def test_euler_undirected(self):
graph = Graph()
for i in range(7, -1, -1):
graph.add_vertex(Vertex(i))
graph.add_2_edges(0, 1)
graph.add_2_edges(1, 2)
graph.add_2_edges(0, 3)
graph.add_2_edges(1, 3)
graph.add_2_edges(1, 4)
graph.add_2_edges(2, 4)
graph.add_2_edges(3, 5)
graph.add_2_edges(3, 6)
graph.add_2_edges(4, 6)
graph.add_2_edges(4, 7)
graph.add_2_edges(5, 6)
graph.add_2_edges(6, 7)
self.assertSequenceEqual([0, 1, 2, 4, 6, 3, 5, 6, 7, 4, 1, 3, 0],
euler_tour_undirected(graph))
graph = Graph()
for i in range(6):
graph.add_vertex(Vertex(i))
graph.add_2_edges(0, 1)
graph.add_2_edges(0, 2)
graph.add_2_edges(0, 3)
graph.add_2_edges(0, 4)
graph.add_2_edges(1, 2)
graph.add_2_edges(1, 3)
graph.add_2_edges(1, 4)
graph.add_2_edges(2, 3)
graph.add_2_edges(3, 4)
graph.add_2_edges(2, 5)
graph.add_2_edges(4, 5)
self.assertSequenceEqual([0, 1, 2, 3, 4, 5, 2, 0, 3, 1, 4, 0],
euler_tour_undirected(graph))
def get_transpose(graph: Graph):
"""Ex 22.1-3."""
tr = Graph()
for v in graph.vertex_keys():
tr.add_vertex(Vertex(v))
for u in graph.vertex_keys():
for v, weight in graph.get_vertex(u).successors():
tr.add_edge(v, u, weight)
return tr
def graph_from_adj_matrix(adj_matrix) -> Graph:
vertex_count = len(adj_matrix)
graph = Graph()
for i in range(vertex_count):
graph.add_vertex(Vertex(i))
for i in range(vertex_count):
for j in range(vertex_count):
if adj_matrix[i][j]:
graph.add_edge(i, j)
return graph
def test_mohammed_scimitars(self):
graph = Graph()
for i in range(11):
graph.add_vertex(Vertex(i))
for edge in ((0, 1), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (3, 5),
(3, 6), (4, 5), (4, 8), (5, 6), (5, 8), (6, 7), (6, 10),
(7, 8), (7, 9), (7, 10), (8, 9)):
graph.add_2_edges(edge[0], edge[1])
self.assertSequenceEqual(
[0, 1, 2, 3, 5, 4, 8, 7, 6, 10, 7, 9, 8, 5, 6, 3, 1, 4, 0],
euler_tour_undirected(graph))
def _graph_from_figure_22_9() -> Graph:
graph = Graph()
graph.add_vertex(Vertex('a'))
graph.add_vertex(Vertex('b'))
graph.add_vertex(Vertex('c'))
graph.add_vertex(Vertex('d'))
graph.add_vertex(Vertex('e'))
graph.add_vertex(Vertex('f'))
graph.add_vertex(Vertex('g'))
graph.add_vertex(Vertex('h'))
graph.add_edge('a', 'b')
graph.add_edge('b', 'c')
graph.add_edge('b', 'e')
graph.add_edge('b', 'f')
graph.add_edge('c', 'd')
graph.add_edge('c', 'g')
graph.add_edge('d', 'c')
graph.add_edge('d', 'h')
graph.add_edge('e', 'a')
graph.add_edge('e', 'f')
graph.add_edge('f', 'g')
graph.add_edge('g', 'f')
graph.add_edge('g', 'h')
graph.add_edge('h', 'h')
return graph
def test_bfs(self):
# Figure 22-3
graph = Graph()
graph.add_vertex(Vertex('r'))
graph.add_vertex(Vertex('s'))
graph.add_vertex(Vertex('t'))
graph.add_vertex(Vertex('u'))
graph.add_vertex(Vertex('v'))
graph.add_vertex(Vertex('w'))
graph.add_vertex(Vertex('x'))
graph.add_vertex(Vertex('y'))
graph.add_2_edges('r', 's')
graph.add_2_edges('r', 'v')
graph.add_2_edges('s', 'w')
graph.add_2_edges('t', 'u')
graph.add_2_edges('t', 'w')
