def setUp(self):
self.graph = DirectedGraph()
self.edges = [
# (source, destination, weight)
('A', 'B', 1),
('A', 'C', 1),
('B', 'C', 1),
('B', 'D', 1),
('B', 'I', 1),
('C', 'D', 1),
('D', 'C', 1),
('D', 'H', 1),
('H', 'I', 1),
('E', 'A', 1),
('E', 'F', 1),
('F', 'C', 1),
('F', 'G', 1),
]
self.vertices = set()
for source, destination, weight in self.edges:
self.vertices.add(source)
self.vertices.add(destination)
self.graph.add_vertex(source, value=source)
self.graph.add_vertex(destination, value=destination)
self.graph.add_edge(source, destination, weight)
def test_find_shortest_paths_bfs(self):
graph = DirectedGraph()
edges = [ # https://cs.stackexchange.com/questions/18138/dijkstra-algorithm-vs-breadth-first-search-for-shortest-path-in-graph
('A', 'B', 1),
('B', 'C', 1),
('B', 'D', 1),
('B', 'E', 1),
('C', 'E', 1),
('D', 'E', 1),
('E', 'F', 1),
('G', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_paths_bfs('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'B', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'B', 'D'])
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'A', 'G')
def test_find_shortest_path_dijkstra(self):
graph = DirectedGraph()
edges = [ # https://www.chegg.com/homework-help/questions-and-answers/8-4-14-10-2-figure-2-directed-graph-computing-shortest-path-3-dijkstra-s-algorithm-computi-q25960616#question-transcript
('A', 'B', 4),
('B', 'C', 11),
('B', 'D', 9),
('C', 'A', 8),
('D', 'C', 7),
('D', 'E', 2),
('D', 'F', 6),
('E', 'B', 8),
('E', 'G', 7),
('E', 'H', 4),
('F', 'C', 1),
('F', 'E', 5),
('G', 'H', 14),
('G', 'I', 9),
('H', 'F', 2),
('H', 'I', 10),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
# There is no such path.
with self.assertRaises(ValueError):
graph.find_shortest_path_dijkstra('I', 'A')
path = graph.find_shortest_path_dijkstra('A', 'I')
self.assertEqual(path, ['A', 'B', 'D', 'E', 'H', 'I'])
path = graph.find_shortest_path_dijkstra('E', 'C')
self.assertEqual(path, ['E', 'H', 'F', 'C'])
def test_has_cycles_dfs(self):
self.assertEqual(self.graph.has_cycles_dfs(), True)
graph = DirectedGraph()
edges = [
('A', 'A', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
self.assertEqual(graph.has_cycles_dfs(), True)
graph = DirectedGraph()
edges = [
('A', 'B', 1),
('B', 'C', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
self.assertEqual(graph.has_cycles_dfs(), False)
def test_find_shortest_paths_bfs(self):
graph = DirectedGraph()
edges = [ # https://www.geeksforgeeks.org/shortest-path-unweighted-graph/
(0, 1, 1),
(0, 3, 1),
(1, 0, 1),
(1, 2, 1),
(2, 1, 1),
(3, 0, 1),
(3, 4, 1),
(3, 7, 1),
(4, 3, 1),
(4, 5, 1),
(4, 6, 1),
(4, 7, 1),
(5, 4, 1),
(5, 6, 1),
(6, 4, 1),
(6, 5, 1),
(6, 7, 1),
(7, 3, 1),
(7, 4, 1),
(7, 6, 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_paths_bfs(0)
path = graph.construct_path(previous, 0, 5)
self.assertEqual(path, [0, 3, 4, 5])
path = graph.construct_path(previous, 0, 7)
self.assertEqual(path, [0, 3, 7])
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 0, 10)
class TestCase(unittest.TestCase):
def setUp(self):
self.graph = DirectedGraph()
self.edges = [
# (source, destination, weight)
('A', 'B', 1),
('A', 'C', 1),
('B', 'C', 1),
('B', 'D', 1),
('B', 'I', 1),
('C', 'D', 1),
('D', 'C', 1),
('D', 'H', 1),
('H', 'I', 1),
('E', 'A', 1),
('E', 'F', 1),
('F', 'C', 1),
('F', 'G', 1),
]
self.vertices = set()
for source, destination, weight in self.edges:
self.vertices.add(source)
self.vertices.add(destination)
self.graph.add_vertex(source, value=source)
self.graph.add_vertex(destination, value=destination)
self.graph.add_edge(source, destination, weight)
def test_add_vertex(self):
self.graph.add_vertex('X')
self.assertEqual(self.graph.vertex_count(), len(self.vertices) + 1)
def test_add_edge(self):
self.graph.add_vertex('X', value='X')
self.graph.add_vertex('Y', value='Y')
self.graph.add_edge('X', 'Y', 0)
self.assertEqual(self.graph.vertex_count(), len(self.vertices) + 2)
self.assertEqual(self.graph.edge_count(), len(self.edges) + 1)
def test_remove_vertex(self):
self.graph.remove_vertex('C')
self.assertEqual(self.graph.vertex_count(), len(self.vertices) - 1)
edge_count = 0
for source, destination, _ in self.edges:
if not source == 'C' and not destination == 'C':
edge_count += 1
self.assertEqual(self.graph.edge_count(), edge_count)
def test_remove_edge(self):
self.graph.remove_edge('A', 'B')
self.assertEqual(self.graph.edge_count(), len(self.edges) - 1)
with self.assertRaises(ValueError):
self.graph.remove_edge('Z', 'Z')
def test_vertex_count(self):
self.assertEqual(self.graph.vertex_count(), len(self.vertices))
def test_edge_count(self):
self.assertEqual(self.graph.edge_count(), len(self.edges))
def test_vertices(self):
