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Topological sort with Python (using DFS and gray/black colors)
# Simple:
# a --> b
# --> c --> d
# --> d
graph1 = {
"a": ["b", "c", "d"],
"b": [],
"c": ["d"],
"d": []
}
# 2 components
graph2 = {
"a": ["b", "c", "d"],
"b": [],
"c": ["d"],
"d": [],
"e": ["g", "f", "q"],
"g": [],
"f": [],
"q": []
}
# cycle
graph3 = {
"a": ["b", "c", "d"],
"b": [],
"c": ["d", "e"],
"d": [],
"e": ["g", "f", "q"],
"g": ["c"],
"f": [],
"q": []
}
from collections import deque
GRAY, BLACK = 0, 1
def topological(graph):
order, enter, state = deque(), set(graph), {}
def dfs(node):
state[node] = GRAY
for k in graph.get(node, ()):
sk = state.get(k, None)
if sk == GRAY: raise ValueError("cycle")
if sk == BLACK: continue
enter.discard(k)
dfs(k)
order.appendleft(node)
state[node] = BLACK
while enter: dfs(enter.pop())
return order
# check how it works
print topological(graph1)
print topological(graph2)
try: topological(graph3)
except ValueError: print "Cycle!"
# The MIT License (MIT)
# Copyright (c) 2014 Alexey Kachayev
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation
# files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy,
# modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software
# is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
# WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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