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 Ruby (judge verdict: Accepted)

$selected = []
$distance = 0
INF = 10**12
def prim(matrix)
  matrix.map do |row|
    row[0] = -1
  end
  $selected << matrix[0]
  until $selected.size == matrix.size
    min_index = nil
    min_value = INF
    $selected.each do |row|
      row.each_with_index do |value, index|
        if min_value > value && value >= 0
          min_index = index
          min_value = value
        end
      end
    end
    matrix.map do |row|
      row[min_index] = -1
    end
    $distance += min_value
    $selected << matrix[min_index]
  end
end

n = gets.to_i
matrix = []
n.times do
  matrix << gets.split(' ').map(&:to_i)
end
prim matrix
p $distance