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: Time Limit Exceeded)

#include <stdio.h>
#define inf 100000
#define N 100
#define W -1
#define B 1

int MST(int);
int A[N][N];

int main(){
  int n, i, j;

  scanf("%d", &n);

  for(i = 0; i < n; i++){
    for(j = 0; j < n; j++){
      scanf("%d", &A[i][j]);
      if(A[i][j] == -1)
	A[i][j] = inf;
    }
  }

  printf("%d", MST(n));
  return 0;
}

int MST(int n){
  int i, u, v, min, sum=0;
  int d[N], pi[N], color[N];

  for(i = 0; i < n; i++){
    d[i] = inf;
    pi[i] = -1;
    color[i] = W;
  }

  d[1] = 0;

  while(1){
    min = inf;
    for(i = 0; i < n; i++){
      if(color[i] != B && d[i] < min){
	min = d[i];
	u = i;
      }
    }

    color[u] = B;

    for(v = 0; v < n; v++){
      if(color[v] != B && A[u][v] < d[v]){
	pi[v] = u;
	d[v] = A[u][v];
      }
    }
  }
  
  for(i = 0; i < n; i++)
    sum += d[i];
  
  return sum;
}