self.assertCountEqual(self.graph.vertices(), self.vertices)
def test_edges(self):
self.assertCountEqual(self.graph.edges(), self.edges)
def test_incident_edges(self):
vertex = 'A'
outgoing_edges = [edge for edge in self.edges if edge[0] == vertex]
self.assertCountEqual(
self.graph.incident_edges(vertex, edge_type='outgoing'),
outgoing_edges)
incoming_edges = [edge for edge in self.edges if edge[1] == vertex]
self.assertCountEqual(
self.graph.incident_edges(vertex, edge_type='incoming'),
incoming_edges)
self.assertCountEqual(
self.graph.incident_edges('NOT EXIST', edge_type='outgoing'), [])
self.assertCountEqual(
self.graph.incident_edges('NOT EXIST', edge_type='incoming'), [])
def test_edge_weight(self):
for source, destination, weight in self.edges:
self.assertEqual(self.graph.edge_weight(source, destination),
weight)
with self.assertRaises(ValueError):
self.graph.edge_weight('NOT EXIST', 'NOT EXIST')
def test_depth_first_search(self):
v = 'A'
visited = self.graph.depth_first_search(v)
self.assertCountEqual(visited, ['A', 'B', 'C', 'D', 'H', 'I'])
v = 'E'
visited = self.graph.depth_first_search(v)
self.assertCountEqual(visited,
['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I'])
def test_breadth_first_search(self):
v = 'A'
visited = self.graph.breadth_first_search(v)
self.assertCountEqual(visited, ['A', 'B', 'C', 'D', 'H', 'I'])
v = 'E'
visited = self.graph.breadth_first_search(v)
self.assertCountEqual(visited,
['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I'])
def test_has_cycles_dfs(self):
self.assertEqual(self.graph.has_cycles_dfs(), True)
graph = DirectedGraph()
edges = [
('A', 'A', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
self.assertEqual(graph.has_cycles_dfs(), True)
graph = DirectedGraph()
edges = [
('A', 'B', 1),
('B', 'C', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
self.assertEqual(graph.has_cycles_dfs(), False)
def test_find_shortest_paths_bfs(self):
graph = DirectedGraph()
edges = [ # https://cs.stackexchange.com/questions/18138/dijkstra-algorithm-vs-breadth-first-search-for-shortest-path-in-graph
('A', 'B', 1),
('B', 'C', 1),
('B', 'D', 1),
('B', 'E', 1),
('C', 'E', 1),
('D', 'E', 1),
('E', 'F', 1),
('G', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_paths_bfs('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'B', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'B', 'D'])
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'A', 'G')
def test_find_shortest_path_dijkstra(self):
graph = DirectedGraph()
edges = [ # https://cs.stackexchange.com/questions/18138/dijkstra-algorithm-vs-breadth-first-search-for-shortest-path-in-graph
('A', 'B', 1),
('B', 'C', 1),
('B', 'D', 1),
('B', 'E', 1),
('C', 'E', 1),
('D', 'E', 1),
('E', 'F', 1),
('G', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'B', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'B', 'D'])
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'A', 'G')
graph = DirectedGraph()
edges = [ # https://www.youtube.com/watch?v=pVfj6mxhdMw
('A', 'B', 6),
('A', 'D', 1),
('B', 'A', 6),
('B', 'C', 5),
('B', 'D', 2),
('B', 'E', 2),
('C', 'B', 5),
('C', 'E', 5),
('D', 'A', 1),
('D', 'B', 2),
('D', 'E', 1),
('E', 'B', 2),
('E', 'C', 5),
('E', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'C')
self.assertEqual(path, ['A', 'D', 'E', 'C'])
graph = DirectedGraph()
edges = [ # https://www.chegg.com/homework-help/questions-and-answers/8-4-14-10-2-figure-2-directed-graph-computing-shortest-path-3-dijkstra-s-algorithm-computi-q25960616#question-transcript
('A', 'B', 4),
('B', 'C', 11),
('B', 'D', 9),
('C', 'A', 8),
('D', 'C', 7),
('D', 'E', 2),
('D', 'F', 6),
('E', 'B', 8),
('E', 'G', 7),
('E', 'H', 4),
('F', 'C', 1),
('F', 'E', 5),
('G', 'H', 14),
('G', 'I', 9),
('H', 'F', 2),
('H', 'I', 10),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'I')
self.assertEqual(path, ['A', 'B', 'D', 'E', 'H', 'I'])
previous, distances = graph.find_shortest_path_dijkstra('E')
path = graph.construct_path(previous, 'E', 'C')
self.assertEqual(path, ['E', 'H', 'F', 'C'])
previous, distances = graph.find_shortest_path_dijkstra('I')
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'I', 'A')
graph = DirectedGraph()
edges = [ # https://www.bogotobogo.com/python/python_Prims_Spanning_Tree_Data_Structure.php
('A', 'B', 7),
('A', 'C', 9),
('A', 'F', 14),
('B', 'A', 7),
('B', 'C', 10),
('B', 'D', 15),
('C', 'A', 9),
('C', 'B', 10),
('C', 'D', 11),
('C', 'F', 2),
('D', 'B', 15),
('D', 'C', 11),
('D', 'E', 6),
('E', 'D', 6),
('E', 'F', 9),
('F', 'A', 14),
('F', 'C', 2),
('F', 'E', 9),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'C', 'F', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'C', 'D'])
def test_find_shortest_path_bellman_ford(self):
