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101 lines
2.8 KiB
101 lines
2.8 KiB
3 years ago
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# util/topological.py
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# Copyright (C) 2005-2022 the SQLAlchemy authors and contributors
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# <see AUTHORS file>
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#
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# This module is part of SQLAlchemy and is released under
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# the MIT License: https://www.opensource.org/licenses/mit-license.php
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"""Topological sorting algorithms."""
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from .. import util
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from ..exc import CircularDependencyError
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__all__ = ["sort", "sort_as_subsets", "find_cycles"]
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def sort_as_subsets(tuples, allitems):
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edges = util.defaultdict(set)
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for parent, child in tuples:
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edges[child].add(parent)
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todo = list(allitems)
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todo_set = set(allitems)
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while todo_set:
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output = []
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for node in todo:
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if todo_set.isdisjoint(edges[node]):
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output.append(node)
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if not output:
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raise CircularDependencyError(
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"Circular dependency detected.",
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find_cycles(tuples, allitems),
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_gen_edges(edges),
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)
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todo_set.difference_update(output)
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todo = [t for t in todo if t in todo_set]
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yield output
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def sort(tuples, allitems, deterministic_order=True):
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"""sort the given list of items by dependency.
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'tuples' is a list of tuples representing a partial ordering.
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deterministic_order is no longer used, the order is now always
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deterministic given the order of "allitems". the flag is there
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for backwards compatibility with Alembic.
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"""
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for set_ in sort_as_subsets(tuples, allitems):
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for s in set_:
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yield s
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def find_cycles(tuples, allitems):
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# adapted from:
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# https://neopythonic.blogspot.com/2009/01/detecting-cycles-in-directed-graph.html
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edges = util.defaultdict(set)
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for parent, child in tuples:
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edges[parent].add(child)
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nodes_to_test = set(edges)
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output = set()
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# we'd like to find all nodes that are
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# involved in cycles, so we do the full
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# pass through the whole thing for each
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# node in the original list.
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# we can go just through parent edge nodes.
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# if a node is only a child and never a parent,
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# by definition it can't be part of a cycle. same
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# if it's not in the edges at all.
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for node in nodes_to_test:
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stack = [node]
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todo = nodes_to_test.difference(stack)
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while stack:
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top = stack[-1]
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for node in edges[top]:
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if node in stack:
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cyc = stack[stack.index(node) :]
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todo.difference_update(cyc)
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output.update(cyc)
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if node in todo:
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stack.append(node)
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todo.remove(node)
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break
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else:
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node = stack.pop()
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return output
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def _gen_edges(edges):
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return set([(right, left) for left in edges for right in edges[left]])
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