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Topological sort with Python (using DFS and gray/black colors)
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# 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!" |
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