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 Python3 (judge verdict: Accepted)

def prim(n, cost):
    mincost = [float("inf")]*n
    used = [False] * n
    mincost[0] = 0
    res = 0
    cnt = 1
    while True:
        u = -1
        for i in range(n):
            if (not used[i]) and (u == -1 or mincost[i] < mincost[u]):
                u = i
        if u == -1:
            break
        used[u] = True
        res += mincost[u]
        for v in range(n):
            if cost[u][v] != -1:
                mincost[v] = min(mincost[v], cost[u][v])
    return res


def main():
    n = int(input())
    g = []
    for _ in range(n):
        g.append(list(map(int, input().split())))
    print(prim(n, g))



if __name__ == '__main__':
    main()