def Dijkstra_algorithm(graph: Graph,
starting_node: int) -> DijkstraAlgorithmResult:
dist = [INFINITY for _ in range(graph.nodes_count)]
prev = [None for _ in range(graph.nodes_count)]
dist[starting_node] = 0
prev[starting_node] = starting_node
# prepare list of tuples of nodes labels with their starting distances
dist_nodes = [
PQNode(key=i, priority=dist[i]) for i in range(0, graph.nodes_count)
]
Q = PriorityQueue(raw=dist_nodes)
while not Q.is_empty:
# pick the closest node
fst = Q.pop().key
for e in graph.get_neighbourhood(fst):
# scan the neighbourhood
snd = e.snd
weight = e.weight
if dist[snd] > dist[fst] + weight:
# update if better route found
dist[snd] = dist[fst] + weight
prev[snd] = fst
Q.bottom_bound_flatten_priority(snd, dist[snd])
return DijkstraAlgorithmResult(dist=dist, prev=prev)
def Prim(graph: Graph) -> Iterable[GraphEdge]:
"""Returns a MST using Prim's algorithm.
"""
cost = [INFINITY for _ in range(graph.nodes_count)]
prev = [None for _ in range(graph.nodes_count)]
# take the first node as the starting node
starting_node = 0
cost[starting_node] = 0
prev[starting_node] = starting_node
# build a priority queue
cost_nodes = [
PQNode(key=i, priority=cost[i]) for i in range(0, graph.nodes_count)
]
Q = PriorityQueue(raw=cost_nodes)
while not Q.is_empty:
fst = Q.pop().key
for e in graph.get_neighbourhood(fst):
snd = e.snd
weight = graph.get_edge_weight(fst, snd, twoway=True)
if cost[snd] > weight:
cost[snd] = weight
prev[snd] = fst
Q.bottom_bound_flatten_priority(snd, cost[snd])
# render out actual graph edges using the `prev` list
mst = []
for node in range(0, graph.nodes_count):
if node == starting_node:
continue
mst.append(
GraphEdge(prev[node], node,
graph.get_edge_weight(prev[node], node, twoway=True)))
return mst
