原理解析、私のGitHubのを参照してください。
https://github.com/youhengchan/Yen-Bellman-Ford/blob/master/group2_ppt_yen.pdf
テストデータ：
オリジナルのアルゴリズム：
擬似コード：
実装：
import time
graph_size = 10
counter = 0
class Edge:
def __init__(self, u, v, w):
self.u = u
self.v = v
self.w = w
def recursive_print(dis, pre):
global graph_size
def print_helper(index, destination):
if pre[index] == index:
print("Route : {} -> ".format(index), end="")
return
print_helper(pre[index], destination)
if index == destination:
print("{} Distance = {}".format(destination, dis[destination]), end="")
else:
print("{} -> ".format(index), end="")
for i in range(graph_size):
if pre[i] == i:
print("Route : {} Distance = 0".format(i), end="")
else:
print_helper(i, i)
print("")
def bellman_ford(edges, source):
global graph_size, counter
begin = time.perf_counter()
dis = [] # distance from source to the node
pre = [] # predecessor of node
error = False
for i in range(graph_size):
dis.append(float('inf'))
pre.append(i)
dis[source] = 0
# Initialize the graph
for i in range(graph_size - 1): # |V| - 1 times
counter += 1
# change = False
for edge in edges:
if dis[edge.u] != float("inf") and dis[edge.v] > (dis[edge.u] + edge.w):
dis[edge.v] = dis[edge.u] + edge.w
pre[edge.v] = edge.u
# change = True
# if not change:
# break
# check for the negative-weight cycle
for edge in edges:
if (dis[edge.u] + edge.w) < dis[edge.v]:
print("dis[{}] ({}) < dis[{}] ({}) + {}".format(edge.u, dis[edge.u], edge.v, dis[edge.v], edge.w))
error = True
end = time.perf_counter()
return error, dis, pre, end-begin
def main():
global counter
edges = []
edges.append(Edge(0, 9, 9))
edges.append(Edge(0, 2, 3))
edges.append(Edge(0, 5, 5))
edges.append(Edge(7, 9, 2))
edges.append(Edge(7, 3, 0))
edges.append(Edge(2, 7, 1))
edges.append(Edge(9, 4, 3))
edges.append(Edge(3, 4, 2))
edges.append(Edge(3, 8, 1))
edges.append(Edge(8, 2, 8))
edges.append(Edge(8, 6, 2))
edges.append(Edge(4, 8, -8))
edges.append(Edge(6, 1, 0))
edges.append(Edge(5, 1, 2))
edges.append(Edge(1, 4, 9))
err, dis, pre, time_consumption = bellman_ford(edges, 0)
if err:
print("Negative-weight cycle exist")
else:
print("Time consumption = ", time_consumption)
recursive_print(dis, pre)
print("Counter = ", counter)
if __name__ == "__main__":
main()結果：
円高の最適化：
擬似コード：
実装：
import time
graph_size = 10
counter = 0
class Edge:
def __init__(self, u, v, w):
self.u = u
self.v = v
self.w = w
def recursive_print(dis, pre):
global graph_size
def print_helper(index, destination):
if pre[index] == index:
print("Route : {} -> ".format(index), end="")
return
print_helper(pre[index], destination)
if index == destination:
print("{} Distance = {}".format(destination, dis[destination]), end="")
else:
print("{} -> ".format(index), end="")
for i in range(graph_size):
if pre[i] == i:
print("Route : {} Distance = 0".format(i), end="")
else:
print_helper(i, i)
print("")
def yen_bellman_ford(edges, edge_plus, edge_minus, source):
begin = time.perf_counter()
global graph_size, counter
dis = [] # distance from source to the node
pre = [] # predecessor of node
error = False
for i in range(graph_size):
dis.append(float('inf'))
pre.append(i)
dis[source] = 0
# Initialize the graph
for i in range(graph_size - 1): # |V| - 1 times
counter += 1
change = False
for edge in edge_plus:
if dis[edge.u] != float("inf") and dis[edge.v] > (dis[edge.u] + edge.w):
dis[edge.v] = dis[edge.u] + edge.w
pre[edge.v] = edge.u
change = True
for edge in edge_minus:
if dis[edge.u] != float("inf") and dis[edge.v] > (dis[edge.u] + edge.w):
dis[edge.v] = dis[edge.u] + edge.w
pre[edge.v] = edge.u
change = True
if not change:
break
# check for the negative-weight cycle
for edge in edges:
if (dis[edge.u] + edge.w) < dis[edge.v]:
print("dis[{}] ({}) < dis[{}] ({}) + {}".format(edge.u, dis[edge.u], edge.v, dis[edge.v], edge.w))
error = True
end = time.perf_counter()
return error, dis, pre, end-begin
def main():
edges = []
edge_plus = []
edge_minus = []
edge_plus.append(Edge(0, 2, 3))
edge_plus.append(Edge(0, 5, 5))
edge_plus.append(Edge(0, 9, 9))
edge_plus.append(Edge(1, 4, 9))
edge_plus.append(Edge(2, 7, 1))
edge_plus.append(Edge(3, 4, 2))
edge_plus.append(Edge(3, 8, 1))
edge_plus.append(Edge(4, 5, 0))
edge_plus.append(Edge(4, 8, -8))
edge_plus.append(Edge(7, 9, 2))
edge_minus.append(Edge(9, 4, 3))
edge_minus.append(Edge(8, 6, 2))
edge_minus.append(Edge(8, 2, 8))
edge_minus.append(Edge(7, 3, 0))
edge_minus.append(Edge(6, 1, 0))
edge_minus.append(Edge(5, 1, 2))
edges.extend(edge_minus)
edges.extend(edge_plus)
err, dis, pre, time_consumption = yen_bellman_ford(edges, edge_plus, edge_minus, 0)
if err:
print("Negative-weight cycle exist")
else:
print("Time consumption = ", time_consumption)
recursive_print(dis, pre)
print("Counter = ", counter)
if __name__ == "__main__":
main()結果：
