def mst_kruskal(graph):
# Kruskal's algorithm explanation https://www.youtube.com/watch?v=71UQH7Pr9kU
mst = Graph(False)
min_edge_heap = [
] # use as priority queue to select and edge with minimum weight
# 1. Sort the edges in ascending order of weights
for edge in graph.get_edges():
heapq.heappush(min_edge_heap, edge)
input_graph_num_vertices = len(graph.get_vertices())
# 2. Keep adding edges until MST will reach all vertices
while (len(min_edge_heap) > 0) and (len(mst.get_vertices()) <
input_graph_num_vertices):
# 3. Select an edge with minimum weight (greedy algorithm)
min_edge = heapq.heappop(min_edge_heap)
start_vertex = min_edge.get_start_vertex()
end_vertex = min_edge.get_end_vertex()
# 4. Add edge in MST and check if it form a cycle then remove edge, otherwise leave it in MST
mst.add_vertex(start_vertex.get_label())
mst.add_vertex(end_vertex.get_label())
start_label = start_vertex.get_label()
end_label = end_vertex.get_label()
weight = min_edge.get_weight()
mst.add_edge(start_label, end_label, weight)
if has_cycle(mst):
mst.remove_edge(start_label, end_label, weight)
return mst
def mst_prim(graph):
# Prim's algorithm explanation https://www.youtube.com/watch?v=cplfcGZmX7I
# This algorithm return list of edges, so if we have edges we may recreate MST
mst = Graph(False)
min_edge_heap = []
visited_vertices = set()
# 1. Choose arbitary vertex from which MST algorithm start looking for edges
arbitary_vertex = next(iter(graph.get_vertices()))
visited_vertices.add(arbitary_vertex)
mst.add_vertex(arbitary_vertex)
# 2. Find all adjacent edges of arbitary vertex and add them to heap
for edge in graph.get_vertex(arbitary_vertex).get_outbound_edges():
heapq.heappush(min_edge_heap, edge)
input_graph_num_vertices = len(graph.get_vertices())
while len(mst.get_vertices()) < input_graph_num_vertices:
# 3. Select an edge with minimum weight (greedy algorithm)
while True:
min_edge = heapq.heappop(min_edge_heap)
min_vertex = min_edge.get_end_vertex()
min_vertex_label = min_vertex.get_label()
if min_vertex_label not in visited_vertices:
break
# 4. Mark selected vertex as visited and add selected edge to MST
visited_vertices.add(min_vertex_label)
mst.add_vertex(min_vertex_label)
mst.add_edge(min_edge.get_start_vertex().get_label(),
min_edge.get_end_vertex().get_label(), min_edge.get_weight())
# 4. Find all adjacent edges of min vertex and add them to heap
for edge in min_vertex.get_outbound_edges():
heapq.heappush(min_edge_heap, edge)
return mst