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 Python (judge verdict: Accepted)

def main():
    n = input()
    A = []
    for i in xrange(n):
        A.append(map(int,raw_input().split()))

    inf = float('inf')
    d = [inf]*n
    p = [-1]*n
    c = [-1]*n
    d[0] = 0

    while(True):
        mincost = inf
        for i in xrange(n):
            if(c[i] != 1) & (d[i] < mincost):
                mincost = d[i]
                u = i
        if mincost == inf:
            break

        c[u] = 1
        
        for v in xrange(n):
            if (c[v] != 1) & (A[u][v] != -1):
                if A[u][v] < d[v]:
                    d[v] = A[u][v]
                    p[v] = u
                    c[v] = 0

    cost = 0
    for i in xrange(n):
        if(p[i] != -1):
            cost += A[i][p[i]]

    print cost
    
if __name__ == "__main__":
    main()