graph.add_2_edges('t', 'x')
graph.add_2_edges('u', 'x')
graph.add_2_edges('u', 'y')
graph.add_2_edges('w', 'x')
graph.add_2_edges('x', 'y')
came_from = bfs_with_src(graph, 's')[0]
self.assertDictEqual({
'v': 'r',
'r': 's',
'w': 's',
't': 'w',
'x': 'w',
'y': 'x',
'u': 't',
}, came_from)
def test_topological_sort_with_loop(self):
cases = []
graph = Graph()
graph.add_vertex(Vertex(0))
graph.add_edge(0, 0)
cases.append(graph)
graph = self._graph_from_figure_22_8()
graph.add_edge("v", "p") # Add an edge to form a loop
cases.append(graph)
for graph in cases:
self.assertLess(len(topological_sort_kahn(graph)),
graph.vertex_len)
def terrain_to_graph(terrain):
graph = Graph()
if not terrain or not terrain[0]:
return graph
h = len(terrain)
w = len(terrain[0])
for x in range(0, w):
for y in range(0, h):
graph.add_vertex(Vertex((x, y)))
for x in range(0, w):
for y in range(0, h):
if terrain[y][x] < 0:
continue
if x - 1 >= 0 and terrain[y][x - 1] >= 0:
graph.add_edge((x, y), (x - 1, y), terrain[y][x])
if y - 1 >= 0 and terrain[y - 1][x] >= 0:
graph.add_edge((x, y), (x, y - 1), terrain[y][x])
if x + 1 < w and terrain[y][x + 1] >= 0:
graph.add_edge((x, y), (x + 1, y), terrain[y][x])
if y + 1 < h and terrain[y + 1][x] >= 0:
graph.add_edge((x, y), (x, y + 1), terrain[y][x])
return graph
def test_tree_diameter(self):
methods = (tree_diameter_recur, tree_diameter_bfs)
tree = Graph()
for i in range(0, 16):
tree.add_vertex(Vertex(i))
tree.add_2_edges(0, 1)
tree.add_2_edges(0, 2)
tree.add_2_edges(0, 3)
tree.add_2_edges(1, 4)
tree.add_2_edges(1, 5)
tree.add_2_edges(2, 6)
tree.add_2_edges(3, 7)
tree.add_2_edges(3, 8)
tree.add_2_edges(4, 9)
tree.add_2_edges(5, 10)
tree.add_2_edges(5, 11)
tree.add_2_edges(6, 12)
tree.add_2_edges(6, 13)
tree.add_2_edges(6, 14)
tree.add_2_edges(14, 15)
for tree_diameter_method in methods:
for root in range(0, 16):
# print('root: %d' % root)
self.assertEqual(7, tree_diameter_method(tree, root))
def dijkstra_basic_test_case():
graph = Graph()
vertices = [Vertex(i) for i in range(1, 8)]
for v in vertices:
graph.add_vertex(v)
graph.add_edge(1, 2, 7)
graph.add_edge(2, 1, 7)
graph.add_edge(1, 3, 9)
graph.add_edge(3, 1, 9)
graph.add_edge(1, 6, 14)
graph.add_edge(6, 1, 14)
graph.add_edge(2, 3, 10)
graph.add_edge(3, 2, 10)
graph.add_edge(2, 4, 15)
graph.add_edge(4, 2, 15)
graph.add_edge(3, 4, 11)
graph.add_edge(4, 3, 11)
graph.add_edge(3, 6, 2)
graph.add_edge(6, 3, 2)
graph.add_edge(4, 5, 6)
graph.add_edge(5, 4, 6)
graph.add_edge(5, 6, 9)
graph.add_edge(6, 5, 9)
src = 1
expected_results = {
1: (1, ),
2: (1, 2),
3: (1, 3),
4: (1, 3, 4),
5: (1, 3, 6, 5),
6: (1, 3, 6),
7: (),
}
return graph, src, expected_results
def test_dfs(self):
graph = Graph()
graph.add_vertex(Vertex('s'))
graph.add_vertex(Vertex('t'))
graph.add_vertex(Vertex('u'))
graph.add_vertex(Vertex('v'))
graph.add_vertex(Vertex('w'))
graph.add_vertex(Vertex('x'))
graph.add_vertex(Vertex('y'))
