from collections import deque
import random


def is_topsorted(V,E,sequence):
  sequence = list(sequence)
  #from wikipedia definition of top-sort
  #for every edge uv, u comes before v in the ordering
  for u,v in E:
    ui = sequence.index(u)
    vi = sequence.index(v)
    if not (ui < vi):
      return False
  return True 

#the collection_type should behave like a set:
# it must have add(), pop() and __len__() as members.
def topsort(V,E,collection_type):
  #out edges
  INS = {}
  
  #in edges
  OUTS = {}
  for v in V:
    INS[v] = set()
    OUTS[v] = set()

  #for each edge u,v,
  for u,v in E:
    #record the out-edge from u
    OUTS[u].add(v)
    #record the in-edge to v
    INS[v].add(u)
  
  #1. Store all vertices with indegree 0 in a queue
  #We will start
  topvertices = collection_type()

  for v,in_vertices in INS.iteritems():
    if len(in_vertices) == 0:
      topvertices.add(v)

  result = []

  #4. Perform steps 2 and 3 while the queue is not empty.
  while len(topvertices) != 0:  
    #2. get a vertex U and place it in the sorted sequence (array or another queue).
    u = topvertices.pop()
    result.append(u)

    #3. For all edges (U,V) update the indegree of V,
    # and put V in the queue if the updated indegree is 0.

    for v in OUTS[u]:
      INS[v].remove(u)
      if len(INS[v]) == 0:
        topvertices.add(v)

  return result

class stack_collection:
  def __init__(self):
    self.data = list()
  def add(self,v):
    self.data.append(v)
  def pop(self):
    return self.data.pop()
  def __len__(self):
    return len(self.data)

class queue_collection:
  def __init__(self):
    self.data = deque()
  def add(self,v):
    self.data.append(v)
  def pop(self):
    return self.data.popleft()
  def __len__(self):
    return len(self.data)

class random_orderd_collection:
  def __init__(self):
    self.data = []
  def add(self,v):
    self.data.append(v)
  def pop(self):    
    result = random.choice(self.data)
    self.data.remove(result)
    return result
  def __len__(self):
    return len(self.data)

"""
Poor man's graph generator.
Requires networkx.

Don't make the edge_count too high compared with the vertex count,
 otherwise it will run for a long time or forever.
"""
def nx_generate_random_dag(vertex_count,edge_count):
  import networkx as nx
  
  V = range(1,vertex_count+1)
  random.shuffle(V)
  
  G = nx.DiGraph()
  G.add_nodes_from(V)

  while nx.number_of_edges(G) < edge_count:

    u = random.choice(V)
    v = random.choice(V)
    if u == v:
      continue
    
    for tries in range(2):
      G.add_edge(u,v)
      if not nx.is_directed_acyclic_graph(G):
        G.remove_edge(u,v)
        u,v = v,u
  V = G.nodes()
  E = G.edges()
  
  assert len(E) == edge_count
  assert len(V) == vertex_count
  return V,E
  
  

  
def main():

  graphs = []

  V = [1,2,3,4,5]
  E = [(1,2),(1,5),(1,4),(2,4),(2,5),(3,4),(3,5)]

  graphs.append((V,E))

  """
  Uncomment this section if you have networkx.
  This will generate 3 random graphs.
  """
  """
  for i in range(3):
    G = nx_generate_random_dag(30,120)
    V,E = G
    print 'random E:',E
    graphs.append(G)
  """

