"""
Module defining a topological sort function, see
<http://www.bitformation.com/art/python_toposort.html> for more
information.
Original topological sort code written by Ofer Faigon (www.bitformation.com) and used with permission
"""
def topological_sort(items, partial_order):
"""
Perform topological sort.
items is a list of items to be sorted.
partial_order is a list of pairs. If pair (a,b) is in it, it means
that item a should appear before item b.
Returns a list of the items in one of the possible orders, or None
if partial_order contains a loop.
"""
def add_node(graph, node):
"""Add a node to the graph if not already exists."""
if node not in graph:
graph[node] = [0] # 0 = number of arcs coming into this node.
def add_arc(graph, fromnode, tonode):
"""Add an arc to a graph. Can create multiple arcs.
The end nodes must already exist."""
graph[fromnode].append(tonode)
# Update the count of incoming arcs in tonode.
graph[tonode][0] += 1
# step 1 - create a directed graph with an arc a->b for each input
# pair (a,b).
# The graph is represented by a dictionary. The dictionary contains
# a pair item:list for each node in the graph. /item/ is the value
# of the node. /list/'s 1st item is the count of incoming arcs, and
# the rest are the destinations of the outgoing arcs. For example:
# {'a':[0,'b','c'], 'b':[1], 'c':[1]}
# represents the graph: c <-- a --> b
# The graph may contain loops and multiple arcs.
# Note that our representation does not contain reference loops to
# cause GC problems even when the represented graph contains loops,
# because we keep the node names rather than references to the nodes.
graph = {}
for v in items:
add_node(graph, v)
for a,b in partial_order:
add_arc(graph, a, b)
# Step 2 - find all roots (nodes with zero incoming arcs).
roots = [node for (node,nodeinfo) in graph.items() if nodeinfo[0] == 0]
# step 3 - repeatedly emit a root and remove it from the graph. Removing
# a node may convert some of the node's direct children into roots.
# Whenever that happens, we append the new roots to the list of
# current roots.
sorted = []
while len(roots) != 0:
# If len(roots) is always 1 when we get here, it means that
# the input describes a complete ordering and there is only
# one possible output.
# When len(roots) > 1, we can choose any root to send to the
# output; this freedom represents the multiple complete orderings
# that satisfy the input restrictions. We arbitrarily take one of
# the roots using pop(). Note that for the algorithm to be efficient,
# this operation must be done in O(1) time.
root = roots.pop()
sorted.append(root)
for child in graph[root][1:]:
graph[child][0] = graph[child][0] - 1
if graph[child][0] == 0:
roots.append(child)
del graph[root]
if len(graph.items()) != 0:
# There is a loop in the input.
return None
return sorted