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from collections import namedtuple, defaultdict
class DirectedGraph:
def __init__(self, V, E):
assert all(isinstance(e, tuple) for e in E)
assert all(v1 in V and v2 in V for v1, v2 in E)
self.V = set(V)
self.E = set(E)
self.outgoing = defaultdict(set)
self.incoming = defaultdict(set)
self.neighbors = defaultdict(set)
for v1, v2 in E:
self.outgoing[v1].add(v2)
self.incoming[v2].add(v1)
self.neighbors[v1].add(v2)
self.neighbors[v2].add(v1)
def inverted(self):
return DirectedGraph(self.V, [(v2, v1) for v1, v2 in self.E])
def reachable(self, start_verts):
return self._reachable(start_verts, self.outgoing)
def reachable_inversed(self, start_verts):
return self._reachable(start_verts, self.incoming)
def connected(self, start_verts):
return self._reachable(start_verts, self.neighbors)
def _reachable(self, start_verts, next_map):
if start_verts in self.V:
start_verts = (start_verts, )
assert all(v in self.V for v in start_verts)
verts_to_check = set(start_verts)
found_verts = set()
while len(verts_to_check) > 0:
v = verts_to_check.pop()
found_verts.add(v)
for prev_v in next_map[v]:
if prev_v not in found_verts:
verts_to_check.add(prev_v)
return found_verts
def toposort(self):
return self.toposort_partial(self.V)
def toposort_partial(self, verts_to_sort):
verts_to_sort = set(verts_to_sort)
sorted_verts = list()
temp_marked_verts = set()
finished_verts = set()
def visit(v):
if v in finished_verts:
return
if v in temp_marked_verts:
raise Exception("not a DAG")
temp_marked_verts.add(v)
for prev_v in self.incoming[v]:
visit(prev_v)
finished_verts.add(v)
if v in verts_to_sort:
sorted_verts.append(v)
for v in verts_to_sort:
visit(v)
return tuple(sorted_verts)
class DirectedGraphBuilder:
def __init__(self):
self.V = set()
self.E = set()
def add_vertex(self, v):
self.V.add(v)
def add_directed_edge(self, from_v, to_v):
self.V.add(from_v)
self.V.add(to_v)
self.E.add((from_v, to_v))
def build(self):
return DirectedGraph(self.V, self.E)
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