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 JavaScript (judge verdict: Accepted)

//config = { input: 'tmp', newline: '\r\n' }; // win
config = { input: '/dev/stdin', newline: '\n' }; // linux

A = require('fs').readFileSync(config.input, 'ascii')
  .trim()
  .split(config.newline);
for (i in A) {
  Ai = A[i].trim().split(' ');
  for (j in Ai) Ai[j] = parseInt(Ai[j]);
  A[i] = Ai;
}
n = Number(A.shift()[0]);

cnt = 1;
cost = 0;
conn = new Array(n);
conn[0] = true;
for (i = 1; i < n; i++) conn[i] = false;

while (cnt < n) {
  min = Number.MAX_VALUE;
  for (i in conn) {
    if (!conn[i]) continue;
    Ai = A[i];
    for (j in conn) {
      if (conn[j]) continue;
      if (Ai[j] !== -1 && Ai[j] < min) {
        min = Ai[j];
        min_j = j;
      }
    }
  }
  conn[min_j] = true;
  cost += min;
  cnt++;
}

console.log(cost);