Question

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:

 73 41
 52 40 09
 26 53 06 34
 etc etc until row nr 99

i.e: The edge weight from node 0 to 1 is 73, from 0 to 2 is 41, and from 1 to 3 is 52, etc.

I wish to find the shortest path (with the corresponding edge weight sum) from the root to the end of the tree. As far as I understand, this can be done by multiplying all edge weights by -1 and using the Dijkstra algorithm in Networkx.

1. Is the algorithm choice correct?
2. How do I “easily” import this data set into a Networkx graph object?

(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.)

Answer 1

Is the algorithm choice correct?

Yes. You can use positive weights, and call nx.dijkstra_predecessor_and_distance to get the shortest paths starting from the root node, 0.

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How do I “easily” import this data set into a Networkx graph object?

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()