129 lines
4.1 KiB
Python
129 lines
4.1 KiB
Python
# Adapted from mypy (mypy/build.py) under the MIT license.
|
|
|
|
from typing import *
|
|
|
|
|
|
def strongly_connected_components(
|
|
vertices: AbstractSet[str], edges: Dict[str, AbstractSet[str]]
|
|
) -> Iterator[AbstractSet[str]]:
|
|
"""Compute Strongly Connected Components of a directed graph.
|
|
|
|
Args:
|
|
vertices: the labels for the vertices
|
|
edges: for each vertex, gives the target vertices of its outgoing edges
|
|
|
|
Returns:
|
|
An iterator yielding strongly connected components, each
|
|
represented as a set of vertices. Each input vertex will occur
|
|
exactly once; vertices not part of a SCC are returned as
|
|
singleton sets.
|
|
|
|
From https://github.com/ActiveState/code/tree/master/recipes/Python/578507_Strongly_connected_components_directed/recipe-578507.py.
|
|
"""
|
|
identified: Set[str] = set()
|
|
stack: List[str] = []
|
|
index: Dict[str, int] = {}
|
|
boundaries: List[int] = []
|
|
|
|
def dfs(v: str) -> Iterator[Set[str]]:
|
|
index[v] = len(stack)
|
|
stack.append(v)
|
|
boundaries.append(index[v])
|
|
|
|
for w in edges[v]:
|
|
if w not in index:
|
|
yield from dfs(w)
|
|
elif w not in identified:
|
|
while index[w] < boundaries[-1]:
|
|
boundaries.pop()
|
|
|
|
if boundaries[-1] == index[v]:
|
|
boundaries.pop()
|
|
scc = set(stack[index[v] :])
|
|
del stack[index[v] :]
|
|
identified.update(scc)
|
|
yield scc
|
|
|
|
for v in vertices:
|
|
if v not in index:
|
|
yield from dfs(v)
|
|
|
|
|
|
def topsort(
|
|
data: Dict[AbstractSet[str], Set[AbstractSet[str]]]
|
|
) -> Iterable[AbstractSet[AbstractSet[str]]]:
|
|
"""Topological sort.
|
|
|
|
Args:
|
|
data: A map from SCCs (represented as frozen sets of strings) to
|
|
sets of SCCs, its dependencies. NOTE: This data structure
|
|
is modified in place -- for normalization purposes,
|
|
self-dependencies are removed and entries representing
|
|
orphans are added.
|
|
|
|
Returns:
|
|
An iterator yielding sets of SCCs that have an equivalent
|
|
ordering. NOTE: The algorithm doesn't care about the internal
|
|
structure of SCCs.
|
|
|
|
Example:
|
|
Suppose the input has the following structure:
|
|
|
|
{A: {B, C}, B: {D}, C: {D}}
|
|
|
|
This is normalized to:
|
|
|
|
{A: {B, C}, B: {D}, C: {D}, D: {}}
|
|
|
|
The algorithm will yield the following values:
|
|
|
|
{D}
|
|
{B, C}
|
|
{A}
|
|
|
|
From https://github.com/ActiveState/code/tree/master/recipes/Python/577413_Topological_Sort/recipe-577413.py.
|
|
"""
|
|
# TODO: Use a faster algorithm?
|
|
for k, v in data.items():
|
|
v.discard(k) # Ignore self dependencies.
|
|
for item in set.union(*data.values()) - set(data.keys()):
|
|
data[item] = set()
|
|
while True:
|
|
ready = {item for item, dep in data.items() if not dep}
|
|
if not ready:
|
|
break
|
|
yield ready
|
|
data = {item: (dep - ready) for item, dep in data.items() if item not in ready}
|
|
assert not data, "A cyclic dependency exists amongst %r" % data
|
|
|
|
|
|
def find_cycles_in_scc(
|
|
graph: Dict[str, AbstractSet[str]], scc: AbstractSet[str], start: str
|
|
) -> Iterable[List[str]]:
|
|
"""Find cycles in SCC emanating from start.
|
|
|
|
Yields lists of the form ['A', 'B', 'C', 'A'], which means there's
|
|
a path from A -> B -> C -> A. The first item is always the start
|
|
argument, but the last item may be another element, e.g. ['A',
|
|
'B', 'C', 'B'] means there's a path from A to B and there's a
|
|
cycle from B to C and back.
|
|
"""
|
|
# Basic input checks.
|
|
assert start in scc, (start, scc)
|
|
assert scc <= graph.keys(), scc - graph.keys()
|
|
|
|
# Reduce the graph to nodes in the SCC.
|
|
graph = {src: {dst for dst in dsts if dst in scc} for src, dsts in graph.items() if src in scc}
|
|
assert start in graph
|
|
|
|
# Recursive helper that yields cycles.
|
|
def dfs(node: str, path: List[str]) -> Iterator[List[str]]:
|
|
if node in path:
|
|
yield path + [node]
|
|
return
|
|
path = path + [node] # TODO: Make this not quadratic.
|
|
for child in graph[node]:
|
|
yield from dfs(child, path)
|
|
|
|
yield from dfs(start, [])
|