from __future__ import annotations
from collections import deque
from enum import Enum
from math import atan2, degrees
from sys import maxsize
def graham_scan(points: list[tuple[int, int]]) -> list[tuple[int, int]]:
if len(points) <= 2:
# There is no convex hull
raise ValueError("graham_scan: argument must contain more than 3 points.")
if len(points) == 3:
return points
# find the lowest and the most left point
minidx = 0
miny, minx = maxsize, maxsize
for i, point in enumerate(points):
x = point[0]
y = point[1]
if y < miny:
miny = y
minx = x
minidx = i
if y == miny:
if x < minx:
minx = x
minidx = i
# remove the lowest and the most left point from points for preparing for sort
points.pop(minidx)
def angle_comparer(point: tuple[int, int], minx: int, miny: int) -> float:
"""Return the angle toward to point from (minx, miny) :param point: The target point minx: The starting point's x miny: The starting point's y :return: the angle Examples: >>> angle_comparer((1,1), 0, 0) 45.0 >>> angle_comparer((100,1), 10, 10) -5.710593137499642 >>> angle_comparer((5,5), 2, 3) 33.690067525979785 """
# sort the points accorgind to the angle from the lowest and the most left point
x = point[0]
y = point[1]
angle = degrees(atan2(y - miny, x - minx))
return angle
sorted_points = sorted(points, key=lambda point: angle_comparer(point, minx, miny))
# This insert actually costs complexity,
# and you should instead add (minx, miny) into stack later.
# I'm using insert just for easy understanding.
sorted_points.insert(0, (minx, miny))
# traversal from the lowest and the most left point in anti-clockwise direction
# if direction gets right, the previous point is not the convex hull.
class Direction(Enum):
left = 1
straight = 2
right = 3
def check_direction(
starting: tuple[int, int], via: tuple[int, int], target: tuple[int, int]
) -> Direction:
x0, y0 = starting
x1, y1 = via
x2, y2 = target
via_angle = degrees(atan2(y1 - y0, x1 - x0))
if via_angle < 0:
via_angle += 360
target_angle = degrees(atan2(y2 - y0, x2 - x0))
if target_angle < 0:
target_angle += 360
# t-
# \ \
# \ v
# \|
# s
# via_angle is always lower than target_angle, if direction is left.
# If they are same, it means they are on a same line of convex hull.
if target_angle > via_angle:
return Direction.left
elif target_angle == via_angle:
return Direction.straight
else:
return Direction.right
stack: deque[tuple[int, int]] = deque()
stack.append(sorted_points[0])
stack.append(sorted_points[1])
stack.append(sorted_points[2])
# In any ways, the first 3 points line are towards left.
# Because we sort them the angle from minx, miny.
current_direction = Direction.left
for i in range(3, len(sorted_points)):
while True:
starting = stack[-2]
via = stack[-1]
target = sorted_points[i]
next_direction = check_direction(starting, via, target)
if next_direction == Direction.left:
current_direction = Direction.left
break
if next_direction == Direction.straight:
if current_direction == Direction.left:
# We keep current_direction as left.
# Because if the straight line keeps as straight,
# we want to know if this straight line is towards left.
break
elif current_direction == Direction.right:
# If the straight line is towards right,
# every previous points on those straigh line is not convex hull.
stack.pop()
if next_direction == Direction.right:
stack.pop()
stack.append(sorted_points[i])
return list(stack)
