# topological.py # Copyright (C) 2005,2006 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. """ import string, StringIO from sqlalchemy import util from sqlalchemy.exceptions import * 00037 class _Node(object): """represents 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" + \ string.join([n.safestr(indent + 1) for n in self.children], '') def __repr__(self): return "%s" % (str(self.item)) def is_dependent(self, child): if self.cycles is not None: for c in self.cycles: if child in c.dependencies: return True if child.cycles is not None: for c in child.cycles: if c in self.dependencies: return True return child in self.dependencies 00067 class _EdgeCollection(object): """a collection of directed edges.""" def __init__(self): self.parent_to_children = {} self.child_to_parents = {} 00072 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) 00082 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() 00100 def pop_node(self, node): """remove all edges where the given node is a parent. returns 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 len(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)) 00121 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 FlushError("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 len(nodes) > 0: if len(queue) == 0: # edges remain but no edgeless nodes to remove; this indicates # a cycle if allow_all_cycles: x = self._find_cycles(edges) 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 FlushError("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) 00196 def _create_batched_tree(self, nodes): """given a list of nodes from a topological sort, organizes the nodes into a tree structure, with as many non-dependent nodes set as silbings to each other as possible.""" def sort(index=None, l=None): if index is None: index = 0 if index >= len(nodes): return None node = nodes[index] l2 = [] sort(index + 1, l2) for n in l2: if l is None or search_dep(node, n): node.children.append(n) else: l.append(n) if l is not None: l.append(node) return node def search_dep(parent, child): if child is None: return False elif parent.is_dependent(child): return True else: for c in child.children: x = search_dep(parent, c) if x is True: return True else: return False return sort() 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) for cycle in dict([(id(s), s) for s in cycles.values()]).values(): edgecollection = [] for edge in edges: if edge[0] in cycle and edge[1] in cycle: edgecollection.append(edge) yield edgecollection

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