298 lines
11 KiB
Python
298 lines
11 KiB
Python
|
# topological.py
|
||
|
|
# Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010 Michael Bayer mike_mp@zzzcomputing.com
|
||
|
|
#
|
||
|
|
# This module is part of SQLAlchemy and is released under
|
||
|
|
# the MIT License: http://www.opensource.org/licenses/mit-license.php
|
||
|
|
|
||
|
|
"""Topological sorting algorithms.
|
||
|
|
|
||
|
|
The topological sort is an algorithm that receives this list of
|
||
|
|
dependencies as a *partial ordering*, that is a list of pairs which
|
||
|
|
might say, *X is dependent on Y*, *Q is dependent on Z*, but does not
|
||
|
|
necessarily tell you anything about Q being dependent on X. Therefore,
|
||
|
|
its not a straight sort where every element can be compared to
|
||
|
|
another... only some of the elements have any sorting preference, and
|
||
|
|
then only towards just some of the other elements. For a particular
|
||
|
|
partial ordering, there can be many possible sorts that satisfy the
|
||
|
|
conditions.
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
from sqlalchemy.exc import CircularDependencyError
|
||
|
|
from sqlalchemy import util
|
||
|
|
|
||
|
|
__all__ = ['sort', 'sort_with_cycles', 'sort_as_tree']
|
||
|
|
|
||
|
|
def sort(tuples, allitems):
|
||
|
|
"""sort the given list of items by dependency.
|
||
|
|
|
||
|
|
'tuples' is a list of tuples representing a partial ordering.
|
||
|
|
"""
|
||
|
|
|
||
|
|
return [n.item for n in _sort(tuples, allitems, allow_cycles=False, ignore_self_cycles=True)]
|
||
|
|
|
||
|
|
def sort_with_cycles(tuples, allitems):
|
||
|
|
"""sort the given list of items by dependency, cutting out cycles.
|
||
|
|
|
||
|
|
returns results as an iterable of 2-tuples, containing the item,
|
||
|
|
and a list containing items involved in a cycle with this item, if any.
|
||
|
|
|
||
|
|
'tuples' is a list of tuples representing a partial ordering.
|
||
|
|
"""
|
||
|
|
|
||
|
|
return [(n.item, [n.item for n in n.cycles or []]) for n in _sort(tuples, allitems, allow_cycles=True)]
|
||
|
|
|
||
|
|
def sort_as_tree(tuples, allitems, with_cycles=False):
|
||
|
|
"""sort the given list of items by dependency, and return results
|
||
|
|
as a hierarchical tree structure.
|
||
|
|
|
||
|
|
returns results as an iterable of 3-tuples, containing the item,
|
||
|
|
a list containing items involved in a cycle with this item, if any,
|
||
|
|
and a list of child tuples.
|
||
|
|
|
||
|
|
if with_cycles is False, the returned structure is of the same form
|
||
|
|
but the second element of each tuple, i.e. the 'cycles', is an empty list.
|
||
|
|
|
||
|
|
'tuples' is a list of tuples representing a partial ordering.
|
||
|
|
"""
|
||
|
|
|
||
|
|
return _organize_as_tree(_sort(tuples, allitems, allow_cycles=with_cycles))
|
||
|
|
|
||
|
|
|
||
|
|
class _Node(object):
|
||
|
|
"""Represent each item in the sort."""
|
||
|
|
|
||
|
|
def __init__(self, item):
|
||
|
|
self.item = item
|
||
|
|
self.dependencies = set()
|
||
|
|
self.children = []
|
||
|
|
self.cycles = None
|
||
|
|
|
||
|
|
def __str__(self):
|
||
|
|
return self.safestr()
|
||
|
|
|
||
|
|
def safestr(self, indent=0):
|
||
|
|
return (' ' * indent * 2) + \
|
||
|
|
str(self.item) + \
|
||
|
|
(self.cycles is not None and (" (cycles: " + repr([x for x in self.cycles]) + ")") or "") + \
|
||
|
|
"\n" + \
|
||
|
|
''.join(str(n) for n in self.children)
|
||
|
|
|
||
|
|
def __repr__(self):
|
||
|
|
return str(self.item)
|
||
|
|
|
||
|
|
def all_deps(self):
|
||
|
|
"""Return a set of dependencies for this node and all its cycles."""
|
||
|
|
|
||
|
|
deps = set(self.dependencies)
|
||
|
|
if self.cycles is not None:
|
||
|
|
for c in self.cycles:
|
||
|
|
deps.update(c.dependencies)
|
||
|
|
return deps
|
||
|
|
|
||
|
|
class _EdgeCollection(object):
|
||
|
|
"""A collection of directed edges."""
|
||
|
|
|
||
|
|
def __init__(self):
|
||
|
|
self.parent_to_children = util.defaultdict(set)
|
||
|
|
self.child_to_parents = util.defaultdict(set)
|
||
|
|
|
||
|
|
def add(self, edge):
|
||
|
|
"""Add an edge to this collection."""
