def dsp(graph: list, s, t) -> int:
"""
Find shortest path from two vertices via Dijkstra's shortest-path algorithm.
Args:
s: source vertex
t: the target vertex
Returns:
Shortest path from `s` to `t` vertices
"""
if s == t:
return 0
# Vertices seen so far
visited = []
heap = MinHeap([(10000000, v) for v in range(1, len(graph))])
heap.update_min(0, s)
while not heap.is_empty():
dist, u = heap.pop()
visited.append(u)
if u == t:
return dist
for v, d in graph[u]:
if v not in visited:
heap.update_min(dist + d, v)
class TestMinHeapWithTuples(unittest.TestCase):
def setUp(self):
self.h = MinHeap(
elements=[(4, 101), (12, 9), (13,
5), (2, 1), (6, 1001), (5,
45), (10,
121)])
def test_correct_order(self):
self.assertEqual(
self.h.h,
[(2, 1), (4, 101), (5, 45), (12, 9), (6, 1001), (13, 5),
(10, 121)],
)
def test_insert_99_1(self):
self.assertEqual(self.h.insert((1, 99)), 0)
self.assertEqual(
self.h.h,
[
(1, 99),
(2, 1),
(5, 45),
(4, 101),
(6, 1001),
(13, 5),
(10, 121),
(12, 9),
],
)
def test_update_min(self):
self.assertTrue((13, 5) in self.h)
self.assertTrue((11, 5) not in self.h)
self.h.update_min(11, 5)
self.assertTrue((11, 5) in self.h)
self.assertTrue((13, 5) not in self.h)
self.assertEqual(
self.h.h,
[(2, 1), (4, 101), (5, 45), (12, 9), (6, 1001), (11, 5),
(10, 121)],
)
def test_pop(self):
self.assertEqual(len(self.h.h), 7)
self.assertEqual(self.h.pop(), (2, 1))
self.assertEqual(self.h.pop(), (4, 101))
self.assertEqual(self.h.pop(), (5, 45))
self.assertEqual(self.h.pop(), (6, 1001))
self.assertEqual(len(self.h.h), 3)
self.assertEqual(self.h.h, [(10, 121), (12, 9), (13, 5)])
class TestMinHeap(unittest.TestCase):
def setUp(self):
self.h = MinHeap(elements=[2, 4, 5, 12, 13, 6, 10])
def test_parent_index(self):
self.assertLess(self.h._parent_index(0), 0)
self.assertEqual(self.h._parent_index(1), 0)
self.assertEqual(self.h._parent_index(2), 0)
self.assertEqual(self.h._parent_index(4), 1)
self.assertEqual(self.h._parent_index(6), 2)
def test_left_child_index(self):
self.assertGreaterEqual(self.h._left_child_index(3), len(self.h))
self.assertGreaterEqual(self.h._left_child_index(5), len(self.h))
self.assertEqual(self.h._left_child_index(0), 1)
self.assertEqual(self.h._left_child_index(1), 3)
self.assertEqual(self.h._left_child_index(2), 5)
def test_right_child_index(self):
self.assertGreaterEqual(self.h._right_child_index(3), len(self.h))
self.assertGreaterEqual(self.h._right_child_index(6), len(self.h))
self.assertEqual(self.h._right_child_index(0), 2)
self.assertEqual(self.h._right_child_index(1), 4)
self.assertEqual(self.h._right_child_index(2), 6)
def test_is_empty(self):
self.assertFalse(self.h.is_empty())
self.assertTrue(MinHeap().is_empty())
def test_peek(self):
self.assertEqual(self.h.peek(), self.h.h[0])
self.assertIsNone(MinHeap().peek())
def test_heapify_init(self):
elements = [2, 4, 5, 6, 10, 12, 13]
h = MinHeap(elements)
self.assertEqual(h.h, [2, 4, 5, 6, 10, 12, 13])
def test_heapify_after_init(self):
elements = [2, 4, 5, 6, 10, 12, 13]
h = MinHeap()
self.assertEqual(h.h, [])
h._heapify(elements)
self.assertEqual(h.h, [2, 4, 5, 6, 10, 12, 13])
def test_insert_1(self):
self.assertEqual(self.h.insert(1), 0)
self.assertEqual(self.h.h, [1, 2, 5, 4, 13, 6, 10, 12])
def test_insert_3(self):
self.assertEqual(self.h.insert(3), 1)
self.assertEqual(self.h.h, [2, 3, 5, 4, 13, 6, 10, 12])
def test_insert_10(self):
self.assertEqual(self.h.insert(9), 3)
self.assertEqual(self.h.h, [2, 4, 5, 9, 13, 6, 10, 12])
def test_insert_15(self):
self.assertEqual(self.h.insert(15), 7)
self.assertEqual(self.h.h, [2, 4, 5, 12, 13, 6, 10, 15])
def test_update_min(self):
self.assertTrue(9 not in self.h)
self.assertTrue(10 in self.h)
self.h.update_min(9, 10)
self.assertTrue(9 in self.h)
self.assertTrue(10 not in self.h)
self.assertEqual(self.h.h, [2, 4, 5, 12, 13, 6, 9])
def test_pop_empty(self):
h = MinHeap()
self.assertIsNone(h.pop())
self.assertEqual(h.h, [])
