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Topological sorting is the answer to the following question : in a direct acyclic graph, how can I pick up nodes "in order", such as upstream nodes are always before downstream ones ? Many solutions may exists, many algorithms too.

Alas, it seems I'm too stupid to understand already proposed recipes on topological sorting. Hopefully I do grasp the "write once, read many" concept.

Here, you will find a plain algorithm, optimized only for code clarity, of a topological sorting for direct acyclic graphs, implemented in python from the pseudo code found on wikipedia:

``````L ← Empty list that will contain the sorted elements
S ← Set of all nodes with no incoming edges
while S is non-empty do
remove a node n from S
insert n into L
for each node m with an edge e from n to m do
remove edge e from the graph
if m has no other incoming edges then
insert m into S
if graph has edges then
return error (graph has at least one cycle)
else
return L (a topologically sorted order)
``````

Only tested with python3.2, should work with other versions. Be careful, code indented with tabs, since space is evil è_é

Python, 48 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48``` ```#!/usr/bin/env python3.2 def sort_direct_acyclic_graph(edge_list) : # edge_set is consummed, need a copy edge_set = set([tuple(i) for i in edge_list]) # node_list will contain the ordered nodes node_list = list() # source_set is the set of nodes with no incomming edges node_from_list, node_to_list = zip(* edge_set) source_set = set(node_from_list) - set(node_to_list) while len(source_set) != 0 : # pop node_from off source_set and insert it in node_list node_from = source_set.pop() node_list.append(node_from) # find nodes which have a common edge with node_from from_selection = [e for e in edge_set if e[0] == node_from] for edge in from_selection : # remove the edge from the graph node_to = edge[1] edge_set.discard(edge) # if node_to don't have any remaining incomming edge : to_selection = [e for e in edge_set if e[1] == node_to] if len(to_selection) == 0 : # add node_to to source_set source_set.add(node_to) if len(edge_set) != 0 : raise IndexError # not a direct acyclic graph else : return node_list u = [ ['a', 'b'], # a -> b, etc. ['a', 'c'], ['b', 'e'], ['c', 'd'], ['b', 'd'], ['e', 'f'], ['c', 'f'], ] >>> sort_direct_acyclic_graph(u) ['a', 'c', 'b', 'e', 'd', 'f'] ```
 Created by yota on Mon, 7 Jan 2013 (GPL3)

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