def graham(points: List) -> List:
"""
Graham's scan is a method of finding the convex hull of a finite
set of points in the plane with time complexity O(n log n).
It is named after Ronald Graham, who published the original
algorithm in 1972.The algorithm finds all vertices of the
convex hull ordered along its boundary.
"""
# Find the bottom left point and remove it from the set
bottom_left_point = min(points, key=lambda x: (x[1], x[0]))
# Put the points on a min heap by polar angle
polar_points = [(get_polar_angle(bottom_left_point, x), x) for x in points
if x != bottom_left_point]
point_heap = BinomialHeap(polar_points)
# Push the first 3 elements on a stack
stack = Stack()
stack.push(bottom_left_point)
stack.push(point_heap.pop()[1])
stack.push(point_heap.pop()[1])
for _ in range(len(point_heap)):
_, p3 = point_heap.pop()
while is_counterclockwise(stack.peek(1), stack.peek(), p3) < 0:
stack.pop()
stack.push(p3)
return stack.to_array()
def graham(points: List) -> List:
"""
Graham's scan is a method of finding the convex hull of a finite
set of points in the plane with time complexity O(n log n).
It is named after Ronald Graham, who published the original
algorithm in 1972.The algorithm finds all vertices of the
convex hull ordered along its boundary.
"""
# Find the bottom left point and remove it from the set
bottom_left_point = min(points, key=lambda x: (x[1], x[0]))
# Put the points on a min heap by polar angle
polar_points = [(get_polar_angle(bottom_left_point, x), x) for x in points if x != bottom_left_point]
point_heap = BinomialHeap(polar_points)
# Push the first 3 elements on a stack
stack = Stack()
stack.push(bottom_left_point)
stack.push(point_heap.pop()[1])
stack.push(point_heap.pop()[1])
for _ in range(len(point_heap)):
_, p3 = point_heap.pop()
while is_counterclockwise(stack.peek(1), stack.peek(), p3) < 0:
stack.pop()
stack.push(p3)
return stack.to_array()
class TestBinomialHeap(unittest.TestCase):
def setUp(self):
self.list = [random.randint(1, 20) for _ in range(10)]
self.heap = BinomialHeap(self.list)
self.list2 = [random.randint(1, 20) for _ in range(10)]
self.heap2 = BinomialHeap(self.list2)
def test_pop(self):
start = 0
while True:
try:
value = self.heap.pop()
assert value >= start
assert value in self.list
self.list.remove(value)
start = value
except IndexError:
break
assert len(self.list) == 0
def test_insert(self):
heap = BinomialHeap()
heap.insert(4)
heap.insert(7)
heap.insert(1)
heap.insert(2)
heap.insert(10)
assert heap.pop() == 1
heap.insert(3)
assert heap.pop() == 2
assert heap.pop() == 3
assert heap.pop() == 4
assert heap.pop() == 7
assert heap.pop() == 10
def test_merge(self):
self.heap.merge(self.heap2)
assert len(self.heap) == 20
start = 0
combined_list = self.list + self.list2
while True:
try:
value = self.heap.pop()
assert value >= start
assert value in combined_list
combined_list.remove(value)
start = value
except IndexError:
break
assert len(combined_list) == 0
class TestBinomialHeap(unittest.TestCase):
def setUp(self):
self.list = [random.randint(1,20) for _ in range(10)]
self.heap = BinomialHeap(self.list)
self.list2 = [random.randint(1, 20) for _ in range(10)]
self.heap2 = BinomialHeap(self.list2)
def test_pop(self):
start = 0
while True:
try:
value = self.heap.pop()
assert value >= start
assert value in self.list
self.list.remove(value)
start = value
except IndexError:
break
assert len(self.list) == 0
def test_insert(self):
heap = BinomialHeap()
heap.insert(4)
heap.insert(7)
heap.insert(1)
heap.insert(2)
heap.insert(10)
assert heap.pop() == 1
heap.insert(3)
assert heap.pop() == 2
assert heap.pop() == 3
assert heap.pop() == 4
assert heap.pop() == 7
assert heap.pop() == 10
def test_merge(self):
self.heap.merge(self.heap2)
assert len(self.heap) == 20
start = 0
combined_list = self.list + self.list2
while True:
try:
value = self.heap.pop()
assert value >= start
assert value in combined_list
combined_list.remove(value)
start = value
except IndexError:
break
assert len(combined_list) == 0
def setUp(self):
self.list = [random.randint(1, 20) for _ in range(10)]
self.heap = BinomialHeap(self.list)
self.list2 = [random.randint(1, 20) for _ in range(10)]
self.heap2 = BinomialHeap(self.list2)
def test_insert(self):
heap = BinomialHeap()
heap.insert(4)
heap.insert(7)
heap.insert(1)
heap.insert(2)
heap.insert(10)
assert heap.pop() == 1
heap.insert(3)
assert heap.pop() == 2
assert heap.pop() == 3
assert heap.pop() == 4
assert heap.pop() == 7
assert heap.pop() == 10
def setUp(self):
self.list = [random.randint(1,20) for _ in range(10)]
self.heap = BinomialHeap(self.list)
self.list2 = [random.randint(1, 20) for _ in range(10)]
self.heap2 = BinomialHeap(self.list2)
def test_insert(self):
heap = BinomialHeap()
heap.insert(4)
heap.insert(7)
heap.insert(1)
heap.insert(2)
heap.insert(10)
assert heap.pop() == 1
heap.insert(3)
assert heap.pop() == 2
assert heap.pop() == 3
assert heap.pop() == 4
assert heap.pop() == 7
assert heap.pop() == 10
