def minimum_spanning_tree(adjacency_list):
"""
Get minimum spanning tree for graph represented as adjacency list
"""
remain_vertices = adjacency_list.copy()
edges_by_vertex = {}
mst = UndirectedGraph()
for vertex in remain_vertices.keys():
edges_by_vertex[vertex] = None
while remain_vertices:
(vertex, adjacent_edges) = __extract_next_vertex_with_edges(
remain_vertices, edges_by_vertex)
if edges_by_vertex[vertex]:
mst.add_edge(edges_by_vertex[vertex].start,
edges_by_vertex[vertex].end,
edges_by_vertex[vertex].weight)
for edge in adjacent_edges:
adjacent_vertex = edge.end
is_not_visited = adjacent_vertex in remain_vertices
is_lighter = edge.weight < __get_weight_or_inf(
edges_by_vertex[adjacent_vertex])
if is_not_visited and is_lighter:
edges_by_vertex[adjacent_vertex] = edge
return mst
def test_returns_true_for_graph_with_cycle(self):
g = UndirectedGraph()
g.add_edge(1, 2, 1)
g.add_edge(4, 1, 1)
g.add_edge(2, 3, 1)
g.add_edge(3, 1, 1)
self.assertFalse(is_bipartite(g))
def test_can_add_multiple_edges_between_two_vertices(self):
graph = UndirectedGraph()
graph.add_edge(0, 1, 1)
graph.add_edge(0, 1, 2)
adjacency_list = graph.get_adjacency_list()
self.assertEqual(2, len(adjacency_list))
self.assertEqual(2, len(adjacency_list[0]))
self.assertListEqual([0, 0],
sorted(map(lambda e: e.start, adjacency_list[0])))
self.assertListEqual([1, 1],
sorted(map(lambda e: e.end, adjacency_list[0])))
self.assertListEqual([1, 2],
sorted(map(lambda e: e.weight,
adjacency_list[0])))
self.assertEqual(2, len(adjacency_list[1]))
self.assertListEqual([1, 1],
sorted(map(lambda e: e.start, adjacency_list[1])))
self.assertListEqual([0, 0],
sorted(map(lambda e: e.end, adjacency_list[1])))
self.assertListEqual([1, 2],
sorted(map(lambda e: e.weight,
adjacency_list[1])))
edges = graph.get_edges()
self.assertEqual(4, len(edges))
self.assertListEqual([0, 0, 1, 1], sorted(map(lambda e: e.start,
edges)))
self.assertListEqual([0, 0, 1, 1], sorted(map(lambda e: e.end, edges)))
self.assertListEqual([1, 1, 2, 2],
sorted(map(lambda e: e.weight, edges)))
def test_returns_minimum_edge_when_has_two_edges_with_different_weight(
self):
graph = UndirectedGraph()
graph.add_edge(0, 1, 1)
graph.add_edge(0, 1, 2)
mst = minimum_spanning_tree(graph.get_adjacency_list())
self.__compare_vertices([0, 1], mst.get_adjacency_list())
self.__compare_edges([Edge(0, 1, 1), Edge(1, 0, 1)], mst.get_edges())
def test_returns_two_edges_for_two_edges_starting_in_same_vertex(self):
graph = UndirectedGraph()
graph.add_edge(0, 1, 1)
graph.add_edge(0, 2, 2)
mst = minimum_spanning_tree(graph.get_adjacency_list())
self.__compare_vertices([0, 1, 2], mst.get_adjacency_list())
self.__compare_edges(
[Edge(0, 1, 1),
Edge(1, 0, 1),
Edge(0, 2, 2),
Edge(2, 0, 2)], mst.get_edges())
def fixtured_graph() -> UndirectedGraph:
graph = UndirectedGraph()
graph.add_edge("A", "B", weight=2)
graph.add_edge("A", "C", weight=4)
graph.add_edge("B", "C", weight=1)
graph.add_edge("C", "D", weight=3)
graph.add_edge("B", "D", weight=5)
graph.add_edge("D", "E", weight=6)
graph.add_edge("D", "F", weight=8)
return graph
def count_possible_astronaut_pairs(total_astronauts, astronauts_connections):
"""
Get number of possible astronaut pairs where both of them are
from different countries
"""
graph = UndirectedGraph()
for astronaut in range(0, total_astronauts):
graph.add_vertex(astronaut)
for connection in astronauts_connections:
graph.add_edge(connection[0], connection[1], 0)
country_by_astronaut = vertices_to_components(graph)
count_by_country = {}
for astronaut, country in country_by_astronaut.items():
count_by_country[country] = count_by_country.get(country, 0) + 1
total = 0
pairs = 0
