def dijkstra(graph, source): '''Apply the Dijkstra algorithm and return the a list where each position represents a vertice and its content represents the predecessor''' vertices = [] #list of vertices Q = PriorityQueue() #priority queue #fills 'vertices' and 'Q', each vertex receive the distance iquals infinity for v in range(len(graph)): vertices.append(Vertex(v)) Q.add_with_priority(v, vertices[v].dist) #the source vertex receive the distance zero vertices[source] = Vertex(num=source, dist=0) Q.decrease_priority(source, 0) while len(Q) != 0: u = Q.extract_min() for neighbor in get_adjacent(graph, u.num): alt = graph[u.num][neighbor] + u.dist Alt = Vertex(neighbor, alt) if vertices[neighbor].greater_than(Alt): vertices[neighbor].dist = alt vertices[neighbor].prev = u.num Q.decrease_priority(neighbor, alt) return [v.prev for v in vertices]
def prim(G, r=0):
keys = {}
parents = {}
adj_matrix = G.get_adj_matrix()
for i in range(G.get_len()):
keys[i] = INFINITY
parents[i] = None
keys[r] = 0
array = [[keys[v], v] for v in range(G.get_len())]
Q = PriorityQueue(array)
while not Q.is_empty():
u = Q.extract_min() # u = array di 2 valori [chiave, nodo]
for v in range(
G.get_len()): # per ogni nodo nella lista delle adiacenze di u
# se u è in Q e il valore del nodo è minore di quello della chiave corrente e non è un cappio (elemento
# della diagonale)
if Q.is_there_element(
v) and adj_matrix[u[1]][v] < keys[v] and u != v:
old_val = keys[
v] # salvo il vecchio valore (serve per decrease_key)
keys[v] = adj_matrix[u[1]][v] # aggiorno il nuovo valore
parents[v] = u[1] # modifico il genitore del nodo
Q.decrease_key(
v, old_val, keys[v]
) # decrem valore nell'albero per poi estrarre il minimo al prox giro
return get_prim_result(G, [(v, parents[v])
for v in range(G.get_len()) if v != r])
def get_MST(connections, n):
if n <= 1:
return []
graph = defaultdict(set)
pq = PriorityQueue()
INT_MAX = 2**32 - 1
map = dict()
result = []
for u, v, w in connections:
graph[u].add((v, w))
graph[v].add((u, w))
if not pq.find(u):
pq.insert(u, INT_MAX)
if not pq.find(v):
pq.insert(v, INT_MAX)
pq.update_priority(connections[0][0], 0)
while pq.size() > 0:
curr_node = pq.extract_min()
if curr_node in map:
result.append(map[curr_node])
del map[curr_node]
for nhbr in graph[curr_node]:
node = nhbr[0]
if pq.find(node):
if pq.get_priority(node) > nhbr[1]:
pq.update_priority(node, nhbr[1])
map[node] = [curr_node, node]
if len(result) == n - 1:
return result
else:
return -1