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>

DIRECTORY.md

@@ -545,7 +545,7 @@
 ## Other
   * [Activity Selection](https://github.com/TheAlgorithms/Python/blob/master/other/activity_selection.py)
   * [Date To Weekday](https://github.com/TheAlgorithms/Python/blob/master/other/date_to_weekday.py)
-  * [Davis–Putnam–Logemann–Loveland](https://github.com/TheAlgorithms/Python/blob/master/other/davis–putnam–logemann–loveland.py)
+  * [Davisb Putnamb Logemannb Loveland](https://github.com/TheAlgorithms/Python/blob/master/other/davisb_putnamb_logemannb_loveland.py)
   * [Dijkstra Bankers Algorithm](https://github.com/TheAlgorithms/Python/blob/master/other/dijkstra_bankers_algorithm.py)
   * [Doomsday](https://github.com/TheAlgorithms/Python/blob/master/other/doomsday.py)
   * [Fischer Yates Shuffle](https://github.com/TheAlgorithms/Python/blob/master/other/fischer_yates_shuffle.py)
@@ -860,6 +860,7 @@
   * [Counting Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/counting_sort.py)
   * [Cycle Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/cycle_sort.py)
   * [Double Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/double_sort.py)
+  * [Dutch National Flag Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/dutch_national_flag_sort.py)
   * [Exchange Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/exchange_sort.py)
   * [External Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/external_sort.py)
   * [Gnome Sort](https://github.com/TheAlgorithms/Python/blob/master/sorts/gnome_sort.py)

arithmetic_analysis/in_static_equilibrium.py

@@ -1,14 +1,14 @@
 """
 Checks if a system of forces is in static equilibrium.
 """
-from typing import List
+from __future__ import annotations
 
 from numpy import array, cos, cross, ndarray, radians, sin
 
 
 def polar_force(
     magnitude: float, angle: float, radian_mode: bool = False
-) -> List[float]:
+) -> list[float]:
     """
     Resolves force along rectangular components.
     (force, angle) => (force_x, force_y)

arithmetic_analysis/lu_decomposition.py

@@ -3,12 +3,12 @@
 Reference:
 - https://en.wikipedia.org/wiki/LU_decomposition
 """
-from typing import Tuple
+from __future__ import annotations
 
 import numpy as np
 
 
-def lower_upper_decomposition(table: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
+def lower_upper_decomposition(table: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
     """Lower-Upper (LU) Decomposition
 
     Example:

arithmetic_analysis/newton_forward_interpolation.py

@@ -1,7 +1,7 @@
 # https://www.geeksforgeeks.org/newton-forward-backward-interpolation/
+from __future__ import annotations
 
 import math
-from typing import List
 
 
 # for calculating u value
@@ -22,7 +22,7 @@ def ucal(u: float, p: int) -> float:
 
 def main() -> None:
     n = int(input("enter the numbers of values: "))
-    y: List[List[float]] = []
+    y: list[list[float]] = []
     for i in range(n):
         y.append([])
     for i in range(n):

arithmetic_analysis/newton_raphson.py

@@ -2,15 +2,16 @@
 # Author: Syed Haseeb Shah (github.com/QuantumNovice)
 # The Newton-Raphson method (also known as Newton's method) is a way to
 # quickly find a good approximation for the root of a real-valued function
+from __future__ import annotations
+
 from decimal import Decimal
 from math import *  # noqa: F401, F403
-from typing import Union
 
 from sympy import diff
 
 
 def newton_raphson(
-    func: str, a: Union[float, Decimal], precision: float = 10 ** -10
+    func: str, a: float | Decimal, precision: float = 10 ** -10
 ) -> float:
     """Finds root from the point 'a' onwards by Newton-Raphson method
     >>> newton_raphson("sin(x)", 2)

backtracking/all_combinations.py

@@ -3,16 +3,16 @@
         numbers out of 1 ... n. We use backtracking to solve this problem.
         Time complexity: O(C(n,k)) which is O(n choose k) = O((n!/(k! * (n - k)!)))
 """
-from typing import List
+from __future__ import annotations
 
 
-def generate_all_combinations(n: int, k: int) -> List[List[int]]:
+def generate_all_combinations(n: int, k: int) -> list[list[int]]:
     """
     >>> generate_all_combinations(n=4, k=2)
     [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]
     """
 
