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.



Sample input:
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:
5

Submission status: Runtime Error

Solution code:
INFTY = 1 << 21
WHITE = 0
GRAY = 1
BLACK = 2
d = [INFTY for i in range(n)]
p = [-1 for i in range(n)]
color = [WHITE for i in range(n)]

n = int(input())
M = [list(map(int, input().split())) for i in range(n)]
for i in range(n):
    for j in range(n):
        if (M[i][j] == -1):
            M[i][j] = INFTY

def prim():
    global M, d, p, color
    d[0] = 0
    while(1):
        minv = INFTY
        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] != INFTY):
                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)])

print(prim())

Submission status: Runtime Error

Solution code:
INFTY = 1 << 21
WHITE = 0
GRAY = 1
BLACK = 2
d = [INFTY for i in range(n)]
p = [-1 for i in range(n)]
color = [WHITE for i in range(n)]

n = int(input())
M = [list(map(int, input().split())) for i in range(n)]
for i in range(n):
    for j in range(n):
        if (M[i][j] == -1):
            M[i][j] = INFTY

def prim():
    global M, d, p, color
    d[0] = 0
    while(1):
        minv = INFTY
        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] != INFTY):
                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])

print(prim())

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python
from __future__ import division, print_function
from sys import stdin, maxint


def main():
    num = int(stdin.readline())

    M = []
    for _ in xrange(num):
        M.append([int(s) for s in stdin.readline().split()])

    g = set(xrange(1, num+1))
    index = g.pop()
    h = {index}
    weight = 0

    while g:_
        minimum = maxint
        for j in h:
            mj = M[j-1]
            for i in g:
                if 0 <= mj[i-1] < minimum:
                    index = i
                    minimum = mj[i-1]
        h.add(index)
        g.remove(index)
        weight += minimum

    print(weight)


main()