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# util/topological.py
# Copyright (C) 2005-2024 the SQLAlchemy authors and contributors
# <see AUTHORS file>
#
# This module is part of SQLAlchemy and is released under
# the MIT License: https://www.opensource.org/licenses/mit-license.php
"""Topological sorting algorithms."""
from .. import util
from ..exc import CircularDependencyError
__all__ = ["sort", "sort_as_subsets", "find_cycles"]
def sort_as_subsets(tuples, allitems):
edges = util.defaultdict(set)
for parent, child in tuples:
edges[child].add(parent)
todo = list(allitems)
todo_set = set(allitems)
while todo_set:
output = []
for node in todo:
if todo_set.isdisjoint(edges[node]):
output.append(node)
if not output:
raise CircularDependencyError(
"Circular dependency detected.",
find_cycles(tuples, allitems),
_gen_edges(edges),
)
todo_set.difference_update(output)
todo = [t for t in todo if t in todo_set]
yield output
def sort(tuples, allitems, deterministic_order=True):
"""sort the given list of items by dependency.
'tuples' is a list of tuples representing a partial ordering.
deterministic_order is no longer used, the order is now always
deterministic given the order of "allitems". the flag is there
for backwards compatibility with Alembic.
"""
for set_ in sort_as_subsets(tuples, allitems):
for s in set_:
yield s
def find_cycles(tuples, allitems):
# adapted from:
# https://neopythonic.blogspot.com/2009/01/detecting-cycles-in-directed-graph.html
edges = util.defaultdict(set)
for parent, child in tuples:
edges[parent].add(child)
nodes_to_test = set(edges)
output = set()
# we'd like to find all nodes that are
# involved in cycles, so we do the full
# pass through the whole thing for each
# node in the original list.
# we can go just through parent edge nodes.
# if a node is only a child and never a parent,
# by definition it can't be part of a cycle. same
# if it's not in the edges at all.
for node in nodes_to_test:
stack = [node]
todo = nodes_to_test.difference(stack)
while stack:
top = stack[-1]
for node in edges[top]:
if node in stack:
cyc = stack[stack.index(node) :]
todo.difference_update(cyc)
output.update(cyc)
if node in todo:
stack.append(node)
todo.remove(node)
break
else:
node = stack.pop()
return output
def _gen_edges(edges):
return set([(right, left) for left in edges for right in edges[left]])