# topological.py # Copyright (C) 2005, 2006, 2007 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 key to the unit of work is to assemble a list of dependencies amongst all the different mappers that have been defined for classes. Related tables with foreign key constraints have a definite insert order, deletion order, objects need dependent properties from parent objects set up before saved, etc. These are all encoded as dependencies, in the form *mapper X is dependent on mapper Y*, meaning mapper Y's objects must be saved before those of mapper X, and mapper X's objects must be deleted before those of mapper Y. 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. An intrinsic *gotcha* to this algorithm is that since there are many possible outcomes to sorting a partial ordering, the algorithm can return any number of different results for the same input; just running it on a different machine architecture, or just random differences in the ordering of dictionaries, can change the result that is returned. While this result is guaranteed to be true to the incoming partial ordering, if the partial ordering itself does not properly represent the dependencies, code that works fine will suddenly break, then work again, then break, etc. Most of the bugs I've chased down while developing the *unit of work* have been of this nature - very tricky to reproduce and track down, particularly before I realized this characteristic of the algorithm. """ from sqlalchemy import util from sqlalchemy.exceptions import CircularDependencyError class _Node(object): """Represent each item in the sort. While the topological sort produces a straight ordered list of items, ``_Node`` ultimately stores a tree-structure of those items which are organized so that non-dependent nodes are siblings. """ 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([n.safestr(indent + 1) 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 not self.parent_to_children.has_key(parentnode): self.parent_to_children[parentnode] = util.Set() self.parent_to_children[parentnode].add(childnode) if not self.child_to_parents.has_key(childnode): 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 self.child_to_parents.has_key(node) and len(self.child_to_parents[node]) > 0 def edges_by_parent(self, node): if self.parent_to_children.has_key(node): 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)) class QueueDependencySorter(object): """Topological sort adapted from wikipedia's article on the subject. It creates a straight-line list of elements, then a second pass groups non-dependent actions together to build more of a tree structure with siblings. """ def __init__(self, tuples, allitems): self.tuples = tuples self.allitems = allitems def sort(self, allow_self_cycles=True, allow_all_cycles=False): (tuples, allitems) = (self.tuples, self.allitems) #print "\n---------------------------------\n" #print repr([t for t in tuples]) #print repr([a for a in allitems]) #print "\n---------------------------------\n" nodes = {} edges = _EdgeCollection() for item in allitems + [t[0] for t in tuples] + [t[1] for t in tuples]: if not nodes.has_key(item): node = _Node(item) nodes[item] = node for t in tuples: if t[0] is t[1]: if allow_self_cycles: n = nodes[t[0]] n.cycles = util.Set([n]) continue else: raise CircularDependencyError("Self-referential dependency detected " + repr(t)) 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) cycles = {} output = [] while nodes: if not queue: # edges remain but no edgeless nodes to remove; this indicates # a cycle if allow_all_cycles: for cycle in self._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 self._create_batched_tree(output) def _create_batched_tree(self, 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. """ 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,) # 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] for i in independents] return head def _find_cycles(self, 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 cycles.has_key(x): 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