def a_star_search(start, goal, heuristics=None):
visited = []
frontier = PriorityQueue()
start.set_dist_from_start(0)
if heuristics is None:
h_dist = 0
else:
h_dist = heuristics.get((start.getName(), goal.getName()), 0)
frontier.insertItem(
h_dist, start) #key should be the sum of distance from start and h()
#implement the algorithm
while not frontier.isEmpty():
#start your code here ...
if heuristics is None:
h_dist2 = 0
else:
h_dist2 = heuristics.get(
(frontier.queue[0][1].getName(), goal.getName()), 0)
#update the distance from start in the node
frontier.queue[0][1].set_dist_from_start((frontier.minKey() - h_dist2))
v = frontier.removeMin() #return the 1st node in the priority queue
visited.append(v)
if v.getName() == goal.getName():
#Include this line before returning the path (when the goal is found)
print("\nThe total number of nodes visited:", len(visited))
return retrieve_path(v, start)
else:
neighbors = v.getNeighbors()
for (item, diskey) in neighbors:
if not (item in visited):
if heuristics is None:
h_dist3 = 0
else:
h_dist3 = heuristics.get(
(item.getName(), goal.getName()), 0)
dist = diskey + v.get_dist_from_start() + h_dist3
if not (frontier.contains(item)):
frontier.insertItem(dist, item)
item.setParent(v)
else:
for tup in frontier.queue:
if tup[1] == item:
if dist < tup[0]:
frontier.update(dist, item)
tup[1].setParent(v)
def prims_algorithm_mst(graph):
"""
Prim's algorithm, this algorithm
has the same time complexity as Djikstra's
single source shorted path algorithm.
This particular algorithm is
O((V ** 2) + (V * E))
but with a priority queue or vEB tree this can be reduced
to
O((V * log(V)) + (V * E))
a time complexity equivalent to Djikstra's
"""
if not isinstance(graph, Graph):
raise TypeError('this function expects an instance of Graph')
queue = PriorityQueue(graph)
root = None
nodes = {u: TreeNode(u) for u in graph.vertices}
while not queue.is_empty():
u = queue.pop_min()
if root is None:
root = nodes[u]
for v in graph.adj[u]:
if queue.contains(v):
queue.update(v, graph.weights[(u, v)])
nodes[v].parent = nodes[u]
for n in nodes:
node = nodes[n]
if node.parent is not None:
node.parent.children.append(node)
return root