Pyupgrade to Python 3.9 (#4718)

* Pyupgrade to Python 3.9

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

divide_and_conquer/convex_hull.py

@@ -12,8 +12,9 @@ There are other several other algorithms for the convex hull problem
 which have not been implemented here, yet.
 
 """
+from __future__ import annotations
 
-from typing import Iterable, List, Set, Union
+from typing import Iterable
 
 
 class Point:
@@ -84,8 +85,8 @@ class Point:
 
 
 def _construct_points(
-    list_of_tuples: Union[List[Point], List[List[float]], Iterable[List[float]]]
-) -> List[Point]:
+    list_of_tuples: list[Point] | list[list[float]] | Iterable[list[float]],
+) -> list[Point]:
     """
     constructs a list of points from an array-like object of numbers
 
@@ -114,7 +115,7 @@ def _construct_points(
     []
     """
 
-    points: List[Point] = []
+    points: list[Point] = []
     if list_of_tuples:
         for p in list_of_tuples:
             if isinstance(p, Point):
@@ -130,7 +131,7 @@ def _construct_points(
     return points
 
 
-def _validate_input(points: Union[List[Point], List[List[float]]]) -> List[Point]:
+def _validate_input(points: list[Point] | list[list[float]]) -> list[Point]:
     """
     validates an input instance before a convex-hull algorithms uses it
 
@@ -218,7 +219,7 @@ def _det(a: Point, b: Point, c: Point) -> float:
     return det
 
 
-def convex_hull_bf(points: List[Point]) -> List[Point]:
+def convex_hull_bf(points: list[Point]) -> list[Point]:
     """
     Constructs the convex hull of a set of 2D points using a brute force algorithm.
     The algorithm basically considers all combinations of points (i, j) and uses the
@@ -291,7 +292,7 @@ def convex_hull_bf(points: List[Point]) -> List[Point]:
     return sorted(convex_set)
 
 
-def convex_hull_recursive(points: List[Point]) -> List[Point]:
+def convex_hull_recursive(points: list[Point]) -> list[Point]:
     """
     Constructs the convex hull of a set of 2D points using a divide-and-conquer strategy
     The algorithm exploits the geometric properties of the problem by repeatedly
@@ -362,7 +363,7 @@ def convex_hull_recursive(points: List[Point]) -> List[Point]:
 
 
 def _construct_hull(
-    points: List[Point], left: Point, right: Point, convex_set: Set[Point]
+    points: list[Point], left: Point, right: Point, convex_set: set[Point]
 ) -> None:
     """
 
@@ -405,7 +406,7 @@ def _construct_hull(
             _construct_hull(candidate_points, extreme_point, right, convex_set)
 
 
-def convex_hull_melkman(points: List[Point]) -> List[Point]:
+def convex_hull_melkman(points: list[Point]) -> list[Point]:
     """
     Constructs the convex hull of a set of 2D points using the melkman algorithm.
     The algorithm works by iteratively inserting points of a simple polygonal chain