  
  #This graph was generated using nx_generate_random_dag() from above
  V = range(1,31)
  E = [(1, 10), (1, 11), (1, 14), (1, 17), (1, 18), (1, 21), (1, 23),
       (1, 30), (2, 4), (2, 12), (2, 15), (2, 17), (2, 18), (2, 19),
       (2, 25), (3, 22), (4, 5), (4, 8), (4, 22), (4, 23), (4, 26),
       (5, 27), (5, 23), (6, 24), (6, 28), (6, 27), (6, 20), (6, 29),
       (7, 3), (7, 19), (7, 13), (8, 24), (8, 10), (8, 3), (8, 12),
       (9, 4), (9, 8), (9, 10), (9, 14), (9, 19), (9, 27), (9, 28),
       (9, 29), (10, 18), (10, 5), (10, 23), (11, 27), (11, 5),
       (12, 10), (13, 9), (13, 26), (13, 3), (13, 12), (13, 6), (14, 24),
       (14, 28), (14, 18), (14, 20), (15, 3), (15, 12), (15, 17), (15, 19),
       (15, 25), (15, 27), (16, 4), (16, 5), (16, 8), (16, 18), (16, 20), (16, 23),
       (16, 26), (16, 28), (17, 4), (17, 5), (17, 8), (17, 12), (17, 22), (17, 28),
       (18, 11), (18, 3), (19, 10), (19, 18), (19, 5), (19, 22), (20, 5), (20, 29),
       (21, 25), (21, 12), (21, 30), (21, 17), (22, 11), (24, 3), (24, 10),
       (24, 11), (24, 28), (25, 10), (25, 17), (25, 23), (25, 27), (26, 3),
       (26, 18), (26, 19), (28, 26), (28, 11), (28, 23), (29, 2), (29, 4),
       (29, 11), (29, 15), (29, 17), (29, 22), (29, 23), (30, 3), (30, 7),
       (30, 17), (30, 20), (30, 25), (30, 26), (30, 28), (30, 29)]

  graphs.append((V,E))

  #add other graphs here for testing


  for G in graphs:
    V,E = G

    #sets in python are unordered but in practice their hashes usually order integers.
    top_set = topsort(V,E,set)

    top_stack = topsort(V,E,stack_collection)

    top_queue = topsort(V,E,queue_collection)

    random_results = []
    for i in range(0,10):
      random_results.append(topsort(V,E,random_orderd_collection))
    
    print
    print 'V: ', V
    print 'E: ', E
    print 'top_set ({0}): {1}'.format(is_topsorted(V,E,top_set),top_set)
    print 'top_stack ({0}): {1}'.format(is_topsorted(V,E,top_stack),top_stack)
    print 'top_queue ({0}): {1}'.format(is_topsorted(V,E,top_queue),top_queue)

    for random_result in random_results:
      print 'random_result ({0}): {1}'.format(is_topsorted(V,E,random_result),random_result)
      assert is_topsorted(V,E,random_result)

    assert is_topsorted(V,E,top_set)
    assert is_topsorted(V,E,top_stack)
    assert is_topsorted(V,E,top_queue)
    


main()

