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############################################################################## | ||
# | ||
# Copyright (c) 2022 Zope Foundation and Contributors. | ||
# All Rights Reserved. | ||
# | ||
# This software is subject to the provisions of the Zope Public License, | ||
# Version 2.1 (ZPL). A copy of the ZPL should accompany this distribution. | ||
# THIS SOFTWARE IS PROVIDED "AS IS" AND ANY AND ALL EXPRESS OR IMPLIED | ||
# WARRANTIES ARE DISCLAIMED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED | ||
# WARRANTIES OF TITLE, MERCHANTABILITY, AGAINST INFRINGEMENT, AND FITNESS | ||
# FOR A PARTICULAR PURPOSE. | ||
# | ||
############################################################################## | ||
"""Directed graph | ||
""" | ||
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from itertools import count | ||
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class DiGraph(object): | ||
"""Directed graph. | ||
A directed graph is a set of nodes together with a | ||
neighboring relation. | ||
The class makes intensive use of dicts; therefore, hashability | ||
is important. Therefore, the class usually does not work | ||
with the nodes directly but transforms them via | ||
a ``make_hashable`` function, ``id`` by default. | ||
This works well for object types where equality is identity. | ||
For other types, you may need to deactive the transformation | ||
or use a different ``make_hashable``. | ||
""" | ||
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def __init__(self, nodes=None, make_hashable=id): | ||
self._nodes = set() # transformed nodes | ||
self._neighbors = {} # node --> neighbors -- transformed | ||
if make_hashable: | ||
tr2n = {} # transform -> node | ||
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tr_node = make_hashable | ||
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def utr_node(node): | ||
return tr2n[node] | ||
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def tr_nodes(nodes): | ||
ns = set() | ||
add = ns.add | ||
for n in nodes: | ||
trn = make_hashable(n) | ||
if trn not in tr2n: | ||
tr2n[trn] = n | ||
add(trn) | ||
return ns | ||
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else: | ||
tr_nodes = lambda nodes: set(nodes) # noqa: E731 | ||
utr_node = tr_node = lambda node: node | ||
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self._transform_node = tr_node | ||
self._transform_nodes = tr_nodes | ||
self._untransform_node = utr_node | ||
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if nodes is not None: | ||
self.add_nodes(nodes) | ||
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def add_nodes(self, nodes): | ||
"""add *nodes* (iterator) to the graph's nodes.""" | ||
self._nodes |= self._transform_nodes(nodes) | ||
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def add_neighbors(self, node, neighbors, ignore_unknown=True): | ||
"""add *neighbors* (iterator) as neighbors for *node*. | ||
if *ignore_unknown*, unknown nodes in *neighbors* are | ||
ignored, otherwise a ``KeyError`` is raised. | ||
""" | ||
tr_n = self._transform_node(node) | ||
nodes = self._nodes | ||
nbad = tr_n not in nodes | ||
if nbad: | ||
if ignore_unknown: | ||
return | ||
else: | ||
raise KeyError(node) | ||
tr_neighbors = self._transform_nodes(neighbors) | ||
known_neighbors = tr_neighbors & nodes | ||
if not ignore_unknown and len(known_neighbors) != len(tr_neighbors): | ||
raise KeyError(tr_neighbors - known_neighbors) | ||
nbs = self._neighbors.get(tr_n) | ||
if nbs is None: | ||
self._neighbors[tr_n] = known_neighbors | ||
else: | ||
nbs |= known_neighbors | ||
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def nodes(self): | ||
"""iterate of the graph's nodes.""" | ||
utr = self._untransform_node | ||
for n in self._nodes: | ||
yield utr(n) | ||
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def neighbors(self, node): | ||
"""iterate over *node*'s neighbors.""" | ||
utr = self._untransform_node | ||
for n in self._neighbors.get(self._transform_node(node), ()): | ||
yield utr(n) | ||
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def sccs(self, trivial=False): | ||
"""iteratate over the strongly connected components. | ||
If *trivial*, include the trivial components; otherwise | ||
only the cycles. | ||
This is an implementation of the "Tarjan SCC" algorithm. | ||
""" | ||
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# any node is either in ``unvisited`` or in ``state`` | ||
unvisited = self._nodes.copy() | ||
state = {} # nodes -> state | ||
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ancestors = [] # the ancestors of the currently processed node | ||
stack = [] # the nodes which might still be on a cycle | ||
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# the algorithm visits each node twice in a depth first order | ||
# In the first visit, visits for the unprocessed neighbors | ||
# are scheduled as well as the second visit to this | ||
# node after all neighbors have been processed. | ||
dfs = count() # depth first search visit order | ||
rtn_marker = object() # marks second visit to ``ancestor`` top | ||
visits = [] # scheduled visits | ||
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while unvisited: | ||
node = next(iter(unvisited)) | ||
# determine the depth first spanning tree rooted in *node* | ||
visits.append(node) | ||
while visits: | ||
visit = visits[-1] # ``rtn_marker`` or node | ||
if visit is rtn_marker: | ||
# returned to the top of ``ancestors`` | ||
visits.pop() | ||
node = ancestors.pop() # returned to *node* | ||
nstate = state[node] | ||
if nstate.low == nstate.dfs: | ||
# SCC root | ||
scc = [] | ||
while True: | ||
n = stack.pop() | ||
state[n].stacked = False | ||
scc.append(n) | ||
if n is node: | ||
break | ||
if len(scc) == 1 and not trivial: | ||
# check for triviality | ||
n = scc[0] | ||
if n not in self._neighbors[n]: | ||
continue # tivial -- ignore | ||
utr = self._untransform_node | ||
yield [utr(n) for n in scc] | ||
if not ancestors: | ||
# dfs tree determined | ||
assert not visits | ||
break | ||
pstate = state[ancestors[-1]] | ||
nstate = state[node] | ||
low = nstate.low | ||
if low < pstate.low: | ||
pstate.low = low | ||
else: # scheduled first visit | ||
node = visit | ||
nstate = state.get(node) | ||
if nstate is not None: | ||
# we have already been visited | ||
if nstate.stacked: | ||
# update parent | ||
pstate = state[ancestors[-1]] | ||
if nstate.dfs < pstate.low: | ||
pstate.low = nstate.dfs | ||
visits.pop() | ||
continue | ||
unvisited.remove(node) | ||
nstate = state[node] = _TarjanState(dfs) | ||
ancestors.append(node) | ||
stack.append(node) | ||
nstate.stacked = True | ||
visits[-1] = rtn_marker # schedule return visit | ||
# schedule neighbor visits | ||
visits.extend(self._neighbors.get(node, ())) | ||
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class _TarjanState(object): | ||
"""representation of a node's processing state.""" | ||
__slots__ = "stacked dfs low".split() | ||
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def __init__(self, dfs): | ||
self.stacked = False | ||
self.dfs = self.low = next(dfs) | ||
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def __repr__(self): | ||
return "dfs=%d low=%d stacked=%s" \ | ||
% (self.dfs, self.low, self.stacked) |
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