def shortest_paths(graph, start):
# Dijkstra's algorithm for single source shortest paths
# O(|V| log |V| + |E| log |V|)
paths = {node: None for node in graph}
distances = {node: float('inf') for node in graph}
distances[start] = 0
pq = PriorityQueue()
for node in graph:
if node == start:
pq.put(node, 0)
else:
pq.put(node, float('inf'))
while not pq.is_empty():
node, distance = pq.get()
for neighbour, edge_cost in graph[node]:
new_cost = distance + edge_cost
if new_cost < distances[neighbour]:
distances[neighbour] = new_cost
paths[neighbour] = node
pq.update(neighbour, new_cost)
return paths, distances
def shortest_paths(graph, start):
# Dijkstra's algorithm for single source shortest paths
# O(|V| log |V| + |E| log |V|)
paths = {node: None for node in graph}
distances = {node: float("inf") for node in graph}
distances[start] = 0
pq = PriorityQueue()
for node in graph:
if node == start:
pq.put(node, 0)
else:
pq.put(node, float("inf"))
while not pq.is_empty():
node, distance = pq.get()
for neighbour, edge_cost in graph[node]:
new_cost = distance + edge_cost
if new_cost < distances[neighbour]:
distances[neighbour] = new_cost
paths[neighbour] = node
pq.update(neighbour, new_cost)
return paths, distances