|
||
|
|
|
||
|
|
parentnode, childnode = edge
|
||
|
|
self.parent_to_children[parentnode].add(childnode)
|
||
|
|
self.child_to_parents[childnode].add(parentnode)
|
||
|
|
parentnode.dependencies.add(childnode)
|
||
|
|
|
||
|
|
def remove(self, edge):
|
||
|
|
"""Remove an edge from this collection.
|
||
|
|
|
||
|
|
Return the childnode if it has no other parents.
|
||
|
|
"""
|
||
|
|
|
||
|
|
(parentnode, childnode) = edge
|
||
|
|
self.parent_to_children[parentnode].remove(childnode)
|
||
|
|
self.child_to_parents[childnode].remove(parentnode)
|
||
|
|
if not self.child_to_parents[childnode]:
|
||
|
|
return childnode
|
||
|
|
else:
|
||
|
|
return None
|
||
|
|
|
||
|
|
def has_parents(self, node):
|
||
|
|
return node in self.child_to_parents and bool(self.child_to_parents[node])
|
||
|
|
|
||
|
|
def edges_by_parent(self, node):
|
||
|
|
if node in self.parent_to_children:
|
||
|
|
return [(node, child) for child in self.parent_to_children[node]]
|
||
|
|
else:
|
||
|
|
return []
|
||
|
|
|
||
|
|
def get_parents(self):
|
||
|
|
return self.parent_to_children.keys()
|
||
|
|
|
||
|
|
def pop_node(self, node):
|
||
|
|
"""Remove all edges where the given node is a parent.
|
||
|
|
|
||
|
|
Return the collection of all nodes which were children of the
|
||
|
|
given node, and have no further parents.
|
||
|
|
"""
|
||
|
|
|
||
|
|
children = self.parent_to_children.pop(node, None)
|
||
|
|
if children is not None:
|
||
|
|
for child in children:
|
||
|
|
self.child_to_parents[child].remove(node)
|
||
|
|
if not self.child_to_parents[child]:
|
||
|
|
yield child
|
||
|
|
|
||
|
|
def __len__(self):
|
||
|
|
return sum(len(x) for x in self.parent_to_children.values())
|
||
|
|
|
||
|
|
def __iter__(self):
|
||
|
|
for parent, children in self.parent_to_children.iteritems():
|
||
|
|
for child in children:
|
||
|
|
yield (parent, child)
|
||
|
|
|
||
|
|
def __repr__(self):
|
||
|
|
return repr(list(self))
|
||
|
|
|
||
|
|
def _sort(tuples, allitems, allow_cycles=False, ignore_self_cycles=False):
|
||
|
|
nodes = {}
|
||
|
|
edges = _EdgeCollection()
|
||
|
|
|
||
|
|
for item in list(allitems) + [t[0] for t in tuples] + [t[1] for t in tuples]:
|
||
|
|
item_id = id(item)
|
||
|
|
if item_id not in nodes:
|
||
|
|
nodes[item_id] = _Node(item)
|
||
|
|
|
||
|
|
for t in tuples:
|
||
|
|
id0, id1 = id(t[0]), id(t[1])
|
||
|
|
if t[0] is t[1]:
|
||
|
|
if allow_cycles:
|
||
|
|
n = nodes[id0]
|
||
|
|
n.cycles = set([n])
|
||
|
|
elif not ignore_self_cycles:
|
||
|
|
raise CircularDependencyError("Self-referential dependency detected: %r" % t)
|
||
|
|
continue
|
||
|
|
childnode = nodes[id1]
|
||
|
|
parentnode = nodes[id0]
|
||
|
|
edges.add((parentnode, childnode))
|
||
|
|
|
||
|
|
queue = []
|
||
|
|
for n in nodes.values():
|
||
|
|
if not edges.has_parents(n):
|
||
|
|
queue.append(n)
|
||
|
|
|
||
|
|
output = []
|
||
|
|
while nodes:
|
||
|
|
if not queue:
|
||
|
|
# edges remain but no edgeless nodes to remove; this indicates
|
||
|
|
# a cycle
|
||
|
|
if allow_cycles:
|
||
|
|
for cycle in _find_cycles(edges):
|
||
|
|
lead = cycle[0][0]
|
||
|
|
lead.cycles = set()
|
||
|
|
for edge in cycle:
|
||
|
|
n = edges.remove(edge)
|
||
|
|
lead.cycles.add(edge[0])
|
||
|
|
lead.cycles.add(edge[1])
|
||
|
|
if n is not None:
|
||
|
|
queue.append(n)
|
||
|
|
for n in lead.cycles:
|
||
|
|
if n is not lead:
|
||
|
|
n._cyclical = True
|
||
|
|
for (n, k) in list(edges.edges_by_parent(n)):
|
||
|
|
edges.add((lead, k))
|
||
|
|
edges.remove((n, k))
|
||
|
|
continue
|
||
|
|
else:
|
||
|
|
# long cycles not allowed
|
||
|
|
raise CircularDependencyError("Circular dependency detected: %r %r " % (edges, queue))
|
||
|
|
node = queue.pop()
|
||
|
|
if not hasattr(node, '_cyclical'):
|
||
|
|
output.append(node)
|
||
|
|
del nodes[id(node.item)]
|
||
|
|
for childnode in edges.pop_node(node):
|
||
|
|
queue.append(childnode)
|
||
|
|
return output
|
||
|
|
|
||
|
|
def _organize_as_tree(nodes):
|
||
|
|
"""Given a list of nodes from a topological sort, organize the
|
||
|
|
nodes into a tree structure, with as many non-dependent nodes
|
||
|
|
set as siblings to each other as possible.
