# 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://code.activestate.com/recipes/578507-strongly-connected-components-of-a-directed-graph/.
"""
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://code.activestate.com/recipes/577413-topological-sort/history/1/.
"""
# 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, [])
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