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: Accepted)

#include<stdio.h>

#define MAX  500
static const int INFTY = (1<<21);

int H[MAX],n,bbb=1;
int NOT(int k){
  int i;
  for(i=0;i<bbb;i++){
    if(H[i]==k)return 0;
  }
  return 1;
}

main(){
  int i, j, e, sum,min,k;
  int V[MAX][MAX];
  int M[MAX];
  int aaa=0;
  H[0]=0;
  int flag=0;

  scanf("%d", &n);

  for ( i = 0; i< n; i++ ){
    for ( j = 0; j < n; j++ ){
      scanf("%d", &e);
      V[i][j] = (e==-1)?INFTY:e;
    }
  }
  i=0;
  while(i<n){
    min=INFTY;
    for(j=0;j<bbb;j++){
      for(k=0;k<n;k++){
	if(NOT(k) && V[H[j]][k]<min){
	  min=V[H[j]][k];
	  flag=k;
	}
      }
    }
    M[i]=min;
    H[bbb]=flag;
    bbb++;
    i++;
  }

  sum = 0;
  
  for ( i = 0; i < n-1; i++ ){
    sum+=M[i];
  }
  
  printf("%d\n",sum);
  
  return 0;
}