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/bellman-ford-algorithm
('A', 'B', 2),
('B', 'C', 2),
('B', 'D', 1),
('C', 'D', -4),
('D', 'B', 1),
('D', 'E', 3),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
# There is a negative weight cycle among {B, C, D}.
with self.assertRaises(ValueError):
previous, distances = graph.find_shortest_path_bellman_ford('A')
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/bellman-ford-algorithm
('A', 'B', 4),
('A', 'C', 2),
('B', 'C', 3),
('B', 'D', 2),
('B', 'E', 4),
('C', 'B', 1),
('C', 'D', 3),
('C', 'E', 5),
('E', 'D', -5),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'A')
self.assertEqual(path, [
'A',
])
path = graph.construct_path(previous, 'A', 'B')
self.assertEqual(path, ['A', 'C', 'B'])
path = graph.construct_path(previous, 'A', 'C')
self.assertEqual(path, ['A', 'C'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'C', 'E', 'D'])
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'C', 'E'])
previous, distances = graph.find_shortest_path_bellman_ford('D')
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'D', 'E')
graph = DirectedGraph()
edges = [ # https://cs.stackexchange.com/questions/18138/dijkstra-algorithm-vs-breadth-first-search-for-shortest-path-in-graph
('A', 'B', 1),
('B', 'C', 1),
('B', 'D', 1),
('B', 'E', 1),
('C', 'E', 1),
('D', 'E', 1),
('E', 'F', 1),
('G', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'B', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'B', 'D'])
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'A', 'G')
graph = DirectedGraph()
edges = [ # https://www.youtube.com/watch?v=pVfj6mxhdMw
('A', 'B', 6),
('A', 'D', 1),
('B', 'A', 6),
('B', 'C', 5),
('B', 'D', 2),
('B', 'E', 2),
('C', 'B', 5),
('C', 'E', 5),
('D', 'A', 1),
('D', 'B', 2),
('D', 'E', 1),
('E', 'B', 2),
('E', 'C', 5),
('E', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'C')
self.assertEqual(path, ['A', 'D', 'E', 'C'])
graph = DirectedGraph()
edges = [ # https://www.chegg.com/homework-help/questions-and-answers/8-4-14-10-2-figure-2-directed-graph-computing-shortest-path-3-dijkstra-s-algorithm-computi-q25960616#question-transcript
('A', 'B', 4),
('B', 'C', 11),
('B', 'D', 9),
('C', 'A', 8),
('D', 'C', 7),
('D', 'E', 2),
('D', 'F', 6),
('E', 'B', 8),
('E', 'G', 7),
('E', 'H', 4),
('F', 'C', 1),
('F', 'E', 5),
('G', 'H', 14),
('G', 'I', 9),
('H', 'F', 2),
('H', 'I', 10),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'I')
self.assertEqual(path, ['A', 'B', 'D', 'E', 'H', 'I'])
previous, distances = graph.find_shortest_path_bellman_ford('E')
path = graph.construct_path(previous, 'E', 'C')
self.assertEqual(path, ['E', 'H', 'F', 'C'])
previous, distances = graph.find_shortest_path_bellman_ford('I')
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'I', 'A')
graph = DirectedGraph()
edges = [ # https://www.bogotobogo.com/python/python_Prims_Spanning_Tree_Data_Structure.php
('A', 'B', 7),
('A', 'C', 9),
('A', 'F', 14),
('B', 'A', 7),
('B', 'C', 10),
('B', 'D', 15),
('C', 'A', 9),
('C', 'B', 10),
('C', 'D', 11),
('C', 'F', 2),
('D', 'B', 15),
('D', 'C', 11),
('D', 'E', 6),
('E', 'D', 6),
('E', 'F', 9),
('F', 'A', 14),
('F', 'C', 2),
('F', 'E', 9),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'C', 'F', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'C', 'D'])
def test_find_shortest_path_bellman_ford(self):