for country, count in count_by_country.items():
pairs += total * count
total += count
return pairs
def count_number_of_road_forks(field):
"""
Returns number of times you are able to move in more
than one direction by a given forest
:param field: Array of strings that represent forest
:return: number of road forks
"""
graph = UndirectedGraph()
start = None
end = None
height = len(field)
width = len(field[0])
for i, row in enumerate(field):
for j, symbol in enumerate(row):
if symbol == 'X':
continue
index = __linear_index(i, j, width)
if symbol == 'M':
start = index
if symbol == '*':
end = index
if __can_go_to(i - 1, j, height, width):
if field[i - 1][j] != 'X':
neighbor_index = __linear_index(i - 1, j, width)
graph.add_edge(neighbor_index, index, 1)
if __can_go_to(i, j - 1, height, width):
if field[i][j - 1] != 'X':
neighbor_index = __linear_index(i, j - 1, width)
graph.add_edge(neighbor_index, index, 1)
path = dijkstra_path(graph, start, end)
fork_count = 1 if len(graph.get_edges(start)) > 1 else 0
for vertex in path[1:-1]:
if len(graph.get_edges(vertex)) - 1 > 1:
fork_count += 1
return fork_count
def test_adding_single_edge_produces_two_directed_edges(self):
graph = UndirectedGraph()
graph.add_edge(0, 1, 1)
adjacency_list = graph.get_adjacency_list()
self.assertEqual(2, len(adjacency_list))
self.assertEqual(1, len(adjacency_list[0]))
self.assertEqual(0, adjacency_list[0][0].start)
self.assertEqual(1, adjacency_list[0][0].end)
self.assertEqual(1, adjacency_list[0][0].weight)
self.assertEqual(1, len(adjacency_list[1]))
self.assertEqual(1, adjacency_list[1][0].start)
self.assertEqual(0, adjacency_list[1][0].end)
self.assertEqual(1, adjacency_list[1][0].weight)
edges = graph.get_edges()
self.assertEqual(2, len(edges))
self.assertListEqual([0, 1], sorted(map(lambda e: e.start, edges)))
self.assertListEqual([0, 1], sorted(map(lambda e: e.end, edges)))
self.assertListEqual([1, 1], sorted(map(lambda e: e.weight, edges)))
def test_returns_true_for_graph_with_multiple_connected_componenets(self):
g = UndirectedGraph()
g.add_edge(5, 2, 1)
g.add_edge(4, 2, 1)
g.add_edge(3, 4, 1)
g.add_edge(1, 4, 1)
g.add_edge(6, 7, 1)
self.assertTrue(is_bipartite(g))
def test_returns_mst_for_graph_with_loops(self):
graph = UndirectedGraph()
graph.add_edge('A', 'B', 3)
graph.add_edge('A', 'C', 4)
graph.add_edge('D', 'B', 6)
graph.add_edge('E', 'B', 2)
graph.add_edge('B', 'C', 5)
graph.add_edge('C', 'E', 7)
mst = minimum_spanning_tree(graph.get_adjacency_list())
self.__compare_vertices(['A', 'B', 'C', 'D', 'E'],
mst.get_adjacency_list())
self.__compare_edges([
Edge('A', 'B', 3),
Edge('B', 'A', 3),
Edge('B', 'E', 2),
Edge('E', 'B', 2),
Edge('A', 'C', 4),
Edge('C', 'A', 4),
Edge('B', 'D', 6),
Edge('D', 'B', 6)
], mst.get_edges())
def test_does_not_change_tree(self):
graph = UndirectedGraph()
graph.add_edge(0, 1, 1)
graph.add_edge(0, 6, 1)
graph.add_edge(2, 3, 2)
graph.add_edge(2, 4, 3)
graph.add_edge(4, 5, 4)
mst = minimum_spanning_tree(graph.get_adjacency_list())
self.__compare_vertices([0, 1, 2, 3, 4, 5, 6],
mst.get_adjacency_list())
self.__compare_edges([
Edge(0, 1, 1),
Edge(1, 0, 1),
Edge(0, 6, 1),
Edge(6, 0, 1),
Edge(2, 3, 2),
Edge(3, 2, 2),
Edge(2, 4, 3),
Edge(4, 2, 3),
Edge(4, 5, 4),
Edge(5, 4, 4)
], mst.get_edges())
def test_returns_true_for_graph_as_list(self):
g = UndirectedGraph()
g.add_edge(1, 2, 1)
g.add_edge(2, 3, 1)
self.assertTrue(is_bipartite(g))
def test_returns_single_edge_for_single_edge_in_graph(self):
graph = UndirectedGraph()
graph.add_edge(0, 1, 1)
mst = minimum_spanning_tree(graph.get_adjacency_list())
self.__compare_vertices([0, 1], mst.get_adjacency_list())
self.__compare_edges([Edge(0, 1, 1), Edge(1, 0, 1)], mst.get_edges())