|
||
|
|
|
||
|
|
returns nodes as 3-tuples (item, cycles, children).
|
||
|
|
"""
|
||
|
|
|
||
|
|
if not nodes:
|
||
|
|
return None
|
||
|
|
# a list of all currently independent subtrees as a tuple of
|
||
|
|
# (root_node, set_of_all_tree_nodes, set_of_all_cycle_nodes_in_tree)
|
||
|
|
# order of the list has no semantics for the algorithmic
|
||
|
|
independents = []
|
||
|
|
# in reverse topological order
|
||
|
|
for node in reversed(nodes):
|
||
|
|
# nodes subtree and cycles contain the node itself
|
||
|
|
subtree = set([node])
|
||
|
|
if node.cycles is not None:
|
||
|
|
cycles = set(node.cycles)
|
||
|
|
else:
|
||
|
|
cycles = set()
|
||
|
|
# get a set of dependent nodes of node and its cycles
|
||
|
|
nodealldeps = node.all_deps()
|
||
|
|
if nodealldeps:
|
||
|
|
# iterate over independent node indexes in reverse order so we can efficiently remove them
|
||
|
|
for index in xrange(len(independents) - 1, -1, -1):
|
||
|
|
child, childsubtree, childcycles = independents[index]
|
||
|
|
# if there is a dependency between this node and an independent node
|
||
|
|
if (childsubtree.intersection(nodealldeps) or childcycles.intersection(node.dependencies)):
|
||
|
|
# prepend child to nodes children
|
||
|
|
# (append should be fine, but previous implemetation used prepend)
|
||
|
|
node.children[0:0] = [(child.item, [n.item for n in child.cycles or []], child.children)]
|
||
|
|
# merge childs subtree and cycles
|
||
|
|
subtree.update(childsubtree)
|
||
|
|
cycles.update(childcycles)
|
||
|
|
# remove the child from list of independent subtrees
|
||
|
|
independents[index:index+1] = []
|
||
|
|
# add node as a new independent subtree
|
||
|
|
independents.append((node, subtree, cycles))
|
||
|
|
# choose an arbitrary node from list of all independent subtrees
|
||
|
|
head = independents.pop()[0]
|
||
|
|
# add all other independent subtrees as a child of the chosen root
|
||
|
|
# used prepend [0:0] instead of extend to maintain exact behaviour of previous implementation
|
||
|
|
head.children[0:0] = [(i[0].item, [n.item for n in i[0].cycles or []], i[0].children) for i in independents]
|
||
|
|
return (head.item, [n.item for n in head.cycles or []], head.children)
|
||
|
|
|
||
|
|
def _find_cycles(edges):
|
||
|
|
cycles = {}
|
||
|
|
|
||
|
|
def traverse(node, cycle, goal):
|
||
|
|
for (n, key) in edges.edges_by_parent(node):
|
||
|
|
if key in cycle:
|
||
|
|
continue
|
||
|
|
cycle.add(key)
|
||
|
|
if key is goal:
|
||
|
|
cycset = set(cycle)
|
||
|
|
for x in cycle:
|
||
|
|
if x in cycles:
|
||
|
|
existing_set = cycles[x]
|
||
|
|
existing_set.update(cycset)
|
||
|
|
for y in existing_set:
|
||
|
|
cycles[y] = existing_set
|
||
|
|
cycset = existing_set
|
||
|
|
else:
|
||
|
|
cycles[x] = cycset
|
||
|
|
else:
|
||
|
|
traverse(key, cycle, goal)
|
||
|
|
cycle.pop()
|
||
|
|
|
||
|
|
for parent in edges.get_parents():
|
||
|
|
traverse(parent, set(), parent)
|
||
|
|
|
||
|
|
unique_cycles = set(tuple(s) for s in cycles.values())
|
||
|
|
|
||
|
|
for cycle in unique_cycles:
|
||
|
|
edgecollection = [edge for edge in edges
|
||
|
|
if edge[0] in cycle and edge[1] in cycle]
|
||
|
|
yield edgecollection
|