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/bellman-ford-algorithm
('A', 'B', 2),
('B', 'C', 2),
('B', 'D', 1),
('C', 'D', -4),
('D', 'B', 1),
('D', 'E', 3),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
# There is a negative weight cycle among {B, C, D}.
with self.assertRaises(ValueError):
previous, distances = graph.find_shortest_path_bellman_ford('A')
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/bellman-ford-algorithm
('A', 'B', 4),
('A', 'C', 2),
('B', 'C', 3),
('B', 'D', 2),
('B', 'E', 4),
('C', 'B', 1),
('C', 'D', 3),
('C', 'E', 5),
('E', 'D', -5),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'A')
self.assertEqual(path, [
'A',
])
path = graph.construct_path(previous, 'A', 'B')
self.assertEqual(path, ['A', 'C', 'B'])
path = graph.construct_path(previous, 'A', 'C')
self.assertEqual(path, ['A', 'C'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'C', 'E', 'D'])
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'C', 'E'])
previous, distances = graph.find_shortest_path_bellman_ford('D')
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'D', 'E')
graph = DirectedGraph()
edges = [ # https://cs.stackexchange.com/questions/18138/dijkstra-algorithm-vs-breadth-first-search-for-shortest-path-in-graph
('A', 'B', 1),
('B', 'C', 1),
('B', 'D', 1),
('B', 'E', 1),
('C', 'E', 1),
('D', 'E', 1),
('E', 'F', 1),
('G', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'B', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'B', 'D'])
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'A', 'G')
graph = DirectedGraph()
edges = [ # https://www.youtube.com/watch?v=pVfj6mxhdMw
('A', 'B', 6),
('A', 'D', 1),
('B', 'A', 6),
('B', 'C', 5),
('B', 'D', 2),
('B', 'E', 2),
('C', 'B', 5),
('C', 'E', 5),
('D', 'A', 1),
('D', 'B', 2),
('D', 'E', 1),
('E', 'B', 2),
('E', 'C', 5),
('E', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'C')
self.assertEqual(path, ['A', 'D', 'E', 'C'])
graph = DirectedGraph()
edges = [ # https://www.chegg.com/homework-help/questions-and-answers/8-4-14-10-2-figure-2-directed-graph-computing-shortest-path-3-dijkstra-s-algorithm-computi-q25960616#question-transcript
('A', 'B', 4),
('B', 'C', 11),
('B', 'D', 9),
('C', 'A', 8),
('D', 'C', 7),
('D', 'E', 2),
('D', 'F', 6),
('E', 'B', 8),
('E', 'G', 7),
('E', 'H', 4),
('F', 'C', 1),
('F', 'E', 5),
('G', 'H', 14),
('G', 'I', 9),
('H', 'F', 2),
('H', 'I', 10),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'I')
self.assertEqual(path, ['A', 'B', 'D', 'E', 'H', 'I'])
previous, distances = graph.find_shortest_path_bellman_ford('E')
path = graph.construct_path(previous, 'E', 'C')
self.assertEqual(path, ['E', 'H', 'F', 'C'])
previous, distances = graph.find_shortest_path_bellman_ford('I')
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'I', 'A')
graph = DirectedGraph()
edges = [ # https://www.bogotobogo.com/python/python_Prims_Spanning_Tree_Data_Structure.php
('A', 'B', 7),
('A', 'C', 9),
('A', 'F', 14),
('B', 'A', 7),
('B', 'C', 10),
('B', 'D', 15),
('C', 'A', 9),
('C', 'B', 10),
('C', 'D', 11),
('C', 'F', 2),
('D', 'B', 15),
('D', 'C', 11),
('D', 'E', 6),
('E', 'D', 6),
('E', 'F', 9),
('F', 'A', 14),
('F', 'C', 2),
('F', 'E', 9),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'C', 'F', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'C', 'D'])
def test_find_minimum_spanning_tree_kruskal(self):
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/spanning-tree-and-minimum-spanning-tree
('A', 'B', 1),
('A', 'D', 1),
('B', 'A', 1),
('B', 'C', 1),
('C', 'B', 1),
('C', 'D', 1),
('D', 'A', 1),
('D', 'C', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
tree_edges = graph.find_minimum_spanning_tree_kruskal('A')
total_weights = sum(edge[2] for edge in tree_edges)
self.assertEqual(total_weights, 3)
graph = DirectedGraph()
edges = [ # https://en.wikipedia.org/wiki/Minimum_spanning_tree
('A', 'B', 1),
('A', 'D', 4),
('A', 'E', 3),
('B', 'A', 1),
('B', 'D', 4),
('B', 'E', 2),
('C', 'E', 4),
('C', 'F', 5),
('D', 'A', 4),
('D', 'B', 4),
('D', 'E', 4),
('E', 'A', 3),
('E', 'B', 2),
('E', 'C', 4),
('E', 'D', 4),
('E', 'F', 7),
('F', 'C', 5),
('F', 'E', 7),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
tree_edges = graph.find_minimum_spanning_tree_kruskal('A')
total_weights = sum(edge[2] for edge in tree_edges)
self.assertEqual(total_weights, 16)
graph = DirectedGraph()
edges = [ # http://dev.tutorialspoint.com/design_and_analysis_of_algorithms/design_and_analysis_of_algorithms_quick_guide.htm
(1, 2, 5),
(1, 3, 2),
(2, 1, 5),
(2, 3, 2),
(2, 4, 3),
(2, 5, 7),
(3, 1, 2),
(3, 2, 2),
(3, 4, 3),
(3, 7, 9),
(4, 2, 3),
(4, 3, 3),
(4, 5, 2),
(4, 7, 6),
(5, 2, 7),
(5, 4, 2),
(5, 6, 8),
(5, 7, 5),
(5, 8, 7),
(6, 5, 8),
(6, 8, 3),
(6, 9, 4),
(7, 3, 9),
(7, 4, 6),
(7, 5, 5),
(7, 8, 2),
(8, 5, 7),
(8, 6, 3),
(8, 7, 2),
