<｜begin▁of▁sentence｜>### Instruction:
Given a list of strings ['can', 'canine', 'candy', 'cat', 'cats'], how would you generate a directed prefix tree to represent the prefix structure of these strings, and how would you recover the original strings from the tree?
### Response:
import networkx as nx

# List of paths, which could be strings or lists of integers
paths = ['can', 'canine', 'candy', 'cat', 'cats']

# Create a directed prefix tree from the list of paths
T = nx.prefix_tree(paths)

# Print the edges of the prefix tree
print(list(T.edges()))

# Find the leaf nodes, i.e., the predecessors of the nil node
NIL = -1
leaf_nodes = list(T.predecessors(NIL))
print('Leaf nodes:', leaf_nodes)

# Recover the original paths from the prefix tree
root = 0
recovered = []
for v in leaf_nodes:
    prefix = ''
    while v != root:
        prefix = str(T.nodes[v]['source']) + prefix
        v = next(T.predecessors(v))  # only one predecessor
    recovered.append(prefix)

print('Recovered paths:', sorted(recovered))
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