def test_neighbors(self):
"""Test root()."""
# Create [{1, 2}, {2}, set()].
a_graph = DirectedGraph()
a_graph.connect(0, 1)
a_graph.connect(0, 2)
a_graph.connect(1, 2)
# Check neighbors on existing vertices.
self.assertEqual(a_graph.neighbors(0), {1, 2})
self.assertEqual(a_graph.neighbors(1), {2})
self.assertEqual(a_graph.neighbors(2), set())
# Check neighbors on non-existing vertices.
self.assertEqual(a_graph.neighbors(3), set())
self.assertEqual(a_graph.neighbors(4), set())
def test_linked_list(self):
"""Test public methods on a linked list."""
# Build a linked list:
# 0 -> 1 -> 2
a_graph = DirectedGraph()
a_graph.connect(0, 1)
a_graph.connect(1, 2)
# Sort.
a_sorter = TopologicalSort(a_graph)
sorted_vertices = a_sorter.sort()
# Only one correct sequence.
self.assertEqual(sorted_vertices, (2, 1, 0))
# Check the result using a graph.Reachability object.
a_checker = Reachability(a_graph)
self.assertTrue(self._sorted(sorted_vertices, a_checker))
def test_binary_tree(self):
"""Test public methods on a binary tree."""
# Build a binary tree:
# 0
# / \
# 1 2
a_graph = DirectedGraph()
a_graph.connect(0, 1)
a_graph.connect(0, 2)
# Sort.
a_sorter = TopologicalSort(a_graph)
sorted_vertices = a_sorter.sort()
# Either of the two sequences is correct.
self.assertTrue(sorted_vertices in {(2, 1, 0), (1, 2, 0)})
# Check the result using a graph.Reachability object.
a_checker = Reachability(a_graph)
self.assertTrue(self._sorted(sorted_vertices, a_checker))
def test_binary_tree(self):
"""Test public methods on a binary tree."""
# Build a binary tree:
# 0
# / \
# 1 2
a_graph = DirectedGraph()
a_graph.connect(0, 1)
a_graph.connect(0, 2)
checker = Reachability(a_graph)
# All the vertices are reachable from the root.
self.assertTrue(checker.has_path(0, 1))
self.assertTrue(checker.has_path(0, 2))
# Vertices in another subtree are NOT reachable.
self.assertFalse(checker.has_path(1, 2))
self.assertFalse(checker.has_path(2, 1))
# Parent is NOT reachable.
self.assertFalse(checker.has_path(1, 0))
self.assertFalse(checker.has_path(2, 0))
def test_implicit_adding_by_connecting(self):
"""Test connect(), which implicitly calls add()."""
# Create [].
a_graph = DirectedGraph()
# Implicitly add 0, 1, 2 to [], then connect 1 with 2,
# which makes [set(), {2}, set()].
a_graph.connect(1, 2)
self.assertEqual(a_graph.n_vertices(), 3)
# Trivially connected vertices.
self.assertEqual(a_graph.connected(0, 0), True)
self.assertEqual(a_graph.connected(1, 1), True)
self.assertEqual(a_graph.connected(2, 2), True)
# Uni-directional connection created by connect().
self.assertEqual(a_graph.connected(1, 2), True)
self.assertEqual(a_graph.connected(2, 1), False)
# Disconnected vertices.
self.assertEqual(a_graph.connected(0, 1), False)
self.assertEqual(a_graph.connected(1, 0), False)
self.assertEqual(a_graph.connected(0, 2), False)
self.assertEqual(a_graph.connected(2, 0), False)
def test_linked_list(self):
"""Test public methods on a linked list."""
# Build a linked list:
# 0 -> 1 -> 2
a_graph = DirectedGraph()
a_graph.connect(0, 1)
a_graph.connect(1, 2)
checker = Reachability(a_graph)
# A vertex is always reachable from/to itself.
self.assertTrue(checker.has_path(0, 0))
self.assertTrue(checker.has_path(1, 1))
self.assertTrue(checker.has_path(2, 2))
# A downstream vertex is reachable from an upstream vertex.
self.assertTrue(checker.has_path(0, 1))
self.assertTrue(checker.has_path(1, 2))
self.assertTrue(checker.has_path(0, 2))
# A upstream vertex is NOT reachable from an downstream vertex.
self.assertFalse(checker.has_path(1, 0))
self.assertFalse(checker.has_path(2, 0))
self.assertFalse(checker.has_path(2, 1))
def setUp(self):
dag = DirectedGraph()
dag.add_node(0)
dag.add_node(1)
dag.add_node(2)
dag.add_node(3)
dag.add_node(4)
dag.add_node(5)
dag.connect(0, 1)
dag.connect(0, 2)
dag.connect(0, 3)
dag.connect(3, 4)
dag.connect(4, 5)
self.dag = dag
cyclic = DirectedGraph()
cyclic.add_node(0)
cyclic.add_node(1)
cyclic.add_node(2)
cyclic.add_node(3)
cyclic.add_node(4)
cyclic.connect(0, 1)
cyclic.connect(1, 2)
cyclic.connect(1, 3)
cyclic.connect(2, 3)
cyclic.connect(2, 4)
cyclic.connect(4, 0)
self.cyclic = cyclic
class Scheduler:
"""A scheduler supporting O(1) adding and O(N) scheduling."""
def __init__(self):
self._task_to_id = dict()
self._id_to_task = list()
self._graph = DirectedGraph()
self._union = UnionFind()
def add_a_task(self, task):
"""Add a new task.
Do nothing, if the task has already been added.
"""
if task not in self._task_to_id:
i_task = self.n_tasks()
self._task_to_id[task] = i_task
self._id_to_task.append(task)
assert len(self._id_to_task) == len(self._task_to_id)
assert task == self._id_to_task[self._task_to_id[task]]
def add_tasks(self, tasks):
"""Add multiple tasks."""
for task in tasks:
self.add_a_task(task)
def n_tasks(self):
"""Return the number of tasks being added."""
return len(self._task_to_id)
def add_a_prerequisite(self, task, prerequisite):
"""Add a prerequisite for a task.
Automatically add a new task, if any of the two is new.
Do nothing, if the prerequisite has already been added.
"""
self.add_a_task(task)
self.add_a_task(prerequisite)
i_task = self._task_to_id[task]
i_prerequisite = self._task_to_id[prerequisite]
self._graph.connect(i_task, i_prerequisite)
self._union.connect(i_task, i_prerequisite)
def add_prerequisites(self, task, prerequisites):
"""Add multiple prerequisites for a task."""
for prerequisite in prerequisites:
self.add_a_prerequisite(task, prerequisite)
def schedule(self):
"""Return the tasks in topologically sorted order."""
sorted_tasks = TopologicalSort(self._graph).sort()
# Make immutable copies.
scheduled_tasks = set()
for a_component in self._to_components(sorted_tasks):
scheduled_tasks.add(tuple(a_component))
return scheduled_tasks
def _to_components(self, sorted_tasks):
root_to_component = dict()
for i_task in sorted_tasks:
i_root = self._union.root(i_task)
if i_root not in root_to_component:
root_to_component[i_root] = list()
task = self._id_to_task[i_task]
root_to_component[i_root].append(task)
return root_to_component.values()