(9, 6, 4),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
tree_edges = graph.find_minimum_spanning_tree_kruskal(1)
total_weights = sum(edge[2] for edge in tree_edges)
self.assertEqual(total_weights, 23)
class TestCase(unittest.TestCase):
def setUp(self):
self.graph = DirectedGraph()
self.edges = [
# (source, destination, weight)
('A', 'B', 1),
('A', 'C', 1),
('B', 'C', 1),
('B', 'D', 1),
('B', 'I', 1),
('C', 'D', 1),
('D', 'C', 1),
('D', 'H', 1),
('H', 'I', 1),
('E', 'A', 1),
('E', 'F', 1),
('F', 'C', 1),
('F', 'G', 1),
]
self.vertices = set()
for source, destination, weight in self.edges:
self.vertices.add(source)
self.vertices.add(destination)
self.graph.add_vertex(source, value=source)
self.graph.add_vertex(destination, value=destination)
self.graph.add_edge(source, destination, weight)
def test_add_vertex(self):
self.graph.add_vertex('X')
self.assertEqual(self.graph.vertex_count(), len(self.vertices) + 1)
def test_add_edge(self):
self.graph.add_vertex('X', value='X')
self.graph.add_vertex('Y', value='Y')
self.graph.add_edge('X', 'Y', 0)
self.assertEqual(self.graph.vertex_count(), len(self.vertices) + 2)
self.assertEqual(self.graph.edge_count(), len(self.edges) + 1)
def test_remove_vertex(self):
self.graph.remove_vertex('C')
self.assertEqual(self.graph.vertex_count(), len(self.vertices) - 1)
edge_count = 0
for source, destination, _ in self.edges:
if not source == 'C' and not destination == 'C':
edge_count += 1
self.assertEqual(self.graph.edge_count(), edge_count)
def test_remove_edge(self):
self.graph.remove_edge('A', 'B')
self.assertEqual(self.graph.edge_count(), len(self.edges) - 1)
with self.assertRaises(ValueError):
self.graph.remove_edge('Z', 'Z')
def test_vertex_count(self):
self.assertEqual(self.graph.vertex_count(), len(self.vertices))
def test_edge_count(self):
self.assertEqual(self.graph.edge_count(), len(self.edges))
def test_vertices(self):
self.assertCountEqual(self.graph.vertices(), self.vertices)
def test_edges(self):
self.assertCountEqual(self.graph.edges(), self.edges)
def test_incident_edges(self):
vertex = 'A'
outgoing_edges = [edge for edge in self.edges if edge[0] == vertex]
self.assertCountEqual(
self.graph.incident_edges(vertex, edge_type='outgoing'),
outgoing_edges)
incoming_edges = [edge for edge in self.edges if edge[1] == vertex]
self.assertCountEqual(
self.graph.incident_edges(vertex, edge_type='incoming'),
incoming_edges)
self.assertCountEqual(
self.graph.incident_edges('NOT EXIST', edge_type='outgoing'), [])
self.assertCountEqual(
self.graph.incident_edges('NOT EXIST', edge_type='incoming'), [])
def test_edge_weight(self):
for source, destination, weight in self.edges:
self.assertEqual(self.graph.edge_weight(source, destination),
weight)
with self.assertRaises(ValueError):
self.graph.edge_weight('NOT EXIST', 'NOT EXIST')
def test_breadth_first_search(self):
v = 'A'
visited = self.graph.breadth_first_search(v)
self.assertCountEqual(visited, ['A', 'B', 'C', 'D', 'H', 'I'])
v = 'E'
visited = self.graph.breadth_first_search(v)
self.assertCountEqual(visited,
['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I'])
def test_depth_first_search(self):
v = 'A'
visited = self.graph.depth_first_search(v)
self.assertCountEqual(visited, ['A', 'B', 'C', 'D', 'H', 'I'])
v = 'E'
visited = self.graph.depth_first_search(v)
self.assertCountEqual(visited,
['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I'])
def test_has_cycles_dfs(self):
self.assertEqual(self.graph.has_cycles_dfs(), True)
graph = DirectedGraph()
edges = [
('A', 'A', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
self.assertEqual(graph.has_cycles_dfs(), True)
graph = DirectedGraph()
edges = [
('A', 'B', 1),
('B', 'C', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
self.assertEqual(graph.has_cycles_dfs(), False)
def test_find_shortest_paths_bfs(self):
graph = DirectedGraph()
edges = [ # https://www.geeksforgeeks.org/shortest-path-unweighted-graph/
(0, 1, 1),
(0, 3, 1),
(1, 0, 1),
(1, 2, 1),
(2, 1, 1),
(3, 0, 1),
(3, 4, 1),
(3, 7, 1),
(4, 3, 1),
(4, 5, 1),
(4, 6, 1),
(4, 7, 1),
(5, 4, 1),
(5, 6, 1),
(6, 4, 1),
(6, 5, 1),
(6, 7, 1),
(7, 3, 1),
(7, 4, 1),
(7, 6, 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_paths_bfs(0)
path = graph.construct_path(previous, 0, 5)
self.assertEqual(path, [0, 3, 4, 5])
path = graph.construct_path(previous, 0, 7)
self.assertEqual(path, [0, 3, 7])
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 0, 10)
def test_find_shortest_path_dijkstra(self):
graph = DirectedGraph()
edges = [ # https://cs.stackexchange.com/questions/18138/dijkstra-algorithm-vs-breadth-first-search-for-shortest-path-in-graph
('A', 'B', 1),
('B', 'C', 3),
('B', 'D', 2),
('B', 'E', 1),
('C', 'E', 4),
('D', 'E', 2),
('E', 'F', 3),
('G', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'B', 'D'])
