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bellman_ford.py
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bellman_ford.py
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# Bellman Ford Algorithm
from sys import maxsize as inf
def bell_ford(graph, start):
distances = {}
prev = {}
negative = False
for v in graph:
prev[v] = None
if v == start:
distances[v] = 0
else:
distances[v] = inf
for _ in range(0, len(graph) - 1):
for u in graph:
for v,w in graph[u]:
if distances[u] != inf:
if (distances[u] + w) < distances[v]:
distances[v] = distances[u] + w
prev[v] = u
#checking for negative, if is true, set the new distance as INFINITY
# for _ in range(0, len(graph) - 1):
for u in graph:
for v, w in graph[u]:
if (distances[u] + w) < distances[v]:
print("há negativo")
negative = True
# distances[u] = inf
# negative = True // in case of negative cycles
# do something if there is a negative cycle
return distances,prev,negative
# return the shortest path between 2 nodes
# if there is no path, return []
def bell_ford_between(graph, start, end):
d, prev, neg = bell_ford(graph, start)
path = []
for u in graph:
if u == end:
u = end
while prev[u] and neg == False: #SE PRECISAR para parar quando há negativo
# while prev[u]:
path.insert(0,u) #insert on top of the stack
u = prev[u]
path.insert(0,u)
return path if len(path) >= 2 else []
def bell_ford222C(graph, start):
distances = {x:inf for x in graph.keys()}
distances[start] = 0
negative = False
for _ in range(0, len(graph) - 1):
for u in graph:
for v in graph[u]:
w = graph[u][v]
if (distances[u] + w) < distances[v]:
distances[v] = distances[u] + w
for u in graph:
for v in graph[u]:
w = graph[u][v]
if (distances[u] + w) < distances[v]:
negative = True
return negative
# graph = {
# '1': [('3',6),('4',3)],
# '2': [('1',3)],
# '3': [('4',2)],
# '4': [('3',1),('2',1)],
# '5': [('2',4),('4',2)]
# }
# graph = {
# 'S': [('E',8),('A',10)],
# 'A': [('C',2)],
# 'B': [('A',1)],
# 'C': [('B',-2)],
# 'D': [('C',-1),('A',-4)],
# 'E': [('D',1)]
# }
# graph = {
# 'A': [('B',4),('C',2)],
# 'B': [('C',3),('D',2),('E',3)],
# 'C': [('B',1),('D',4),('E',5)],
# 'D': [],
# 'E': [('D',-5)]
# }
# Nesse aqui há ciclo negativo
# graph = {
# '0': [('1',5),('2',4)],
# '1': [('3',3)],
# '2': [('1',-6)],
# '3': [('2',2)]
# }
# graph = {
# '0': [('1',5),('2',2)],
# '1': [('3',4),('1',3)],
# '2': [('3',6)],
# '3': [('0',-1)]
# }
graph = {
'S': [('A',5),('C',-2)],
'A': [('B',1)],
'B': [('C',2),('D',7),('t',3)],
'C': [('A',2),('D',3)],
'D': [('t',10)],
't': []
}
print(bell_ford_between(graph,'S','D'))