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ConnectedComponents.py
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ConnectedComponents.py
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from collections import deque
from DisjointSet import DisjointSet
from Graph import Graph, Digraph
from Transpose import transpose
# def is_connected(g):
# """
# An undirected graph is connected if every vertex is reachable from all other vertices.
#
# :param g: input Graph
# :return: True if the graph is connected, False otherwise.
# """
#
# def dfs(g, u):
# seen.add(u)
# for v in g.neighbors(u):
# if v not in seen:
# dfs(g, v)
#
# count = 0
# seen = set()
# for u in g.vertices:
# if u not in seen:
# count += 1 # count connected components
# if count > 1:
# return False
# dfs(g, u)
# return True
def is_connected(g):
"""
An undirected graph is connected if every vertex is reachable from all other vertices.
:param g: input Graph
:return: True if the graph is connected, False otherwise.
"""
def dfs(g, u):
seen.add(u)
for v in g.neighbors(u):
if v not in seen:
dfs(g, v)
first_pass = True
seen = set()
for u in g.vertices:
if u not in seen:
if first_pass:
first_pass = False
else:
return False
dfs(g, u)
return True
def is_connected_bfs(g):
visited = set()
first_pass = True
q = deque()
for u in g.vertices:
if u not in visited:
if first_pass:
first_pass = False
else:
return False
q.append(u)
visited.add(u)
while q:
u = q.popleft()
for v in g.neighbors(u):
if v not in visited:
q.append(v)
visited.add(v)
return True
def connected_components(g):
"""
The connected components of a graph represent pieces of a graph. Two vertices are in the same
component of a graph if and only if there exists some path between them.
:param g: input Graph
:return: list of sets contaning the connected vertices
"""
def dfs(g, u):
seen.add(u)
conns[-1].append(u)
for v in g.neighbors(u):
if v not in seen:
dfs(g, v)
conns = []
seen = set()
for u in g.vertices:
if u not in seen:
conns.append([])
dfs(g, u)
return conns
def connected_components_bfs(g):
visited = set()
conns = []
q = deque()
for u in g.vertices:
if u not in visited:
visited.add(u)
conns.append([u])
q.append(u)
while q:
u = q.popleft()
for v in g.neighbors(u):
if v not in visited:
visited.add(v)
conns[-1].append(v)
q.append(v)
return conns
def connected_components_dj(g):
djset = DisjointSet()
for v in g.vertices:
djset.make_set(v)
for v1, v2 in g.edges:
if djset.find_set(v1) != djset.find_set(v2):
djset.union(v1, v2)
return djset.get_set()
def strongly_connected_components(g):
"""
The strongly connected components of a directed graph are the equivalence classes of
vertices under the “are mutually reachable” relation.
:param g: input graph
:return: list of sets containing the strongly connected vertices
"""
def dfs(g, u):
seen.add(u)
for v in g.neighbors(u):
if v not in seen:
dfs(g, v)
verts.appendleft(u)
def dfs_gt(gt, u):
seen.add(u)
conns[-1].append(u)
for v in gt.neighbors(u):
if v not in seen:
dfs_gt(gt, v)
seen = set()
verts = deque() # vertices in order of decreasing finishing time
for u in g.vertices:
if u not in seen:
dfs(g, u)
gt = transpose(g)
seen = set()
conns = []
for u in verts:
if u not in seen:
conns.append([])
dfs_gt(gt, u)
return conns
if __name__ == '__main__':
g = Graph()
g.add_edges_from([('a', 'b'), ('a', 'c'), ('b', 'c'), ('b', 'd'),
('e', 'f'), ('e', 'g'), ('h', 'i')])
g.add_vertex('j')
print(f'connected: {is_connected(g)}')
# print(connected_components_dj(g))
print(connected_components(g))
assert connected_components(g) == [['a', 'b', 'c', 'd'], ['e', 'f', 'g'], ['h', 'i'], ['j']]
g = Graph() # clrs Figure B.2(b)
g.add_edges_from([(1, 2), (1, 5), (2, 5), (3, 6)])
g.add_vertex(4)
print(f'connected: {is_connected(g)}')
# print(connected_components_dj(g))
print(connected_components(g))
print(connected_components_bfs(g))
assert connected_components(g) == [[1, 2, 5], [3, 6], [4]]
g = Graph()
g.add_edges_from([(1, 2), (1, 5), (2, 3), (2, 5), (3, 6), (4, 5)])
print(f'connected: {is_connected(g)}')
# print(connected_components_dj(g))
print(connected_components(g))
assert connected_components(g) == [[1, 2, 3, 6, 5, 4]]
print(connected_components_bfs(g))
assert connected_components_bfs(g) == [[1, 2, 5, 3, 4, 6]]
print(connected_components_dj(g))
assert connected_components_dj(g) == [{1, 2, 5, 3, 4, 6}]
dg = Digraph()
dg.add_edges_from([('a', 'b'), ('b', 'c'), ('b', 'e'), ('c', 'd'), ('c', 'g'), ('d', 'c'), ('d', 'h'),
('e', 'a'), ('e', 'f'), ('f', 'g'), ('g', 'f'), ('g', 'h'), ('h', 'h'), ])
print(strongly_connected_components(dg))
assert strongly_connected_components(dg) == [['a', 'e', 'b'], ['c', 'd'], ['g', 'f'], ['h']]
dg = Digraph()
dg.add_edges_from([(0, 1), (1, 3), (2, 1), (3, 2), (3, 4), (4, 5), (5, 7), (6, 4), (7, 6)])
print(strongly_connected_components(dg))
assert strongly_connected_components(dg) == [[0], [1, 2, 3], [4, 6, 7, 5]]
dg = Digraph()
dg.add_edges_from([(0, 1), (0, 2), (0, 3), (1, 3), (1, 4), (2, 4), (3, 4)])
print(strongly_connected_components(dg))
assert strongly_connected_components(dg) == [[0], [2], [1], [3], [4]]