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'B', 'E'])
path = graph.construct_path(previous, 'A', 'F')
self.assertEqual(path, ['A', 'B', 'E', 'F'])
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'A', 'G')
graph = DirectedGraph()
edges = [ # https://www.youtube.com/watch?v=pVfj6mxhdMw
('A', 'B', 6),
('A', 'D', 1),
('B', 'A', 6),
('B', 'C', 5),
('B', 'D', 2),
('B', 'E', 2),
('C', 'B', 5),
('C', 'E', 5),
('D', 'A', 1),
('D', 'B', 2),
('D', 'E', 1),
('E', 'B', 2),
('E', 'C', 5),
('E', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'B')
self.assertEqual(path, ['A', 'D', 'B'])
path = graph.construct_path(previous, 'A', 'C')
self.assertEqual(path, ['A', 'D', 'E', 'C'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'D'])
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'D', 'E'])
graph = DirectedGraph()
edges = [ # https://www.chegg.com/homework-help/questions-and-answers/8-4-14-10-2-figure-2-directed-graph-computing-shortest-path-3-dijkstra-s-algorithm-computi-q25960616#question-transcript
('A', 'B', 4),
('B', 'C', 11),
('B', 'D', 9),
('C', 'A', 8),
('D', 'C', 7),
('D', 'E', 2),
('D', 'F', 6),
('E', 'B', 8),
('E', 'G', 7),
('E', 'H', 4),
('F', 'C', 1),
('F', 'E', 5),
('G', 'H', 14),
('G', 'I', 9),
('H', 'F', 2),
('H', 'I', 10),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'I')
self.assertEqual(path, ['A', 'B', 'D', 'E', 'H', 'I'])
previous, distances = graph.find_shortest_path_dijkstra('E')
path = graph.construct_path(previous, 'E', 'C')
self.assertEqual(path, ['E', 'H', 'F', 'C'])
previous, distances = graph.find_shortest_path_dijkstra('I')
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'I', 'A')
graph = DirectedGraph()
edges = [ # https://www.bogotobogo.com/python/python_Prims_Spanning_Tree_Data_Structure.php
('A', 'B', 7),
('A', 'C', 9),
('A', 'F', 14),
('B', 'A', 7),
('B', 'C', 10),
('B', 'D', 15),
('C', 'A', 9),
('C', 'B', 10),
('C', 'D', 11),
('C', 'F', 2),
('D', 'B', 15),
('D', 'C', 11),
('D', 'E', 6),
('E', 'D', 6),
('E', 'F', 9),
('F', 'A', 14),
('F', 'C', 2),
('F', 'E', 9),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'C', 'F', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'C', 'D'])
graph = DirectedGraph()
adj_list = { # https://adityakamath.com/2018/06/17/Dijktra%27s-Algorithm-In-Python.html
'S': {'A': 7, 'B': 2, 'C': 3},
'A': {'S': 7, 'B': 3, 'D': 4},
'B': {'S': 2, 'A': 3, 'D': 4, 'H': 1, 'C': 12},
'C': {'S': 3, 'L': 2},
'D': {'A': 4, 'B': 4, 'F': 5},
'E': {'G': 2, 'K': 5},
'F': {'D': 5, 'H': 3},
'G': {'H': 2, 'I': 10, 'E': 2},
'H': {'B': 1, 'F': 3, 'G': 2},
'I': {'J': 6, 'K': 4, 'L': 4},
'J': {'K': 4, 'L': 4},
'K': {'I': 4, 'J': 4, 'E': 5},
'L': {'C': 2, 'I': 4, 'J': 4},
}
for src, neighbors in adj_list.items():
for des, weight in neighbors.items():
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('S')
path = graph.construct_path(previous, 'S', 'E')
self.assertEqual(path, ['S', 'B', 'H', 'G', 'E'])
def test_find_shortest_path_bellman_ford(self):
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/bellman-ford-algorithm
('A', 'B', 2),
('B', 'C', 2),
('B', 'D', 1),
('C', 'D', -4),
('D', 'B', 1),
('D', 'E', 3),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
# There is a negative weight cycle among {B, C, D}.
with self.assertRaises(ValueError):
previous, distances = graph.find_shortest_path_bellman_ford('A')
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/bellman-ford-algorithm
('A', 'B', 4),
('A', 'C', 2),
('B', 'C', 3),
('B', 'D', 2),
('B', 'E', 4),
('C', 'B', 1),
('C', 'D', 3),
('C', 'E', 5),
('E', 'D', -5),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'A')
self.assertEqual(path, [
'A',
])
path = graph.construct_path(previous, 'A', 'B')
self.assertEqual(path, ['A', 'C', 'B'])
path = graph.construct_path(previous, 'A', 'C')
self.assertEqual(path, ['A', 'C'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'C', 'E', 'D'])
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'C', 'E'])
previous, distances = graph.find_shortest_path_bellman_ford('D')
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'D', 'E')
graph = DirectedGraph()
edges = [ # https://cs.stackexchange.com/questions/18138/dijkstra-algorithm-vs-breadth-first-search-for-shortest-path-in-graph
('A', 'B', 1),
('B', 'C', 1),
('B', 'D', 1),
('B', 'E', 1),
('C', 'E', 1),
('D', 'E', 1),
('E', 'F', 1),
('G', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'B', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'B', 'D'])
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'A', 'G')
graph = DirectedGraph()
edges = [ # https://www.youtube.com/watch?v=pVfj6mxhdMw
('A', 'B', 6),
('A', 'D', 1),
('B', 'A', 6),
('B', 'C', 5),
('B', 'D', 2),
('B', 'E', 2),
('C', 'B', 5),
('C', 'E', 5),
('D', 'A', 1),
('D', 'B', 2),
('D', 'E', 1),
('E', 'B', 2),
('E', 'C', 5),
