I am trying to self study algorithms and this is my attempt at topological sort using Tarjan's version of DFS. It runs correctly for the graph I included. Can someone tell me if this is correct and if/what optimizations I can make?

graph = {
'B': ['C', 'D'],
'C': ['E'],
'D': ['F'],
'E': ['F'],
'F': ['G'],
'G': [],

def topological_sort(graph):
    visited, stack = set(), []

    for vertex in graph:
        handle_vertex(graph, vertex, visited, stack) 


def handle_vertex(graph, vertex, visited, stack):
    if vertex not in visited:

    for neighbors in graph[vertex]:
        if neighbors not in visited:
            handle_vertex(graph, neighbors, visited, stack)

    if vertex not in stack:
       stack.insert(0, vertex)
    return stack

  • 2
    \$\begingroup\$ Do you only have one test case? Does the code work correctly for other test cases? \$\endgroup\$ – Phrancis Dec 2 '16 at 23:27
  • \$\begingroup\$ @Phrancis it also works for the test case: graph2={ 0 : [], 1: [], 2: [3], 3: [1], 4: [0, 1], 5: [2, 0] } \$\endgroup\$ – driftdrift Dec 2 '16 at 23:36
  • 1
    \$\begingroup\$ Excuse my ignorance, but can you please explain what's the output you expect for the graph in the code ? More, could you please add more context to what your code does ? Having some recursion going on there doesn't help :). PS: for example, when I'm testing you're first graph, I receive different outputs at every run, so I suspect your code as being broken. \$\endgroup\$ – Grajdeanu Alex Dec 3 '16 at 6:11
  • \$\begingroup\$ @Dex'ter A topological sort returns things in order, where given an edge U->V in a graph, U always comes before V. \$\endgroup\$ – driftdrift Dec 3 '16 at 15:48
  1. I don't get the point of returning the stack from the handle_vertex function. The return value is never used (and the stack which is passed as an argument is modified in place).

  2. The topological_sort functions prints the stack, doesn't return anything and then it's returned value is printed: print(topological_sort(graph)). There're two reasonable options here:

    • not printing the returned value of the topological_sort and just calling it instead
    • Returning the stack from it instead of printing it inside the function.
  3. The neighbors name here: for neighbors in graph[vertex] is misleading. This variable represent just one neighbor at a time. I don't see why would you make it plural.


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