    v = -1;
	    for(int i=0; i<n; i++){
		if(!used[i] && (v==-1 || minCost[i] < minCost[v]))v=i;
	    }

	    if(v==-1)break;
	    used[v]=true;
	    count+=minCost[v];

	    for(int i=0; i<n; i++){
		minCost[i]=Math.min(minCost[i], graph[v][i]);
	    }
	}

	//print
	System.out.println(count);
    }
}