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}
def installer(graph: Graph, root: Graph.Vertex):
"""
Install the software on the minimum number of vertices so that for every pair of vertices,
at least one of them has the software.
Return a 2 elements tuple composed by the number of vertices on which the software is
installed and a list of such vertices
"""
if not graph.degree(root): # Base Case single vertex tree
return (1, [root])
# Start iteration
return install(graph, root, None, {}, [])