('E', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'C')
self.assertEqual(path, ['A', 'D', 'E', 'C'])
graph = DirectedGraph()
edges = [ # https://www.chegg.com/homework-help/questions-and-answers/8-4-14-10-2-figure-2-directed-graph-computing-shortest-path-3-dijkstra-s-algorithm-computi-q25960616#question-transcript
('A', 'B', 4),
('B', 'C', 11),
('B', 'D', 9),
('C', 'A', 8),
('D', 'C', 7),
('D', 'E', 2),
('D', 'F', 6),
('E', 'B', 8),
('E', 'G', 7),
('E', 'H', 4),
('F', 'C', 1),
('F', 'E', 5),
('G', 'H', 14),
('G', 'I', 9),
('H', 'F', 2),
('H', 'I', 10),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'I')
self.assertEqual(path, ['A', 'B', 'D', 'E', 'H', 'I'])
previous, distances = graph.find_shortest_path_bellman_ford('E')
path = graph.construct_path(previous, 'E', 'C')
self.assertEqual(path, ['E', 'H', 'F', 'C'])
previous, distances = graph.find_shortest_path_bellman_ford('I')
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'I', 'A')
graph = DirectedGraph()
edges = [ # https://www.bogotobogo.com/python/python_Prims_Spanning_Tree_Data_Structure.php
('A', 'B', 7),
('A', 'C', 9),
('A', 'F', 14),
('B', 'A', 7),
('B', 'C', 10),
('B', 'D', 15),
('C', 'A', 9),
('C', 'B', 10),
('C', 'D', 11),
('C', 'F', 2),
('D', 'B', 15),
('D', 'C', 11),
('D', 'E', 6),
('E', 'D', 6),
('E', 'F', 9),
('F', 'A', 14),
('F', 'C', 2),
('F', 'E', 9),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'C', 'F', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'C', 'D'])
def test_find_minimum_spanning_tree_prim_jarnik(self):
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/spanning-tree-and-minimum-spanning-tree
('A', 'B', 1),
('A', 'D', 1),
('B', 'A', 1),
('B', 'C', 1),
('C', 'B', 1),
('C', 'D', 1),
('D', 'A', 1),
('D', 'C', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
tree_edges = graph.find_minimum_spanning_tree_prim_jarnik('A')
total_weights = sum(edge[2] for edge in tree_edges)
self.assertEqual(total_weights, 3)
graph = DirectedGraph()
edges = [ # https://en.wikipedia.org/wiki/Minimum_spanning_tree
('A', 'B', 1),
('A', 'D', 4),
('A', 'E', 3),
('B', 'A', 1),
('B', 'D', 4),
('B', 'E', 2),
('C', 'E', 4),
('C', 'F', 5),
('D', 'A', 4),
('D', 'B', 4),
('D', 'E', 4),
('E', 'A', 3),
('E', 'B', 2),
('E', 'C', 4),
('E', 'D', 4),
('E', 'F', 7),
('F', 'C', 5),
('F', 'E', 7),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
tree_edges = graph.find_minimum_spanning_tree_prim_jarnik('A')
total_weights = sum(edge[2] for edge in tree_edges)
self.assertEqual(total_weights, 16)
graph = DirectedGraph()
edges = [ # http://dev.tutorialspoint.com/design_and_analysis_of_algorithms/design_and_analysis_of_algorithms_quick_guide.htm
(1, 2, 5),
(1, 3, 2),
(2, 1, 5),
(2, 3, 2),
(2, 4, 3),
(2, 5, 7),
(3, 1, 2),
(3, 2, 2),
(3, 4, 3),
(3, 7, 9),
(4, 2, 3),
(4, 3, 3),
(4, 5, 2),
(4, 7, 6),
(5, 2, 7),
(5, 4, 2),
(5, 6, 8),
(5, 7, 5),
(5, 8, 7),
(6, 5, 8),
(6, 8, 3),
(6, 9, 4),
(7, 3, 9),
(7, 4, 6),
(7, 5, 5),
(7, 8, 2),
(8, 5, 7),
(8, 6, 3),
(8, 7, 2),
(9, 6, 4),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
tree_edges = graph.find_minimum_spanning_tree_prim_jarnik(1)
total_weights = sum(edge[2] for edge in tree_edges)
self.assertEqual(total_weights, 23)
def test_find_minimum_spanning_tree_kruskal(self):
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/spanning-tree-and-minimum-spanning-tree
('A', 'B', 1),
('A', 'D', 1),
('B', 'A', 1),
('B', 'C', 1),
('C', 'B', 1),
('C', 'D', 1),
('D', 'A', 1),
('D', 'C', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
tree_edges = graph.find_minimum_spanning_tree_kruskal('A')
total_weights = sum(edge[2] for edge in tree_edges)
self.assertEqual(total_weights, 3)
graph = DirectedGraph()
edges = [ # https://en.wikipedia.org/wiki/Minimum_spanning_tree
('A', 'B', 1),
('A', 'D', 4),
('A', 'E', 3),
('B', 'A', 1),
('B', 'D', 4),
('B', 'E', 2),
('C', 'E', 4),
('C', 'F', 5),
('D', 'A', 4),
('D', 'B', 4),
('D', 'E', 4),
('E', 'A', 3),
('E', 'B', 2),
('E', 'C', 4),
('E', 'D', 4),
('E', 'F', 7),
('F', 'C', 5),
('F', 'E', 7),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
tree_edges = graph.find_minimum_spanning_tree_kruskal('A')
total_weights = sum(edge[2] for edge in tree_edges)
self.assertEqual(total_weights, 16)
graph = DirectedGraph()
edges = [ # http://dev.tutorialspoint.com/design_and_analysis_of_algorithms/design_and_analysis_of_algorithms_quick_guide.htm
(1, 2, 5),
(1, 3, 2),
(2, 1, 5),
(2, 3, 2),
(2, 4, 3),
(2, 5, 7),
(3, 1, 2),
(3, 2, 2),
(3, 4, 3),
(3, 7, 9),
(4, 2, 3),
(4, 3, 3),
(4, 5, 2),
(4, 7, 6),
(5, 2, 7),
(5, 4, 2),
(5, 6, 8),
(5, 7, 5),
(5, 8, 7),
(6, 5, 8),
(6, 8, 3),
(6, 9, 4),
(7, 3, 9),
(7, 4, 6),
(7, 5, 5),
(7, 8, 2),
(8, 5, 7),
(8, 6, 3),
(8, 7, 2),
(9, 6, 4),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
tree_edges = graph.find_minimum_spanning_tree_kruskal(1)
total_weights = sum(edge[2] for edge in tree_edges)