-    result: List[List[int]] = []
+    result: list[list[int]] = []
     create_all_state(1, n, k, [], result)
     return result
 
@@ -21,8 +21,8 @@ def create_all_state(
     increment: int,
     total_number: int,
     level: int,
-    current_list: List[int],
+    current_list: list[int],
-    total_list: List[List[int]],
+    total_list: list[list[int]],
 ) -> None:
     if level == 0:
         total_list.append(current_list[:])
@@ -34,7 +34,7 @@ def create_all_state(
         current_list.pop()
 
 
-def print_all_state(total_list: List[List[int]]) -> None:
+def print_all_state(total_list: list[list[int]]) -> None:
     for i in total_list:
         print(*i)
 

backtracking/all_permutations.py

@@ -5,18 +5,18 @@
         Time complexity: O(n! * n),
         where n denotes the length of the given sequence.
 """
-from typing import List, Union
+from __future__ import annotations
 
 
-def generate_all_permutations(sequence: List[Union[int, str]]) -> None:
+def generate_all_permutations(sequence: list[int | str]) -> None:
     create_state_space_tree(sequence, [], 0, [0 for i in range(len(sequence))])
 
 
 def create_state_space_tree(
-    sequence: List[Union[int, str]],
+    sequence: list[int | str],
-    current_sequence: List[Union[int, str]],
+    current_sequence: list[int | str],
     index: int,
-    index_used: List[int],
+    index_used: list[int],
 ) -> None:
     """
     Creates a state space tree to iterate through each branch using DFS.
@@ -44,8 +44,8 @@ print("Enter the elements")
 sequence = list(map(int, input().split()))
 """
 
-sequence: List[Union[int, str]] = [3, 1, 2, 4]
+sequence: list[int | str] = [3, 1, 2, 4]
 generate_all_permutations(sequence)
 
-sequence_2: List[Union[int, str]] = ["A", "B", "C"]
+sequence_2: list[int | str] = ["A", "B", "C"]
 generate_all_permutations(sequence_2)

backtracking/all_subsequences.py

@@ -5,15 +5,17 @@ of the given sequence. We use backtracking to solve this problem.
 Time complexity: O(2^n),
 where n denotes the length of the given sequence.
 """
-from typing import Any, List
+from __future__ import annotations
+
+from typing import Any
 
 
-def generate_all_subsequences(sequence: List[Any]) -> None:
+def generate_all_subsequences(sequence: list[Any]) -> None:
     create_state_space_tree(sequence, [], 0)
 
 
 def create_state_space_tree(
-    sequence: List[Any], current_subsequence: List[Any], index: int
+    sequence: list[Any], current_subsequence: list[Any], index: int
 ) -> None:
     """
     Creates a state space tree to iterate through each branch using DFS.
@@ -32,7 +34,7 @@ def create_state_space_tree(
 
 
 if __name__ == "__main__":
-    seq: List[Any] = [3, 1, 2, 4]
+    seq: list[Any] = [3, 1, 2, 4]
     generate_all_subsequences(seq)
 
     seq.clear()

backtracking/coloring.py

@@ -5,11 +5,10 @@
 
     Wikipedia: https://en.wikipedia.org/wiki/Graph_coloring
 """
-from typing import List
 
 
 def valid_coloring(
-    neighbours: List[int], colored_vertices: List[int], color: int
+    neighbours: list[int], colored_vertices: list[int], color: int
 ) -> bool:
     """
     For each neighbour check if coloring constraint is satisfied
@@ -35,7 +34,7 @@ def valid_coloring(
 
 
 def util_color(
-    graph: List[List[int]], max_colors: int, colored_vertices: List[int], index: int
+    graph: list[list[int]], max_colors: int, colored_vertices: list[int], index: int
 ) -> bool:
     """
     Pseudo-Code
@@ -86,7 +85,7 @@ def util_color(
     return False
 
 
-def color(graph: List[List[int]], max_colors: int) -> List[int]:
+def color(graph: list[list[int]], max_colors: int) -> list[int]:
     """
     Wrapper function to call subroutine called util_color
     which will either return True or False.

