Stable topological sort

Question

Let say I have a graph where the nodes is stored in a sorted list. I now want to topological sort this graph while keeping the original order where the topological order is

Answer 1

Interpreting "stable topological sort" as a linearization of a DAG such that ranges in the linearization where the topological order doesn't matter, are sorted lexicographically. This can be solved with the DFS method of linearization, with the modification that nodes are visited in lexicographical order.

I have a Python Digraph class with a linearization method which looks like this:

def linearize_as_needed(self):
    if self.islinearized:
        return

    # Algorithm: DFS Topological sort
    # https://en.wikipedia.org/wiki/Topological_sorting#Depth-first_search

    temporary = set()
    permanent = set()

    L = [ ]

    def visit(vertices):
        for vertex in sorted(vertices, reverse=True):
            if vertex in permanent:
                pass
            elif vertex in temporary:
                raise NotADAG
            else:
                temporary.add(vertex)

                if vertex in self.arrows:
                    visit(self.arrows[vertex])

                L.append(vertex)

                temporary.remove(vertex)
                permanent.add(vertex)

        # print('visit: {} => {}'.format(vertices, L))

    visit(self.vertices)
    self._linear = list(reversed(L))
    self._iter = iter(self._linear)
    self.islinearized = True

Here

self.vertices

is the set of all vertices, and

self.arrows

holds the adjacency relation as a dict of left nodes to sets of right nodes.