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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
import collections
from dataclasses import dataclass
from typing import FrozenSet
@dataclass(frozen=True)
class Graph:
"""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`..
"""
nodes: FrozenSet
edges: FrozenSet
def transitive_closure(self, nodes, reverse=False):
"""Return the transitive closure of <nodes>: the graph containing all
specified nodes as well as any nodes reachable from them, and any
intervening edges.
If `reverse` is true, the "reachability" will be reversed and this
will return the set of nodes that can reach the specified nodes.
Example:
.. code-block::
a ------> b ------> c
|
`-------> d
transitive_closure([b]).nodes == set([a, b])
transitive_closure([c]).nodes == set([c, b, a])
transitive_closure([c], reverse=True).nodes == set([c])
transitive_closure([b], reverse=True).nodes == set([b, c, d])
"""
assert isinstance(nodes, set)
if not (nodes <= self.nodes):
raise Exception(
f"Unknown nodes in transitive closure: {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 = {
(left, right, name)
for (left, right, name) in self.edges
if (right if reverse else left) in nodes
}
add_nodes = {(left if reverse else right) for (left, right, _) in add_edges}
new_nodes = nodes | add_nodes
new_edges = edges | add_edges
return Graph(new_nodes, new_edges)
def _visit(self, reverse):
queue = collections.deque(sorted(self.nodes))
links_by_node = self.reverse_links_dict() if reverse else 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 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.
"""
return self._visit(False)
def visit_preorder(self):
"""
Like visit_postorder, but in reverse: evrey node is visited *before*
any nodes it links to.
"""
return self._visit(True)
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