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# This Source Code Form is subject to the terms of the Mozilla Public
# License, v. 2.0. If a copy of the MPL was not distributed with this
# file, You can obtain one at http://mozilla.org/MPL/2.0/.
from __future__ import absolute_import, print_function, unicode_literals
import collections
class Graph(object):
"""
Generic representation of a directed acyclic graph with labeled edges
connecting the nodes. Graph operations are implemented in a functional
manner, so the data structure is immutable.
It permits at most one edge of a given name between any set of nodes. The
graph is not checked for cycles, and methods may hang or otherwise fail if
given a cyclic graph.
The `nodes` and `edges` attributes may be accessed in a read-only fashion.
The `nodes` attribute is a set of node names, while `edges` is a set of
`(left, right, name)` tuples representing an edge named `name` going from
node `left` to node `right..
"""
def __init__(self, nodes, edges):
"""
Create a graph. Nodes and edges are both as described in the class
documentation. Both values are used by reference, and should not be
modified after building a graph.
"""
assert isinstance(nodes, set)
assert isinstance(edges, set)
self.nodes = nodes
self.edges = edges
def __eq__(self, other):
return self.nodes == other.nodes and self.edges == other.edges
def __repr__(self):
return "<Graph nodes={!r} edges={!r}>".format(self.nodes, self.edges)
def transitive_closure(self, nodes):
"""
Return the transitive closure of <nodes>: the graph containing all
specified nodes as well as any nodes reachable from them, and any
intervening edges.
"""
assert isinstance(nodes, set)
assert nodes <= self.nodes
# generate a new graph by expanding along edges until reaching a fixed
# point
new_nodes, new_edges = nodes, set()
nodes, edges = set(), set()
while (new_nodes, new_edges) != (nodes, edges):
nodes, edges = new_nodes, new_edges
add_edges = set((left, right, name)
for (left, right, name) in self.edges
if left in nodes)
add_nodes = set(right for (_, right, _) in add_edges)
new_nodes = nodes | add_nodes
new_edges = edges | add_edges
return Graph(new_nodes, new_edges)
def visit_postorder(self):
"""
Generate a sequence of nodes in postorder, such that every node is
visited *after* any nodes it links to.
Behavior is undefined (read: it will hang) if the graph contains a
cycle.
"""
queue = collections.deque(sorted(self.nodes))
links_by_node = self.links_dict()
seen = set()
while queue:
node = queue.popleft()
if node in seen:
continue
links = links_by_node[node]
if all((n in seen) for n in links):
seen.add(node)
yield node
else:
queue.extend(n for n in links if n not in seen)
queue.append(node)
def links_dict(self):
"""
Return a dictionary mapping each node to a set of the nodes it links to
(omitting edge names)
"""
links = collections.defaultdict(set)
for left, right, _ in self.edges:
links[left].add(right)
return links
def named_links_dict(self):
"""
Return a two-level dictionary mapping each node to a dictionary mapping
edge names to labels.
"""
links = collections.defaultdict(dict)
for left, right, name in self.edges:
links[left][name] = right
return links
def reverse_links_dict(self):
"""
Return a dictionary mapping each node to a set of the nodes linking to
it (omitting edge names)
"""
links = collections.defaultdict(set)
for left, right, _ in self.edges:
links[right].add(left)
return links
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