graph.add_vertex(Vertex('z'))
graph.add_edge('z', 'y')
graph.add_edge('s', 'z')
graph.add_edge('y', 'x')
graph.add_edge('x', 'z')
graph.add_edge('z', 'w')
graph.add_edge('s', 'w')
graph.add_edge('v', 's')
graph.add_edge('t', 'v')
graph.add_edge('t', 'u')
graph.add_edge('u', 't')
graph.add_edge('w', 'x')
graph.add_edge('v', 'w')
graph.add_edge('u', 'v')
pre_visit_array = []
def pre_visit(v):
pre_visit_array.append(v)
return True
post_visit_array = []
def post_visit(v):
post_visit_array.append(v)
return True
result = dfs(graph, pre_visit, post_visit)
expected_result = DFSResult()
expected_result.discover_times = {
's': 1,
'w': 2,
'x': 3,
'z': 4,
'y': 5,
't': 11,
'u': 12,
'v': 13
}
expected_result.finish_times = {
'y': 6,
'z': 7,
'x': 8,
'w': 9,
's': 10,
'v': 14,
'u': 15,
't': 16
}
expected_result.came_from = {
's': None,
'w': 's',
'x': 'w',
'z': 'x',
'y': 'z',
't': None,
'u': 't',
'v': 'u'
}
expected_pre_visit_array = ['s', 'w', 'x', 'z', 'y', 't', 'u', 'v']
expected_post_visit_array = ['y', 'z', 'x', 'w', 's', 'v', 'u', 't']
self.assertEqual(expected_result, result)
self.assertSequenceEqual(expected_pre_visit_array, pre_visit_array)
self.assertSequenceEqual(expected_post_visit_array, post_visit_array)
def _graph_from_figure_22_8(self):
graph = Graph()
graph.add_vertex(Vertex("m"))
graph.add_vertex(Vertex("n"))
graph.add_vertex(Vertex("o"))
graph.add_vertex(Vertex("p"))
graph.add_vertex(Vertex("q"))
graph.add_vertex(Vertex("r"))
graph.add_vertex(Vertex("s"))
graph.add_vertex(Vertex("t"))
graph.add_vertex(Vertex("u"))
graph.add_vertex(Vertex("v"))
graph.add_vertex(Vertex("w"))
graph.add_vertex(Vertex("x"))
graph.add_vertex(Vertex("y"))
graph.add_vertex(Vertex("z"))
graph.add_edge("m", "q")
graph.add_edge("m", "r")
graph.add_edge("m", "x")
graph.add_edge("n", "o")
graph.add_edge("n", "q")
graph.add_edge("n", "u")
graph.add_edge("o", "r")
graph.add_edge("o", "s")
graph.add_edge("o", "v")
graph.add_edge("p", "o")
graph.add_edge("p", "s")
graph.add_edge("p", "z")
graph.add_edge("q", "t")
graph.add_edge("r", "u")
graph.add_edge("r", "y")
graph.add_edge("s", "r")
graph.add_edge("u", "t")
graph.add_edge("v", "w")
graph.add_edge("v", "x")
graph.add_edge("w", "z")
graph.add_edge("y", "v")
return graph
def _graph_from_figure_22_7(self):
graph = Graph()
graph.add_vertex(Vertex("undershorts"))
graph.add_vertex(Vertex("socks"))
graph.add_vertex(Vertex("watch"))
graph.add_vertex(Vertex("pants"))
graph.add_vertex(Vertex("shoes"))
graph.add_vertex(Vertex("belt"))
graph.add_vertex(Vertex("shirt"))
graph.add_vertex(Vertex("tie"))
graph.add_vertex(Vertex("jacket"))
graph.add_edge("undershorts", "pants")
graph.add_edge("undershorts", "shoes")
graph.add_edge("socks", "shoes")
graph.add_edge("pants", "shoes")
graph.add_edge("pants", "belt")
graph.add_edge("shirt", "belt")
graph.add_edge("shirt", "tie")
graph.add_edge("tie", "jacket")
graph.add_edge("belt", "jacket")
return graph