Source code for galaxy.util.topsort

Topological sort.

From Tim Peters, see:

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.

   topsort( [(1,2), (3,3)] )

Valid topological sorts would be any of (but nothing other than)

   [3, 1, 2]
   [1, 3, 2]
   [1, 2, 3]

... however this variant ensures that 'key' order (first element of
tuple) is preserved so the following will be result returned:

   [1, 3, 2]

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!

[docs]class CycleError(Exception):
[docs] 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
[docs] def get_partial(self): return self[1]
# return remaining elt -> count of predecessors map
[docs] def get_pred_counts(self): return self[2]
# return remaining elt -> list of successors map
[docs] def get_succs(self): return self[3]
# return remaining elements (== those that don't appear in # get_partial())
[docs] 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.
[docs] def get_pairlist(self): succs = self.get_succs() answer = [] for x in self.get_elements(): if x in succs: 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
[docs] 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 x in succs: 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
[docs] 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 _numpreds_and_successors_from_pairlist(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 first not in numpreds: numpreds[first] = 0 if second not in numpreds: 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 first in successors: successors[first].append(second) else: successors[first] = [second] return numpreds, successors
[docs]def topsort(pairlist): numpreds, successors = _numpreds_and_successors_from_pairlist(pairlist) # suck up everything without a predecessor answer = [x for x in numpreds.keys() if numpreds[x] == 0] # 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 x in successors: 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
[docs]def topsort_levels(pairlist): numpreds, successors = _numpreds_and_successors_from_pairlist(pairlist) answer = [] while 1: # Suck up everything without a predecessor. levparents = [x for x in numpreds.keys() if numpreds[x] == 0] if not levparents: break answer.append(levparents) for levparent in levparents: del numpreds[levparent] if levparent in successors: for levparentsucc in successors[levparent]: numpreds[levparentsucc] -= 1 del successors[levparent] if numpreds: # Everything in num_parents has at least one child -> # there's a cycle. raise CycleError(answer, numpreds, successors) return answer