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>
#include <stdlib.h>


typedef struct edge {
    int w, f, t;
} edge;
edge E[(100*100)/2];
  
int A[100][100];
int group[100];
int comp(const void *x, const void *y)
{
    return ((edge*)x)->w - ((edge*)y)->w;
}
  
int kru(int n)
{
    int i, j, en, s, from, to;
    for(i=0; i<n; i++) group[i]=i;
    en=0;
    for(i=0; i<n; i++) {
        for(j=0; j<i; j++) {
            if(A[i][j]!=-1) {
                E[en].w=A[i][j];
                E[en].f=i;
                E[en].t=j;
                en++;
            }
        }
    }
    qsort(E, en, sizeof(edge), comp);
      
    s=0;
    for(i=0; i<en; i++) {
        from=group[E[i].f];
        to=group[E[i].t];
        if(from != to) {
            s+=E[i].w;
            for(j=0; j<n; j++) {
                if(group[j]==from) group[j]=to;
            }
            for(j=1; j<n && group[j-1]==group[j]; j++);
            if(j==n) break;
        }
    }
      return s;
}
int main(int argc,char * argv[])
{
    int i=0, j, n, s;
    scanf("%d", &n);
  for(i=0;i<n;n++){
        for(j=0; j<n; j++) {
            scanf("%d", &A[i][j]);
        }
    }
      
    s=kru(n);
    printf("%d\n", s);
    return 0;
}