backtracking/hamiltonian_cycle.py

@@ -6,11 +6,10 @@
 
     Wikipedia: https://en.wikipedia.org/wiki/Hamiltonian_path
 """
-from typing import List
 
 
 def valid_connection(
-    graph: List[List[int]], next_ver: int, curr_ind: int, path: List[int]
+    graph: list[list[int]], next_ver: int, curr_ind: int, path: list[int]
 ) -> bool:
     """
     Checks whether it is possible to add next into path by validating 2 statements
@@ -47,7 +46,7 @@ def valid_connection(
     return not any(vertex == next_ver for vertex in path)
 
 
-def util_hamilton_cycle(graph: List[List[int]], path: List[int], curr_ind: int) -> bool:
+def util_hamilton_cycle(graph: list[list[int]], path: list[int], curr_ind: int) -> bool:
     """
     Pseudo-Code
     Base Case:
@@ -108,7 +107,7 @@ def util_hamilton_cycle(graph: List[List[int]], path: List[int], curr_ind: int)
     return False
 
 
-def hamilton_cycle(graph: List[List[int]], start_index: int = 0) -> List[int]:
+def hamilton_cycle(graph: list[list[int]], start_index: int = 0) -> list[int]:
     r"""
     Wrapper function to call subroutine called util_hamilton_cycle,
     which will either return array of vertices indicating hamiltonian cycle

backtracking/knight_tour.py

@@ -1,9 +1,9 @@
 # Knight Tour Intro: https://www.youtube.com/watch?v=ab_dY3dZFHM
 
-from typing import List, Tuple
+from __future__ import annotations
 
 
-def get_valid_pos(position: Tuple[int, int], n: int) -> List[Tuple[int, int]]:
+def get_valid_pos(position: tuple[int, int], n: int) -> list[tuple[int, int]]:
     """
     Find all the valid positions a knight can move to from the current position.
 
@@ -32,7 +32,7 @@ def get_valid_pos(position: Tuple[int, int], n: int) -> List[Tuple[int, int]]:
     return permissible_positions
 
 
-def is_complete(board: List[List[int]]) -> bool:
+def is_complete(board: list[list[int]]) -> bool:
     """
     Check if the board (matrix) has been completely filled with non-zero values.
 
@@ -47,7 +47,7 @@ def is_complete(board: List[List[int]]) -> bool:
 
 
 def open_knight_tour_helper(
-    board: List[List[int]], pos: Tuple[int, int], curr: int
+    board: list[list[int]], pos: tuple[int, int], curr: int
 ) -> bool:
     """
     Helper function to solve knight tour problem.
@@ -68,7 +68,7 @@ def open_knight_tour_helper(
     return False
 
 
-def open_knight_tour(n: int) -> List[List[int]]:
+def open_knight_tour(n: int) -> list[list[int]]:
     """
     Find the solution for the knight tour problem for a board of size n. Raises
     ValueError if the tour cannot be performed for the given size.

backtracking/minimax.py

@@ -7,12 +7,13 @@ if move is of maximizer return true else false
 leaves of game tree is stored in scores[]
 height is maximum height of Game tree
 """
+from __future__ import annotations
+
 import math
-from typing import List
 
 
 def minimax(
-    depth: int, node_index: int, is_max: bool, scores: List[int], height: float
+    depth: int, node_index: int, is_max: bool, scores: list[int], height: float
 ) -> int:
     """
     >>> import math

backtracking/n_queens.py

@@ -7,12 +7,12 @@
  diagonal lines.
 
 """
-from typing import List
+from __future__ import annotations
 
 solution = []
 
 
-def isSafe(board: List[List[int]], row: int, column: int) -> bool:
+def isSafe(board: list[list[int]], row: int, column: int) -> bool:
     """
     This function returns a boolean value True if it is safe to place a queen there
     considering the current state of the board.
@@ -40,7 +40,7 @@ def isSafe(board: List[List[int]], row: int, column: int) -> bool:
     return True
 
 
-def solve(board: List[List[int]], row: int) -> bool:
+def solve(board: list[list[int]], row: int) -> bool:
     """
     It creates a state space tree and calls the safe function until it receives a
     False Boolean and terminates that branch and backtracks to the next
@@ -70,7 +70,7 @@ def solve(board: List[List[int]], row: int) -> bool:
     return False
 
 
-def printboard(board: List[List[int]]) -> None:
+def printboard(board: list[list[int]]) -> None:
     """
     Prints the boards that have a successful combination.
     """

backtracking/n_queens_math.py

@@ -75,14 +75,14 @@ Applying this two formulas we can check if a queen in some position is being att
 for another one or vice versa.
 
