Please complete questions (3), (4), and (5) in the screenshot provided into the code given in the other screenshot. Given below is the implementations of dijkstras and bellman ford already completed. Python 3.10 or later def bellman_ford(self,s) : """Bellman Ford Algorithm for single source shortest path. Keyword Arguments: s - The source vertex. """ distances = {v: float('inf') for v in self.adjacency_list} distances[s] = 0 parents = {v: None for v in self.adjacency_list} for _ in range(len(self.adjacency_list) - 1): for from_vertex in self.adjacency_list: for to_vertex in self.adjacency_list[from_vertex]: if distances[from_vertex] + self.weights[(from_vertex, to_vertex)] < distances[to_vertex]: distances[to_vertex] = distances[from_vertex] + self.weights[(from_vertex, to_vertex)] parents[to_vertex] = from_vertex for from_vertex in self.adjacency_list: for to_vertex in self.adjacency_list[from_vertex]: if distances[from_vertex] + self.weights[(from_vertex, to_vertex)] < distances[to_vertex]: # Negative cycle found, return empty list return [] # No negative cycles found, return list of 3-tuples return [(v, distances[v], parents[v]) for v in distances] def dijkstra(self,s) : """Dijkstra's Algorithm using a binary heap as the PQ. Keyword Arguments: s - The source vertex. """ distance = [math.inf for x in self._adj] parent = [None for x in self._adj] Q = PQ() distance[s] = 0 Q.add(s, 0) S = [] for u in range(len(self._adj)): if u != s: Q.add(u, math.inf) while not Q.is_empty(): u = Q.extract_min() S.append(u) for v, w in self._adj[u].__iter__(True): if (distance[u] + w) < distance[v]: parent[v] = u distance[v] = (distance[u] + w) returnlist = [] for v in S: returnlist.append((v, distance[v], parent[v])) return returnlist
Please complete questions (3), (4), and (5) in the screenshot provided into the code given in the other screenshot. Given below is the implementations of dijkstras and bellman ford already completed. Python 3.10 or later
def bellman_ford(self,s) :
"""Bellman Ford
Keyword Arguments:
s - The source vertex.
"""
distances = {v: float('inf') for v in self.adjacency_list}
distances[s] = 0
parents = {v: None for v in self.adjacency_list}
for _ in range(len(self.adjacency_list) - 1):
for from_vertex in self.adjacency_list:
for to_vertex in self.adjacency_list[from_vertex]:
if distances[from_vertex] + self.weights[(from_vertex, to_vertex)] < distances[to_vertex]:
distances[to_vertex] = distances[from_vertex] + self.weights[(from_vertex, to_vertex)]
parents[to_vertex] = from_vertex
for from_vertex in self.adjacency_list:
for to_vertex in self.adjacency_list[from_vertex]:
if distances[from_vertex] + self.weights[(from_vertex, to_vertex)] < distances[to_vertex]:
# Negative cycle found, return empty list
return []
# No negative cycles found, return list of 3-tuples
return [(v, distances[v], parents[v]) for v in distances]
def dijkstra(self,s) :
"""Dijkstra's Algorithm using a binary heap as the PQ.
Keyword Arguments:
s - The source vertex.
"""
distance = [math.inf for x in self._adj]
parent = [None for x in self._adj]
Q = PQ()
distance[s] = 0
Q.add(s, 0)
S = []
for u in range(len(self._adj)):
if u != s:
Q.add(u, math.inf)
while not Q.is_empty():
u = Q.extract_min()
S.append(u)
for v, w in self._adj[u].__iter__(True):
if (distance[u] + w) < distance[v]:
parent[v] = u
distance[v] = (distance[u] + w)
returnlist = []
for v in S:
returnlist.append((v, distance[v], parent[v]))
return returnlist
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