def graph_randomize(n: int):
graph = Graph()
random = Random()
for i in range(0, n):
graph.insert_vertex(i)
for v in graph.vertices():
for u in graph.vertices():
if bool(random.getrandbits(1)) and u != v and graph.get_edge(
u, v) is None:
graph.insert_edge(u, v)
print("number of vertices " + str(graph.vertex_count()) +
"\nnumber of edges " + str(graph.edge_count()))
return graph
def bacefook_greedy_algorithm(graph: Graph):
"""
greedy algorithm to compute the minimum number of nodes
with software
map structure:
-Key store all vertices of the graph
-Value is a dict
dict structure:
-token store locator from priority queue
-so_sw_count store the number of adj nodes
-has_sw bool if the node has the software
Priority queue store all the nodes of the graph ordered by number of adj nodes
"""
priority_queue = AdaptableHeapPriorityQueue()
map = {}
for v in graph.vertices():
token = priority_queue.add(-graph.degree(v), v)
map[v] = {
'token': token,
'no_sw_count': graph.degree(v),
'has_sw': False
}
for i in range(0, graph.vertex_count()):
k, v = priority_queue.remove_min()
if graph.degree(v) == 0:
continue
if k == 0:
break
map[v]['has_sw'] = True
for e in graph.incident_edges(v):
adj_v = e.opposite(v)
if not map[adj_v]['has_sw']:
map[adj_v]['no_sw_count'] -= 1
priority_queue.update(map[adj_v]['token'],
-map[adj_v]['no_sw_count'], adj_v)
return {v._element: map[v]['has_sw'] for v in map}