Tim,
Thanks for the topsort code. It would be useful in a project I'm
working on. Can I use the code for free under public domain? Thanks!
On Jun 30 1999, 11:00 pm, "Tim Peters"
<[EMAIL PROTECTED]> wrote:
> From: "Tim Peters" <[EMAIL PROTECTED]>
>
> [Dinu C. Gherman]
>
> > Does anybody have a simple-minded-but-working full-Python
> > implementation of topsort, the topological sorting algorithm?
> > Or maybe *any* topsort? I remember only one such algorithm...
> > python.org/search doesn't reveal any...
>
> Searching for "topological" instead turns up two hits there, a few more on
> DejaNews. Apparently "the std" algorithm I posted years ago predates
> DejaNews, though. So here's a fancier version ...
>
> check-out-aaron's-kjbuckets-too-ly y'rs - tim
>
> # topsort takes a list of pairs, where each pair (x, y) is taken to
> # mean that x <= y wrt some abstract partial ordering. The return
> # value is a list, representing a total ordering that respects all
> # the input constraints.
> # E.g.,
> # topsort( [(1,2), (3,3)] )
> # may return any of (but nothing other than)
> # [3, 1, 2]
> # [1, 3, 2]
> # [1, 2, 3]
> # because those are the permutations of the input elements that
> # respect the "1 precedes 2" and "3 precedes 3" input constraints.
> # Note that a constraint of the form (x, x) is really just a trick
> # to make sure x appears *somewhere* in the output list.
> #
> # If there's a cycle in the constraints, say
> # topsort( [(1,2), (2,1)] )
> # then CycleError is raised, and the exception object supports
> # many methods to help analyze and break the cycles. This requires
> # a good deal more code than topsort itself!
>
> from exceptions import Exception
>
> class CycleError(Exception):
> def __init__(self, sofar, numpreds, succs):
> Exception.__init__(self, "cycle in constraints",
> sofar, numpreds, succs)
> self.preds = None
>
> # return as much of the total ordering as topsort was able to
> # find before it hit a cycle
> def get_partial(self):
> return self[1]
>
> # return remaining elt -> count of predecessors map
> def get_pred_counts(self):
> return self[2]
>
> # return remaining elt -> list of successors map
> def get_succs(self):
> return self[3]
>
> # return remaining elements (== those that don't appear in
> # get_partial())
> def get_elements(self):
> return self.get_pred_counts().keys()
>
> # Return a list of pairs representing the full state of what's
> # remaining (if you pass this list back to topsort, it will raise
> # CycleError again, and if you invoke get_pairlist on *that*
> # exception object, the result will be isomorphic to *this*
> # invocation of get_pairlist).
> # The idea is that you can use pick_a_cycle to find a cycle,
> # through some means or another pick an (x,y) pair in the cycle
> # you no longer want to respect, then remove that pair from the
> # output of get_pairlist and try topsort again.
> def get_pairlist(self):
> succs = self.get_succs()
> answer = []
> for x in self.get_elements():
> if succs.has_key(x):
> for y in succs[x]:
> answer.append( (x, y) )
> else:
> # make sure x appears in topsort's output!
> answer.append( (x, x) )
> return answer
>
> # return remaining elt -> list of predecessors map
> def get_preds(self):
> if self.preds is not None:
> return self.preds
> self.preds = preds = {}
> remaining_elts = self.get_elements()
> for x in remaining_elts:
> preds[x] = []
> succs = self.get_succs()
>
> for x in remaining_elts:
> if succs.has_key(x):
> for y in succs[x]:
> preds[y].append(x)
>
> if __debug__:
> for x in remaining_elts:
> assert len(preds[x]) > 0
> return preds
>
> # return a cycle [x, ..., x] at random
> def pick_a_cycle(self):
> remaining_elts = self.get_elements()
>
> # We know that everything in remaining_elts has a predecessor,
> # but don't know that everything in it has a successor. So
> # crawling forward over succs may hit a dead end. Instead we
> # crawl backward over the preds until we hit a duplicate, then
> # reverse the path.
> preds = self.get_preds()
> from random import choice
> x = choice(remaining_elts)
> answer = []
> index = {}
> in_answer = index.has_key
> while not in_answer(x):
> index[x] = len(answer) # index of x in answer
> answer.append(x)
> x = choice(preds[x])
> answer.append(x)
> answer = answer[index[x]:]
> answer.reverse()
> return answer
>
> def topsort(pairlist):
> numpreds = {} # elt -> # of predecessors
> successors = {} # elt -> list of successors
> for first, second in pairlist:
> # make sure every elt is a key in numpreds
> if not numpreds.has_key(first):
> numpreds[first] = 0
> if not numpreds.has_key(second):
> numpreds[second] = 0
>
> # if they're the same, there's no real dependence
> if first == second:
> continue
>
> # since first < second, second gains a pred ...
> numpreds[second] = numpreds[second] + 1
>
> # ... and first gains a succ
> if successors.has_key(first):
> successors[first].append(second)
> else:
> successors[first] = [second]
>
> # suck up everything without a predecessor
> answer = filter(lambda x, numpreds=numpreds: numpreds[x] == 0,
> numpreds.keys())
>
> # for everything in answer, knock down the pred count on
> # its successors; note that answer grows *in* the loop
> for x in answer:
> assert numpreds[x] == 0
> del numpreds[x]
> if successors.has_key(x):
> for y in successors[x]:
> numpreds[y] = numpreds[y] - 1
> if numpreds[y] == 0:
> answer.append(y)
> # following "del" isn't needed; just makes
> # CycleError details easier to grasp
> del successors[x]
>
> if numpreds:
> # everything in numpreds has at least one predecessor ->
> # there's a cycle
> if __debug__:
> for x in numpreds.keys():
> assert numpreds[x] > 0
> raise CycleError(answer, numpreds, successors)
> return answer
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