minimum spanning tree gfg code example

Example 1: number of spanning tree gfg

If a graph is a complete graph with n vertices, then total number of spanning trees is n(n-2) where n is the number of nodes in the graph.
## Abhay Tiwari IITP

Example 2: prims minimum spanning tree

import math
def empty_tree (n):
    lst = []
    for i in range(n):
        lst.append([0]*n)
    return lst
def min_extension (con,graph,n):
    min_weight = math.inf
    for i in con:
        for j in range(n):
            if j not in con and 0 < graph[i][j] < min_weight:
                min_weight = graph[i][j]
                v,w = i,j
    return v,w
            
def min_span(graph):
    con = [0]
    n = len(graph)
    tree = empty_tree(n)
    while len(con) < n :
        i ,j  = min_extension(con,graph,n)
        tree[i][j],tree[j][i] = graph[i][j], graph[j][i]
        con += [j]
    return tree

def find_weight_of_edges(graph):
    tree = min_span(graph)
    lst = []
    lst1 = []
    x = 0
    for i in tree:
        lst += i 
    for i in lst:
        if i not in lst1:
            lst1.append(i)
            x += i
    return x

graph = [[0,1,0,0,0,0,0,0,0],
         [1,0,3,4,0,3,0,0,0],
         [0,3,0,0,0,4,0,0,0],
         [0,4,0,0,2,9,1,0,0],
         [0,0,0,2,0,6,0,0,0],
         [0,3,4,9,6,0,0,0,6],
         [0,0,0,1,0,0,0,2,8],
         [0,0,0,0,0,0,2,0,3],
         [0,0,0,0,0,6,8,3,0]]
graph1 = [[0,3,5,0,0,6],
          [3,0,4,1,0,0],
          [5,4,0,4,5,2],
          [0,1,4,0,6,0],
          [0,0,5,6,0,8],
          [6,0,2,0,8,0]]
print(min_span(graph1))
print("Total weight of the tree is: " + str(find_weight_of_edges(graph1)))