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# -*- coding: utf-8 -*-
# Copyright (C) 2012 by
# Sergio Nery Simoes <sergionery@gmail.com>
# All rights reserved.
# BSD license.
import networkx as nx
__author__ = """\n""".join(['Sérgio Nery Simões <sergionery@gmail.com>',
'Aric Hagberg <aric.hagberg@gmail.com>'])
__all__ = ['all_simple_paths']
def all_simple_paths(G, source, target, cutoff=None):
"""Generate all simple paths in the graph G from source to target.
A simple path is a path with no repeated nodes.
Parameters
----------
G : NetworkX graph
source : node
Starting node for path
target : node
Ending node for path
cutoff : integer, optional
Depth to stop the search. Only paths of length <= cutoff are returned.
Returns
-------
path_generator: generator
A generator that produces lists of simple paths. If there are no paths
between the source and target within the given cutoff the generator
produces no output.
Examples
--------
>>> G = nx.complete_graph(4)
>>> for path in nx.all_simple_paths(G, source=0, target=3):
... print(path)
...
[0, 1, 2, 3]
[0, 1, 3]
[0, 2, 1, 3]
[0, 2, 3]
[0, 3]
>>> paths = nx.all_simple_paths(G, source=0, target=3, cutoff=2)
>>> print(list(paths))
[[0, 1, 3], [0, 2, 3], [0, 3]]
Notes
-----
This algorithm uses a modified depth-first search to generate the
paths [1]_. A single path can be found in `O(V+E)` time but the
number of simple paths in a graph can be very large, e.g. `O(n!)` in
the complete graph of order n.
References
----------
.. [1] R. Sedgewick, "Algorithms in C, Part 5: Graph Algorithms",
Addison Wesley Professional, 3rd ed., 2001.
See Also
--------
all_shortest_paths, shortest_path
"""
if source not in G:
raise nx.NetworkXError('source node %s not in graph'%source)
if target not in G:
raise nx.NetworkXError('target node %s not in graph'%target)
if cutoff is None:
cutoff = len(G)-1
if G.is_multigraph():
return _all_simple_paths_multigraph(G, source, target, cutoff=cutoff)
else:
return _all_simple_paths_graph(G, source, target, cutoff=cutoff)
def _all_simple_paths_graph(G, source, target, cutoff=None):
if cutoff < 1:
return
visited = [source]
stack = [iter(G[source])]
while stack:
children = stack[-1]
child = next(children, None)
if child is None:
stack.pop()
visited.pop()
elif len(visited) < cutoff:
if child == target:
yield visited + [target]
elif child not in visited:
visited.append(child)
stack.append(iter(G[child]))
else: #len(visited) == cutoff:
if child == target or target in children:
yield visited + [target]
stack.pop()
visited.pop()
def _all_simple_paths_multigraph(G, source, target, cutoff=None):
if cutoff < 1:
return
visited = [source]
stack = [(v for u,v in G.edges(source))]
while stack:
children = stack[-1]
child = next(children, None)
if child is None:
stack.pop()
visited.pop()
elif len(visited) < cutoff:
if child == target:
yield visited + [target]
elif child not in visited:
visited.append(child)
stack.append((v for u,v in G.edges(child)))
else: #len(visited) == cutoff:
count = ([child]+list(children)).count(target)
for i in range(count):
yield visited + [target]
stack.pop()
visited.pop()
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