Reduce the complexity of other/graham_scan.py

Author: MaximSmolskiy

other/graham_scan.py

@@ -13,6 +13,82 @@
 from math import atan2, degrees
 from sys import maxsize
 
+# 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 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
+
+
+def check_direction(
+    starting: tuple[int, int], via: tuple[int, int], target: tuple[int, int]
+) -> Direction:
+    """Return the direction toward to the line from via to target from starting
+
+    :param starting: The starting point
+           via: The via point
+           target: The target point
+    :return: the Direction
+
+    Examples:
+    >>> check_direction((1,1), (2,2), (3,3))
+    Direction.straight
+
+    >>> check_direction((60,1), (-50,199), (30,2))
+    Direction.left
+
+    >>> check_direction((0,0), (5,5), (10,0))
+    Direction.right
+    """
+    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
+
 
 def graham_scan(points: list[tuple[int, int]]) -> list[tuple[int, int]]:
     """Pure implementation of graham scan algorithm in Python
@@ -57,86 +133,12 @@ def graham_scan(points: list[tuple[int, int]]) -> list[tuple[int, int]]:
     # 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:
-        """Return the direction toward to the line from via to target from starting
-
-        :param starting: The starting point
-               via: The via point
-               target: The target point
-        :return: the Direction
-
-        Examples:
-        >>> check_direction((1,1), (2,2), (3,3))
-        Direction.straight
-
-        >>> check_direction((60,1), (-50,199), (30,2))
-        Direction.left
-
-        >>> check_direction((0,0), (5,5), (10,0))
-        Direction.right
-        """
-        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])