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)

import sys
from operator import add

n = int(sys.stdin.readline().strip())
A = [ [0] for i in range(n)]
for i in range(n):
	temp = map(int ,sys.stdin.readline().strip().split(" "))
	A[i] = temp


weight = [None for i in range(n)]
mitayatu=[False for i in range(n)]

def min(array):
	temp = 100000
	index= 0
	for i in range(n):
		if array[i] is not None and mitayatu[i]==False:
			if temp>=array[i]:
				temp = array[i]
				index = i
	return index

def owari():
	for i in mitayatu:
		if i is False:
			return False
	return True
# zero origin
def prim(nodeid):
	#print(nodeid)
	if owari() == True:
		return
	if mitayatu[nodeid]==True:
		return
	mitayatu[nodeid]=True
	for i in range(n):
		if A[nodeid][i]!=-1:
			if weight[i] is None:
				weight[i]=A[nodeid][i]
			elif weight[i]>A[nodeid][i] and mitayatu[i]==False:
				weight[i]=A[nodeid][i]
	prim(min(weight))

weight[0]=0
prim(0)

#print(weight)
print(reduce(add, weight))