def test_topological_sort(self):
# cp3 4.4 dag in https://visualgo.net/en/dfsbfs
dg = Digraph()
dg.add_edges_from([(0, 1), (0, 2), (1, 2), (1, 3), (2, 3), (2, 5),
(3, 4), (7, 6)])
self.assertEqual([7, 6, 0, 1, 2, 5, 3, 4], topological_sort(dg))
# cp3 4.17 dag in https://visualgo.net/en/dfsbfs
dg = Digraph()
dg.add_edges_from([(0, 1), (0, 2), (0, 3), (1, 3), (1, 4), (2, 4),
(3, 4)])
self.assertEqual([0, 2, 1, 3, 4], topological_sort(dg))
# cp3 4.18 dag bipartite in https://visualgo.net/en/dfsbfs
dg = Digraph()
dg.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (3, 4)])
self.assertEqual([0, 2, 1, 3, 4], topological_sort(dg))
if v == 0] # vertices with in-degree = 0
for u in list0:
for v in g.neighbors(u):
in_degrees[v] -= 1
if in_degrees[v] == 0:
list0.append(v)
return len(list0) == len(g.vertices)
if __name__ == '__main__':
dress_order = [['shirt', 'tie'], ['tie', 'jacket'], ['belt', 'jacket'],
['shirt', 'belt'], ['undershorts', 'pants'],
['pants', 'shoes'], ['socks', 'shoes']]
g = Digraph()
g.add_edges_from(dress_order)
g.add_vertex('jacket')
g.add_vertex('watch')
g.add_vertex('shoes')
print(g)
print(is_directed_acyclic_graph(g))
print(is_directed_acyclic_dfs(g))
# print(is_directed_acyclic_bfs(g))
# g1 = Digraph()
# g1.add_vertex(1)
# g1.add_vertex(2)
# print(is_directed_acyclic_bfs(g1))
# g2 = Digraph()
# g2.add_edge(1, 2)
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]]
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))
from Graph import Digraph
def topological_sort(g):
def dfs(g, u):
seen.add(u)
for v in g.neighbors(u):
if v not in seen:
dfs(g, v)
sortedv.appendleft(u)
seen = set()
sortedv = deque()
for u in g.vertices:
if u not in seen:
dfs(g, u)
return list(sortedv)
if __name__ == '__main__':
dress_order = [['shirt', 'tie'], ['tie', 'jacket'], ['belt', 'jacket'],
['shirt', 'belt'], ['undershorts', 'pants'],
['pants', 'shoes'], ['socks', 'shoes']]
g = Digraph()
g.add_edges_from(dress_order)
g.add_vertex('jacket')
g.add_vertex('watch')
g.add_vertex('shoes')
print(g)
print(topological_sort(g))
for v in g.neighbors(u):
queue.append((v, path + [v]))
return paths
# def all_simple_paths_bfs(g, s, t):
# seen = set()
# paths = []
# queue = deque([(s, s)])
# while queue:
# u, path = queue.popleft()
# if u == t:
# paths.append(path)
# else:
# for v in g.neighbors(u):
# if v not in seen:
# queue.append((v, path + v))
# seen.add(v)
# return paths
if __name__ == '__main__':
g = Digraph() # clrs Figure 22.8
g.add_edges_from([
('m', 'q'), ('m', 'r'), ('m', 'x'), ('n', 'o'), ('n', 'q'), ('n', 'u'),
('o', 'r'), ('o', 's'), ('o', 'v'), ('p', 'o'), ('p', 's'), ('p', 'z'),
('q', 't'), ('r', 'u'), ('r', 'y'), ('s', 'r'), ('v', 'w'), ('v', 'x'),
('y', 'v')
])
print(all_simple_paths_dfs(g, 'p', 'v'))
print(all_simple_paths_bfs(g, 'p', 'v'))
def dfs_tree(g, src):
def dfs(g, u):
for v in g.neighbors(u):
if v not in seen:
tree.add_edge(u, v)
seen.add(v)
dfs(g, v)
tree = Graph()
tree.add_vertex(src)
seen = {src}
dfs(g, src)
return tree
if __name__ == '__main__':
# dg = Digraph() # clrs book example
# dg.add_edges_from([('u', 'v'), ('u', 'x'), ('v', 'y'), ('w', 'y'),
# ('w', 'z'), ('x', 'v'), ('y', 'x'), ('z', 'z')])
# t = dfs_tree(dg, 'u')
# print(t.vertices)
# print(t.edges)
dg = Digraph()
# dg.add_edges_from([(0, 1), (1, 0), (2, 1)])
dg.add_edges_from([(1, 0), (1, 4), (4, 0), (4, 2)])
t = dfs_tree(dg, 0)
print(t.vertices)
print(t.edges)
# The transpose of a directed graph G=(V, E) is the graph Gᵀ = (V, Eᵀ) , where
# Eᵀ = {(v,u) ∈ V x V : (u,v) ∈ E}. Thus, GT is G with all its edges reversed.
from Graph import Digraph
def transpose(g):
gt = Digraph()
for u in g.vertices:
gt.add_vertex(u)
for u, v in g.edges:
gt.add_edge(v, u, g.weight(u, v))
return gt
if __name__ == '__main__':
g = Digraph()
g.add_edges_from([
('a', 'b'), ('b', 'c'), ('b', 'e'), ('b', 'f'), ('c', 'd'), ('c', 'g'),
('d', 'c'), ('d', 'h'), ('e', 'a'), ('e', 'f'), ('f', 'g'), ('g', 'f'),
('g', 'h'), ('h', 'h')
])
gt = transpose(g)
print(gt.edges)