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)

// Minimum_Spanning_Tree.cs

using System;

class Minimum_Spanning_Tree {
	public static void Main() {

		int n = int.Parse(Console.ReadLine());
		int[,] matrix = new int[n, n];
		int count = 0;
		bool[] memoryPosition = new bool[n];
		int[] m = new int[n];

		for(int i = 0; i < n; i++) {
			m[i] = int.MaxValue;
		}

		m[0] = 0;

		for(int i = 0; i < n; i++) {
			string testString = Console.ReadLine();
			char c = ' ';
			string ss = testString.Trim(c);
		//	Console.WriteLine(ss);
			string[] str = ss.Split();

/*
			foreach(string s in str) {
				Console.WriteLine(s);
			}
*/
			for(int j = 0; j < n; j++) {
				matrix[i, j] = int.Parse(str[j]);
			}
		}
/*
		foreach(int ii in matrix) {
			Console.WriteLine(ii);
		}
*/


		for(int i = 0; i < n; i++) {

			int min = int.MaxValue;
			int position = -1;

			for(int j = 0; j < n; j++) {
				if(!memoryPosition[j] && m[j] < min) {
					min = m[j];
					position = j;
				}
			}
//			Console.WriteLine("test");
			memoryPosition[position] = true;
//			Console.WriteLine("test");
			count += m[position];

			for(int j = 0; j < n; j++) {
				m[j] = Math.Min(m[j], matrix[position, j] < 0 ? int.MaxValue : matrix[position, j]);
			}
		}

		Console.WriteLine(count);

	}
}