def steiner_tree(graph):
leaf_nodes = graph.find_non_terminal_leaves()
# Get a copy of the graph edges
# we are going to delete edges from this dictionary (by setting their value to an empty list)
new_edges = graph.edges.copy()
# Same with the nodes
new_nodes = graph.nodes.copy()
# For all non-terminal leaves in the MST
for leaf in leaf_nodes:
node_num = leaf[0]
edge_num = list(leaf[1].values())[0]
leaf_edge = graph.edges[edge_num]
# Second node connected to the edge
second_node = leaf_edge[0] if leaf_edge[
1] == node_num else leaf_edge[1]
# Setting the value of the chosen edge and node to [] (as if we have deleted it)
new_edges[edge_num] = []
new_nodes[node_num] = []
# Update the second node's degree and edges dictionary
graph.nodes[second_node][0] -= 1
graph.nodes[second_node][1].pop(node_num)
# Checking if the remaining node is a leaf and not a terminal
while graph.nodes[second_node][2] == 0 and graph.nodes[
second_node][0] == 1:
node_num = second_node
node_edges = graph.nodes[second_node][1]
edge_num = list(node_edges.values())[0]
leaf_edge = graph.edges[edge_num]
second_node = leaf_edge[0] if leaf_edge[
1] == node_num else leaf_edge[1]
new_edges[edge_num] = []
new_nodes[node_num] = []
graph.nodes[second_node][0] -= 1
graph.nodes[second_node][1].pop(node_num)
# Making new dictionaries of the updated nodes and edges to make a graph from them
new_graph_nodes = {k: v[2] for k, v in new_nodes.items() if v != []}
edge_number = 1
new_graph_edges = {}
for k, v in new_edges.items():
if v:
new_graph_edges[edge_number] = v
edge_number += 1
steiner_tree = Graph(len(new_graph_nodes), len(new_graph_edges),
new_graph_nodes, new_graph_edges)
return steiner_tree, steiner_tree.graph_weight()
def kruskal_algorithm(graph):
union_find = UnionFind(graph.number_of_nodes)
sorted_edges_list = graph.sort_edges()
mst_nodes = {}
mst_edges = {}
edge_number = 1
for edge in sorted_edges_list:
first_node = graph.edges[edge[0]][0]
second_node = graph.edges[edge[0]][1]
weight = edge[1]
result = union_find.union(first_node - 1, second_node - 1)
# The nodes were in different sets and union was successful, update the graph
if result == 1:
# Adding the nodes to the MST, also setting their terminal status
mst_nodes[first_node] = graph.nodes[first_node][2]
mst_nodes[second_node] = graph.nodes[second_node][2]
# Adding the edge to the MST
mst_edges[edge_number] = [first_node, second_node, weight]
edge_number += 1
minimum_spanning_tree = Graph(len(mst_nodes), len(mst_edges),
mst_nodes, mst_edges)
return minimum_spanning_tree, minimum_spanning_tree.graph_weight()
