def jarvis(points: List) -> List[Point]:
"""
In computational geometry, the gift wrapping algorithm is an algorithm
for computing the convex hull of a given set of points.
Complexity: O(nh)
:return: the set of points which span the convex hull
"""
# Take the leftmost point as the starting point of the hull
leftmost_point = last_point = min(points, key=lambda point: point.x)
current_point = max(points, key=lambda x: get_polar_angle(last_point, x))
result = [leftmost_point]
# Keep tracking the convex hull clockwise
while current_point != leftmost_point:
result.append(current_point)
# Choose the point which result in the largest inner angle
new_point = max(
points,
key=lambda x: get_internal_angle(last_point, current_point, x)
if x != current_point else 0)
last_point, current_point = current_point, new_point
return result
def jarvis(points: List) -> List[Point]:
"""
In computational geometry, the gift wrapping algorithm is an algorithm
for computing the convex hull of a given set of points.
Complexity: O(nh)
:return: the set of points which span the convex hull
"""
# Take the leftmost point as the starting point of the hull
leftmost_point = last_point = min(points, key=lambda point: point.x)
current_point = max(points, key=lambda x: get_polar_angle(last_point, x))
result = [leftmost_point]
# Keep tracking the convex hull clockwise
while current_point != leftmost_point:
result.append(current_point)
# Choose the point which result in the largest inner angle
new_point = max(points, key=lambda x: get_internal_angle(last_point, current_point, x) if x != current_point else 0)
last_point, current_point = current_point, new_point
return result
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()
