topological.py

SQLAlchemy. 经典的Python ORM框架。学习必看。

# topological.py
# Copyright (C) 2005, 2006, 2007, 2008 Michael Bayer [e-mail]
#
# 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 import util
from sqlalchemy.exceptions import CircularDependencyError

__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,
    and 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 = util.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 "%s" % (str(self.item))

    def all_deps(self):
        """Return a set of dependencies for this node and all its cycles."""

        deps = util.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 = {}
        self.child_to_parents = {}

    def add(self, edge):
        """Add an edge to this collection."""

        (parentnode, childnode) = edge
        if parentnode not in self.parent_to_children:
            self.parent_to_children[parentnode] = util.Set()
        self.parent_to_children[parentnode].add(childnode)
        if childnode not in self.child_to_parents:
            self.child_to_parents[childnode] = util.Set()
        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 len(self.child_to_parents[childnode]) == 0:
            return childnode
        else:
            return None

    def has_parents(self, node):
        return node in self.child_to_parents and len(self.child_to_parents[node]) > 0

    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 __str__(self):
        return repr(list(self))

    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]:
        if id(item) not in nodes:
            node = _Node(item)
            nodes[item] = node

    for t in tuples:
        if t[0] is t[1]:
            if allow_cycles:
                n = nodes[t[0]]
                n.cycles = util.Set([n])
            elif not ignore_self_cycles:
                raise CircularDependencyError("Self-referential dependency detected " + repr(t))
            continue
        childnode = nodes[t[1]]
        parentnode = nodes[t[0]]
        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 = util.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 " + repr(edges) + repr(queue))
        node = queue.pop()
        if not hasattr(node, '_cyclical'):
            output.append(node)
        del nodes[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 util.reversed(nodes):
        # nodes subtree and cycles contain the node itself
        subtree = util.Set([node])
        if node.cycles is not None:
            cycles = util.Set(node.cycles)
        else:
            cycles = util.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):
    involved_in_cycles = util.Set()
    cycles = {}
    def traverse(node, goal=None, cycle=None):
        if goal is None:
            goal = node
            cycle = []
        elif node is goal:
            return True

        for (n, key) in edges.edges_by_parent(node):
            if key in cycle:
                continue
            cycle.append(key)
            if traverse(key, goal, cycle):
                cycset = util.Set(cycle)
                for x in cycle:
                    involved_in_cycles.add(x)
                    if x in cycles:
                        existing_set = cycles[x]
                        [existing_set.add(y) for y in cycset]
                        for y in existing_set:
                            cycles[y] = existing_set
                        cycset = existing_set
                    else:
                        cycles[x] = cycset
            cycle.pop()

    for parent in edges.get_parents():
        traverse(parent)

    # sets are not hashable, so uniquify with id
    unique_cycles = dict([(id(s), s) for s in cycles.values()]).values()
    for cycle in unique_cycles:
        edgecollection = [edge for edge in edges
                          if edge[0] in cycle and edge[1] in cycle]
        yield edgecollection