/usr/share/pyshared/enthought/util/graph.py is in python-enthoughtbase 3.1.0-2build1.
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#
# Copyright (c) 2005, Enthought, Inc.
# All rights reserved.
#
# This software is provided without warranty under the terms of the BSD
# license included in enthought/LICENSE.txt and may be redistributed only
# under the conditions described in the aforementioned license. The license
# is also available online at http://www.enthought.com/licenses/BSD.txt
# Thanks for using Enthought open source!
#
# Author: Enthought, Inc.
# Description: <Enthought util package component>
#
#-----------------------------------------------------------------------------
""" Graph algorithms.
A graph is represented by a dictionary which represents the adjacency relation,
where node ``a`` has an arc to node ``b`` if and only if ``b in d[a]``.
"""
import __builtin__
from itertools import chain
from enthought.util.cbook import flatten
from enthought.util.dict import map_items, map_values
class CyclicGraph(Exception):
"""
Exception for cyclic graphs.
"""
def __init__(self):
Exception.__init__(self, "Graph is cyclic")
def topological_sort(graph):
"""
Returns the nodes in the graph in topological order.
"""
discovered = {}
explored = {}
order = []
def explore(node):
children = graph.get(node, [])
for child in children:
if child in explored:
pass
elif child in discovered:
raise CyclicGraph()
else:
discovered[child] = 1
explore(child)
explored[node] = 1
order.append(node)
for node in graph.keys():
if node not in explored:
explore(node)
order.reverse()
return order
def closure(graph, sorted=True):
"""
Returns the transitive closure of the graph.
If sorted is True then the successor nodes will
be sorted into topological order.
"""
order = topological_sort(graph)
# Map nodes to their index in the topologically sorted list for later use.
idxorder = {}
for i, obj in enumerate(order):
idxorder[obj] = i
reachable = {}
for i in range(len(order)-1, -1, -1):
node = order[i]
# We are going through in reverse topological order so we
# are guaranteed that all of the children of the node
# are already in reachable
# We are using dicts to emulate sets for speed in Python 2.3.
node_reachable = {}
for child in graph.get(node, []):
node_reachable[child] = 1
node_reachable.update(reachable[child])
reachable[node] = node_reachable
# Now, build the return graph by doing a topological sort of
# each reachable set, if required
retval = {}
for node, node_reachable in reachable.items():
if not sorted:
retval[node] = node_reachable.keys()
else:
# Create a tuple list so the faster built-in sort
# comparator can be used.
tmp = []
reachable_list = node_reachable.keys()
for n in reachable_list:
tmp.append((idxorder[n], n))
tmp.sort()
reachable_list = [x[1] for x in tmp]
retval[node] = reachable_list
return retval
def reverse(graph):
"""
Returns the reverse of a graph, that is the graph made when all
of the edges are reversed.
"""
retval = {}
for node, successors in graph.items():
# Make sure we keep isolated nodes, too.
if node not in retval:
retval[node] = []
for s in successors:
retval.setdefault(s, []).append(node)
return retval
def map(f, graph):
''' Maps function f over the nodes in graph.
>>> map(str, { 1:[2,3] })
{'1': ['2', '3']}
'''
return map_items(lambda k,v: (f(k), __builtin__.map(f,v)), graph)
# FIXME Implement graphs with sets of values instead of lists of values
def eq(g1, g2):
return map_values(set, g1) == map_values(set, g2)
def reachable_graph(graph, nodes):
''' Return the subgraph of the given graph reachable from the given nodes.
>>> reachable_graph({'a':'bc', 'b':'c' }, 'a')
{'a': 'bc', 'b': 'c'}
>>> reachable_graph({'a':'bc', 'b':'c' }, 'b')
{'b': 'c'}
>>> reachable_graph({'a':'bc', 'b':'c' }, 'c')
{}
'''
ret = {}
closed = closure(graph)
for n in chain(nodes, flatten([ closed[n] for n in nodes ])):
if n in graph.keys():
ret[n] = graph[n]
return ret
if __name__ == "__main__":
g = {1:[2,3],
2:[3,4],
6:[3],
4:[6]}
print topological_sort(g)
print closure(g)
#### EOF ######################################################################
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