def dijkstra(graph, root):
vertices = graph.keys()
n = len(vertices)
# Initialize the priority queue
inf = float("inf")
pq = MinHeap([(v, inf) for v in graph.keys()])
pq.change_priority(root, 0)
# Other initializations
parent = collections.defaultdict(lambda: None)
selected = set()
cost = collections.defaultdict(lambda: inf)
cost[root] = 0
while len(selected) < n:
u = pq.min()
du = cost[u] = pq.get_priority(u)
selected.add(u)
pq.take_min()
for (v, w) in graph[u].items():
if v not in selected and pq.get_priority(v) > du + w:
pq.change_priority(v, du + w)
parent[v] = u
return cost, parent
def dijkstra(graph, root):
vertices = graph.keys()
n = len(vertices)
# Initialize the priority queue
inf = float("inf")
pq = MinHeap([(v, inf) for v in graph.keys()])
pq.change_priority(root, 0)
# Other initializations
parent = collections.defaultdict(lambda: None)
selected = set()
cost = collections.defaultdict(lambda: inf)
cost[root] = 0
while len(selected) < n:
u = pq.min()
du = cost[u] = pq.get_priority(u)
selected.add(u)
pq.take_min()
for (v, w) in graph[u].items():
if v not in selected and pq.get_priority(v) > du + w:
pq.change_priority(v, du + w)
parent[v] = u
return cost, parent
def prim(graph, root):
vertices = graph.keys()
n = len(vertices)
# Initialize the priority queue
inf = float("inf")
pq = MinHeap([(v, inf) for v in graph.keys()])
pq.change_priority(root, 0)
# Other initializations
parent = collections.defaultdict(lambda: None)
selected = set()
cost = 0
mst = []
while len(selected) < n:
u = pq.take_min()
selected.add(u)
for (v, w) in graph[u].items():
if not v in selected and w < pq.get_priority(v):
pq.change_priority(v, w)
parent[v] = u
pu = parent[u]
if pu != None:
mst.append( (min(u,pu), max(u,pu)) )
cost += graph[u][pu]
return cost, mst
def prim(graph, root):
vertices = graph.keys()
n = len(vertices)
# Initialize the priority queue
inf = float("inf")
pq = MinHeap([(v, inf) for v in graph.keys()])
pq.change_priority(root, 0)
# Other initializations
parent = collections.defaultdict(lambda: None)
selected = set()
cost = 0
mst = []
while len(selected) < n:
u = pq.take_min()
selected.add(u)
for (v, w) in graph[u].items():
if not v in selected and w < pq.get_priority(v):
pq.change_priority(v, w)
parent[v] = u
pu = parent[u]
if pu != None:
mst.append((min(u, pu), max(u, pu)))
cost += graph[u][pu]
return cost, mst
