def toposort(edges):
""" Topological sort algorithm by Kahn [1] - O(nodes + vertices)
inputs:
edges - a dict of the form {a: {b, c}} where b and c depend on a
outputs:
L - an ordered list of nodes that satisfy the dependencies of edges
>>> toposort({1: {2, 3}, 2: (3, )})
[1, 2, 3]
Closely follows the wikipedia page [2]
[1] Kahn, Arthur B. (1962), "Topological sorting of large networks",
Communications of the ACM
[2] http://en.wikipedia.org/wiki/Toposort#Algorithms
"""
incoming_edges = reverse_dict(edges)
incoming_edges = dict((k, set(val)) for k, val in incoming_edges.items())
S = set((v for v in edges if v not in incoming_edges))
L = []
while S:
n = S.pop()
L.append(n)
for m in edges.get(n, ()):
assert n in incoming_edges[m]
incoming_edges[m].remove(n)
if not incoming_edges[m]:
S.add(m)
if any(incoming_edges.get(v, None) for v in edges):
raise ValueError("Input has cycles")
return L
def test_reverse_dict():
d = {'a': (1, 2), 'b': (2, 3), 'c': ()}
assert reverse_dict(d) == {1: {'a'}, 2: {'a', 'b'}, 3: {'b'}}
