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)

N = gets.to_i

INFTY = 1<<21
WHITE = 0
GRAY  = 1
BLACK = 2

@m = N.times.map{gets.split.map{|i| i == '-1' ? INFTY : i.to_i }}

def prim
  d = Array.new(N){INFTY}
  p = Array.new(N){-1}
  color = Array.new(N){WHITE}

  d[0] = 0

  loop do
    minv = INFTY
    u = -1
    (0...N).each do |i|
      if minv > d[i] && color[i] != BLACK
        u = i
        minv = d[i]
      end
    end

    break if u == -1
    color[u] = BLACK

    (0...N).each do |v|
      if color[v] != BLACK && @m[u][v] != INFTY
        if d[v] > @m[u][v]
          d[v] = @m[u][v]
          p[v] = u
          color[v] = GRAY
        end
      end
    end
  end

  sum = 0

  (0...N).each do |i|
    sum += @m[i][p[i]] if p[i] != -1
  end

  return sum
end

puts prim