self.assertEqual(total_weights, 23)
def test_find_shortest_path_dijkstra(self):
graph = DirectedGraph()
edges = [ # https://cs.stackexchange.com/questions/18138/dijkstra-algorithm-vs-breadth-first-search-for-shortest-path-in-graph
('A', 'B', 1),
('B', 'C', 3),
('B', 'D', 2),
('B', 'E', 1),
('C', 'E', 4),
('D', 'E', 2),
('E', 'F', 3),
('G', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'B', 'D'])
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'B', 'E'])
path = graph.construct_path(previous, 'A', 'F')
self.assertEqual(path, ['A', 'B', 'E', 'F'])
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'A', 'G')
graph = DirectedGraph()
edges = [ # https://www.youtube.com/watch?v=pVfj6mxhdMw
('A', 'B', 6),
('A', 'D', 1),
('B', 'A', 6),
('B', 'C', 5),
('B', 'D', 2),
('B', 'E', 2),
('C', 'B', 5),
('C', 'E', 5),
('D', 'A', 1),
('D', 'B', 2),
('D', 'E', 1),
('E', 'B', 2),
('E', 'C', 5),
('E', 'D', 1),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'B')
self.assertEqual(path, ['A', 'D', 'B'])
path = graph.construct_path(previous, 'A', 'C')
self.assertEqual(path, ['A', 'D', 'E', 'C'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'D'])
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'D', 'E'])
graph = DirectedGraph()
edges = [ # https://www.chegg.com/homework-help/questions-and-answers/8-4-14-10-2-figure-2-directed-graph-computing-shortest-path-3-dijkstra-s-algorithm-computi-q25960616#question-transcript
('A', 'B', 4),
('B', 'C', 11),
('B', 'D', 9),
('C', 'A', 8),
('D', 'C', 7),
('D', 'E', 2),
('D', 'F', 6),
('E', 'B', 8),
('E', 'G', 7),
('E', 'H', 4),
('F', 'C', 1),
('F', 'E', 5),
('G', 'H', 14),
('G', 'I', 9),
('H', 'F', 2),
('H', 'I', 10),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'I')
self.assertEqual(path, ['A', 'B', 'D', 'E', 'H', 'I'])
previous, distances = graph.find_shortest_path_dijkstra('E')
path = graph.construct_path(previous, 'E', 'C')
self.assertEqual(path, ['E', 'H', 'F', 'C'])
previous, distances = graph.find_shortest_path_dijkstra('I')
# No such path.
with self.assertRaises(ValueError):
graph.construct_path(previous, 'I', 'A')
graph = DirectedGraph()
edges = [ # https://www.bogotobogo.com/python/python_Prims_Spanning_Tree_Data_Structure.php
('A', 'B', 7),
('A', 'C', 9),
('A', 'F', 14),
('B', 'A', 7),
('B', 'C', 10),
('B', 'D', 15),
('C', 'A', 9),
('C', 'B', 10),
('C', 'D', 11),
('C', 'F', 2),
('D', 'B', 15),
('D', 'C', 11),
('D', 'E', 6),
('E', 'D', 6),
('E', 'F', 9),
('F', 'A', 14),
('F', 'C', 2),
('F', 'E', 9),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('A')
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'C', 'F', 'E'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'C', 'D'])
graph = DirectedGraph()
adj_list = { # https://adityakamath.com/2018/06/17/Dijktra%27s-Algorithm-In-Python.html
'S': {'A': 7, 'B': 2, 'C': 3},
'A': {'S': 7, 'B': 3, 'D': 4},
'B': {'S': 2, 'A': 3, 'D': 4, 'H': 1, 'C': 12},
'C': {'S': 3, 'L': 2},
'D': {'A': 4, 'B': 4, 'F': 5},
'E': {'G': 2, 'K': 5},
'F': {'D': 5, 'H': 3},
'G': {'H': 2, 'I': 10, 'E': 2},
'H': {'B': 1, 'F': 3, 'G': 2},
'I': {'J': 6, 'K': 4, 'L': 4},
'J': {'K': 4, 'L': 4},
'K': {'I': 4, 'J': 4, 'E': 5},
'L': {'C': 2, 'I': 4, 'J': 4},
}
for src, neighbors in adj_list.items():
for des, weight in neighbors.items():
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_dijkstra('S')
path = graph.construct_path(previous, 'S', 'E')
self.assertEqual(path, ['S', 'B', 'H', 'G', 'E'])
def test_find_shortest_path_bellman_ford(self):
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/bellman-ford-algorithm
('A', 'B', 4),
('A', 'C', 2),
('B', 'C', 3),
('B', 'D', 2),
('B', 'E', 4),
('C', 'B', 1),
('C', 'D', 3),
('C', 'E', 5),
('E', 'D', -5),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
previous, distances = graph.find_shortest_path_bellman_ford('A')
path = graph.construct_path(previous, 'A', 'A')
self.assertEqual(path, ['A', ])
path = graph.construct_path(previous, 'A', 'B')
self.assertEqual(path, ['A', 'C', 'B'])
path = graph.construct_path(previous, 'A', 'C')
self.assertEqual(path, ['A', 'C'])
path = graph.construct_path(previous, 'A', 'D')
self.assertEqual(path, ['A', 'C', 'E', 'D'])
path = graph.construct_path(previous, 'A', 'E')
self.assertEqual(path, ['A', 'C', 'E'])
previous, distances = graph.find_shortest_path_bellman_ford('D')
with self.assertRaises(ValueError):
graph.construct_path(previous, 'D', 'E')
graph = DirectedGraph()
edges = [ # https://www.programiz.com/dsa/bellman-ford-algorithm
('A', 'B', 2),
('B', 'C', 2),
('B', 'D', 1),
('C', 'D', -4),
('D', 'B', 1),
('D', 'E', 3),
]
for src, des, weight in edges:
graph.add_edge(src, des, weight)
# There is a negative weight cycle among {B, C, D}.
with self.assertRaises(ValueError):
previous, distances = graph.find_shortest_path_bellman_ford('A')