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 C# (judge verdict: Accepted)

using System;
using System.Linq;
using System.IO;
using System.Text;
using System.Collections;
using System.Collections.Generic;
using System.Text.RegularExpressions;
 
class Program
{
    static int n;
    static int[,] A;

    static void Main()
    {
        n = int.Parse(Console.ReadLine());
        A = new int[n, n];
        for (int i = 0; i < n; i++)
        {
            string[] inputs = Console.ReadLine().Trim().Split(' ');
            for (int j = 0; j < n; j++)
            {
                A[i, j] = inputs[j] == "-1" ? int.MaxValue : int.Parse(inputs[j]);
            }
        }

        Prim();
        Console.WriteLine(TotalWeight());
    }

    static int[] parent;
    static void Prim()
    {
        int[] weight = Enumerable.Repeat(int.MaxValue, n).ToArray();
        weight[0] = 0;
        bool[] isFinal = new bool[n];
        parent = Enumerable.Repeat(-1, n).ToArray();
        while (true)
        {
            int u = -1;
            int minv = int.MaxValue;
            for (int i = 0; i < n; i++)
            {
                if(minv > weight[i] && !isFinal[i])
                {
                    u = i;
                    minv = weight[i];
                }
            }
            if(u == -1) break;
            isFinal[u] = true;
            for (int i = 0; i < n; i++)
            {
                if(!isFinal[i] && weight[i] > A[u, i])
                {
                    weight[i] = A[u, i];
                    parent[i] = u;
                }
            }
        }
    }
    static int TotalWeight()
    {
        int sum = 0;
        for (int i = 0; i < n; i++)
        {
            if(parent[i] != -1) sum += A[parent[i], i];
        }
        return sum;
    }
}