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_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_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')
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_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_dijkstra(self):
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')
with self.assertRaises(ValueError):
graph.construct_path(previous, 'I', 'A')