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LCAoMTMsIDMpLCAoMTMsIDEyKSwgKDEzLCA2KSwgKDE0LCAyNCksCiAgICAgICAoMTQsIDI4KSwgKDE0LCAxOCksICgxNCwgMjApLCAoMTUsIDMpLCAoMTUsIDEyKSwgKDE1LCAxNyksICgxNSwgMTkpLAogICAgICAgKDE1LCAyNSksICgxNSwgMjcpLCAoMTYsIDQpLCAoMTYsIDUpLCAoMTYsIDgpLCAoMTYsIDE4KSwgKDE2LCAyMCksICgxNiwgMjMpLAogICAgICAgKDE2LCAyNiksICgxNiwgMjgpLCAoMTcsIDQpLCAoMTcsIDUpLCAoMTcsIDgpLCAoMTcsIDEyKSwgKDE3LCAyMiksICgxNywgMjgpLAogICAgICAgKDE4LCAxMSksICgxOCwgMyksICgxOSwgMTApLCAoMTksIDE4KSwgKDE5LCA1KSwgKDE5LCAyMiksICgyMCwgNSksICgyMCwgMjkpLAogICAgICAgKDIxLCAyNSksICgyMSwgMTIpLCAoMjEsIDMwKSwgKDIxLCAxNyksICgyMiwgMTEpLCAoMjQsIDMpLCAoMjQsIDEwKSwKICAgICAgICgyNCwgMTEpLCAoMjQsIDI4KSwgKDI1LCAxMCksICgyNSwgMTcpLCAoMjUsIDIzKSwgKDI1LCAyNyksICgyNiwgMyksCiAgICAgICAoMjYsIDE4KSwgKDI2LCAxOSksICgyOCwgMjYpLCAoMjgsIDExKSwgKDI4LCAyMyksICgyOSwgMiksICgyOSwgNCksCiAgICAgICAoMjksIDExKSwgKDI5LCAxNSksICgyOSwgMTcpLCAoMjksIDIyKSwgKDI5LCAyMyksICgzMCwgMyksICgzMCwgNyksCiAgICAgICAoMzAsIDE3KSwgKDMwLCAyMCksICgzMCwgMjUpLCAoMzAsIDI2KSwgKDMwLCAyOCksICgzMCwgMjkpXQoKICBncmFwaHMuYXBwZW5kKChWLEUpKQoKICAjYWRkIG90aGVyIGdyYXBocyBoZXJlIGZvciB0ZXN0aW5nCgoKICBmb3IgRyBpbiBncmFwaHM6CiAgICBWLEUgPSBHCgogICAgI3NldHMgaW4gcHl0aG9uIGFyZSB1bm9yZGVyZWQgYnV0IGluIHByYWN0aWNlIHRoZWlyIGhhc2hlcyB1c3VhbGx5IG9yZGVyIGludGVnZXJzLgogICAgdG9wX3NldCA9IHRvcHNvcnQoVixFLHNldCkKCiAgICB0b3Bfc3RhY2sgPSB0b3Bzb3J0KFYsRSxzdGFja19jb2xsZWN0aW9uKQoKICAgIHRvcF9xdWV1ZSA9IHRvcHNvcnQoVixFLHF1ZXVlX2NvbGxlY3Rpb24pCgogICAgcmFuZG9tX3Jlc3VsdHMgPSBbXQogICAgZm9yIGkgaW4gcmFuZ2UoMCwxMCk6CiAgICAgIHJhbmRvbV9yZXN1bHRzLmFwcGVuZCh0b3Bzb3J0KFYsRSxyYW5kb21fb3JkZXJkX2NvbGxlY3Rpb24pKQogICAgCiAgICBwcmludAogICAgcHJpbnQgJ1Y6ICcsIFYKICAgIHByaW50ICdFOiAnLCBFCiAgICBwcmludCAndG9wX3NldCAoezB9KTogezF9Jy5mb3JtYXQoaXNfdG9wc29ydGVkKFYsRSx0b3Bfc2V0KSx0b3Bfc2V0KQogICAgcHJpbnQgJ3RvcF9zdGFjayAoezB9KTogezF9Jy5mb3JtYXQoaXNfdG9wc29ydGVkKFYsRSx0b3Bfc3RhY2spLHRvcF9zdGFjaykKICAgIHByaW50ICd0b3BfcXVldWUgKHswfSk6IHsxfScuZm9ybWF0KGlzX3RvcHNvcnRlZChWLEUsdG9wX3F1ZXVlKSx0b3BfcXVldWUpCgogICAgZm9yIHJhbmRvbV9yZXN1bHQgaW4gcmFuZG9tX3Jlc3VsdHM6CiAgICAgIHByaW50ICdyYW5kb21fcmVzdWx0ICh7MH0pOiB7MX0nLmZvcm1hdChpc190b3Bzb3J0ZWQoVixFLHJhbmRvbV9yZXN1bHQpLHJhbmRvbV9yZXN1bHQpCiAgICAgIGFzc2VydCBpc190b3Bzb3J0ZWQoVixFLHJhbmRvbV9yZXN1bHQpCgogICAgYXNzZXJ0IGlzX3RvcHNvcnRlZChWLEUsdG9wX3NldCkKICAgIGFzc2VydCBpc190b3Bzb3J0ZWQoVixFLHRvcF9zdGFjaykKICAgIGFzc2VydCBpc190b3Bzb3J0ZWQoVixFLHRvcF9xdWV1ZSkKICAgIAoKCm1haW4oKQoKCg==