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)

from sys import maxsize
from functools import reduce

WHITE = 0
GRAY = 1
BLACK = 2


def read_adj_mat():
    n = int(input())
    M = []
    for _ in range(n):
        M.append([maxsize if x == "-1" else int(x)
                  for x
                  in input().split()])
    return n, M


def min_sp_tree(n, M):
    d = [maxsize] * n
    p = [-1] * n
    color = [WHITE] * n

    d[0] = 0

    while True:
        minv = maxsize
        u = -1

        for i in range(n):
            if minv > d[i] and color[i] != BLACK:
                u = i
                minv = d[i]

        if u == -1:
            break

        color[u] = BLACK
        for v in range(n):
            if color[v] != BLACK and M[u][v] != maxsize:
                if d[v] > M[u][v]:
                    d[v] = M[u][v]
                    p[v] = u
                    color[v] = GRAY

    return sum([M[i][p[i]] for i in range(n) if p[i] != -1])


def main():
    n, M = read_adj_mat()
    print(min_sp_tree(n, M))


if __name__ == '__main__':
    main()