[英]Directed, weighted balanced tree import and shortest path in networkx
I have a balanced tree with branching factor 2 and height 100, and each edge has a weight given by a text file that looks like: 我有一个平衡的树,分支因子2和高度100,每个边都有一个由文本文件给出的权重,如下所示:
73 41
52 40 09
26 53 06 34
etc etc until row nr 99
ie: The edge weight from node 0 to 1 is 73, from 0 to 2 is 41, and from 1 to 3 is 52, etc. 即:从节点0到1的边缘权重是73,从0到2是41,从1到3是52,等等。
I wish to find the shortest path (with the corresponding edge weight sum) from the root to the end of the tree. 我希望找到从树的根到末尾的最短路径(具有相应的边权重和)。 As far as I understand, this can be done by multiplying all edge weights by -1 and using the Dijkstra algorithm in Networkx.
据我所知,这可以通过将所有边权重乘以-1并使用Networkx中的Dijkstra算法来完成。
( PS: This is Project Euler Problem 67 , finding the maximum sum in a triangle of numbers. I have solved the question with recursion with memoization, but I want to try and solve it with the Networkx package. ) ( PS:这是项目欧拉问题67 ,找到数字三角形的最大总和。我已经通过memoization递归解决了问题,但我想尝试用Networkx包解决它。 )
Is the algorithm choice correct?
算法选择是否正确?
Yes. 是。 You can use positive weights, and call nx.dijkstra_predecessor_and_distance to get the shortest paths starting from the root node,
0
. 您可以使用正权重,并调用nx.dijkstra_predecessor_and_distance以获取从根节点
0
开始的最短路径。
How do I "easily" import this data set into a Networkx graph object?
如何“轻松”将此数据集导入Networkx图形对象?
import networkx as nx
import matplotlib.pyplot as plt
def flatline(iterable):
for line in iterable:
for val in line.split():
yield float(val)
with open(filename, 'r') as f:
G = nx.balanced_tree(r = 2, h = 100, create_using = nx.DiGraph())
for (a, b), val in zip(G.edges(), flatline(f)):
G[a][b]['weight'] = val
# print(G.edges(data = True))
pred, distance = nx.dijkstra_predecessor_and_distance(G, 0)
# Find leaf whose distance from `0` is smallest
min_dist, leaf = min((distance[node], node)
for node, degree in G.out_degree_iter()
if degree == 0)
nx.draw(G)
plt.show()
I'm not sure I quite understand the input format. 我不确定我是否完全理解输入格式。 But something similar to this should work:
但类似的东西应该工作:
from itertools import count
import networkx as nx
adj ="""73 41
52 40 09
26 53 06 34"""
G = nx.Graph()
target = 0
for source,line in zip(count(),adj.split('\n')):
for weight in line.split():
target += 1
print source,target,weight
G.add_edge(source,target,weight=float(weight))
# now call shortest path with weight="weight" and source=0
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