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.Collections.Generic;
using System.Linq;
using System.Text;

namespace Practice
{
    class Program
    {
        const int WHITE = -10;
        const int GRAY = -9;
        const int BLACK = -8;
        static void Main(string[] args)
        {
            SolveA(args);
            //SolveB(args);
            //SolveC(args);
            //SolveD(args);


        }
        static void SolveA(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[,] m = new int[n, n];
            for(int i = 0; i < n; ++i)
            {
                var szarr = Console.ReadLine().Split(' ');
                for(int j=1;j<szarr.Length;++j)
                {
                    m[i, j-1] = int.Parse(szarr[j]);
                }
            }

            int[] color = new int[n];
            int[] d = new int[n];
            int[] p = new int[n];

            prime(n, m, color, d, p);

            int sum = 0;
            for(int i=1;i<p.Length;++i)
            {
                int w = m[i, p[i]];
                if (w != -1)
                {
                    sum += w;
                }
            }
            Console.WriteLine(sum);
        }
        static void prime(int n ,int[,] m, int [] color, int[] d, int[] p)
        {
            for(int i = 0; i < color.Length; ++i) { color[i] = WHITE; }
            for(int i = 0; i < d.Length; ++i) { d[i] = int.MaxValue; }
            d[0] = 0;
            p[0] = -1;
            while(true)
            {
                int u = -1;
                int mincost = int.MaxValue;
                for(int i=0;i<n;++i)
                {
                    if( color[i] != BLACK && d[i] < mincost)
                    {
                        mincost = d[i];
                        u = i;
                    }
                }
                if( mincost == int.MaxValue) { break; }
                color[u] = BLACK;
                for(int v = 0;v<n;++v)
                {
                    if( color[v] != BLACK && m[u,v] != -1)
                    {
                        if( m[u,v] < d[v])
                        {
                            d[v] = m[u, v];
                            p[v] = u;
                            color[v] = GRAY;
                        }
                    }
                }
            }
        }
    }

}