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)

#-- alds1-12-a :: MinimumSpanningTree
INF = 2001

n = gets.to_i
graph = []       # Graph
ps = [nil] * n   # parents
ws = [INF] * n   # weights (input : 0 <= w <= 2000)
vs = [false] * n # validates (true : validated)

# create graph
n.times { graph << gets.split.map(&:to_i) }

# prim algorithm
while vs.include? false
  ps[0] = -1
  ws[0] = 0
  mv = -1
  minimum = INF

  # wsの中で未検証かつ最小の重みを持つノード(mv = minimum vertex)を見つける
  ws.each_with_index do |w, i|
    if (vs[i] == false) && (w < minimum)
      minimum = w
      mv = i
    end
  end

  # mvから未検証の隣接点までの重みを調べ、隣接点の現在の重み(wsの値)より小さいなら重みを更新する
  # その際、接続元のノード(psの値)も更新する
  graph[mv].each_with_index do |nw, i|
    if (vs[i] == false) && (nw != -1) && (nw < ws[i])
      ws[i] = nw
      ps[i] = mv
    end
  end

  # mvまでの最短は検証済にする
  vs[mv] = true
end

puts ws.sum