 """
-from typing import List
+from __future__ import annotations
 
 
 def depth_first_search(
-    possible_board: List[int],
+    possible_board: list[int],
-    diagonal_right_collisions: List[int],
+    diagonal_right_collisions: list[int],
-    diagonal_left_collisions: List[int],
+    diagonal_left_collisions: list[int],
-    boards: List[List[str]],
+    boards: list[list[str]],
     n: int,
 ) -> None:
     """
@@ -139,7 +139,7 @@ def depth_first_search(
 
 
 def n_queens_solution(n: int) -> None:
-    boards: List[List[str]] = []
+    boards: list[list[str]] = []
     depth_first_search([], [], [], boards, n)
 
     # Print all the boards

backtracking/rat_in_maze.py

@@ -1,7 +1,7 @@
-from typing import List
+from __future__ import annotations
 
 
-def solve_maze(maze: List[List[int]]) -> bool:
+def solve_maze(maze: list[list[int]]) -> bool:
     """
     This method solves the "rat in maze" problem.
     In this problem we have some n by n matrix, a start point and an end point.
@@ -70,7 +70,7 @@ def solve_maze(maze: List[List[int]]) -> bool:
     return solved
 
 
-def run_maze(maze: List[List[int]], i: int, j: int, solutions: List[List[int]]) -> bool:
+def run_maze(maze: list[list[int]], i: int, j: int, solutions: list[list[int]]) -> bool:
     """
     This method is recursive starting from (i, j) and going in one of four directions:
     up, down, left, right.

backtracking/sudoku.py

@@ -9,9 +9,9 @@ function on the next column to see if it returns True. if yes, we
 have solved the puzzle. else, we backtrack and place another number
 in that cell and repeat this process.
 """
-from typing import List, Optional, Tuple
+from __future__ import annotations
 
-Matrix = List[List[int]]
+Matrix = list[list[int]]
 
 # assigning initial values to the grid
 initial_grid: Matrix = [
@@ -59,7 +59,7 @@ def is_safe(grid: Matrix, row: int, column: int, n: int) -> bool:
     return True
 
 
-def find_empty_location(grid: Matrix) -> Optional[Tuple[int, int]]:
+def find_empty_location(grid: Matrix) -> tuple[int, int] | None:
     """
     This function finds an empty location so that we can assign a number
     for that particular row and column.
@@ -71,7 +71,7 @@ def find_empty_location(grid: Matrix) -> Optional[Tuple[int, int]]:
     return None
 
 
-def sudoku(grid: Matrix) -> Optional[Matrix]:
+def sudoku(grid: Matrix) -> Matrix | None:
     """
     Takes a partially filled-in grid and attempts to assign values to
     all unassigned locations in such a way to meet the requirements

backtracking/sum_of_subsets.py

@@ -6,12 +6,12 @@
         Summation of the chosen numbers must be equal to given number M and one number
         can be used only once.
 """
-from typing import List
+from __future__ import annotations
 
 
-def generate_sum_of_subsets_soln(nums: List[int], max_sum: int) -> List[List[int]]:
+def generate_sum_of_subsets_soln(nums: list[int], max_sum: int) -> list[list[int]]:
-    result: List[List[int]] = []
+    result: list[list[int]] = []
-    path: List[int] = []
+    path: list[int] = []
     num_index = 0
     remaining_nums_sum = sum(nums)
     create_state_space_tree(nums, max_sum, num_index, path, result, remaining_nums_sum)
@@ -19,11 +19,11 @@ def generate_sum_of_subsets_soln(nums: List[int], max_sum: int) -> List[List[int
 
 
 def create_state_space_tree(
-    nums: List[int],
+    nums: list[int],
     max_sum: int,
     num_index: int,
-    path: List[int],
+    path: list[int],
-    result: List[List[int]],
+    result: list[list[int]],
     remaining_nums_sum: int,
 ) -> None:
     """

blockchain/chinese_remainder_theorem.py

@@ -11,11 +11,11 @@ Algorithm :
 1. Use extended euclid algorithm to find x,y such that a*x + b*y = 1
 2. Take n = ra*by + rb*ax
 """
-from typing import Tuple
+from __future__ import annotations
 
 
 # Extended Euclid
-def extended_euclid(a: int, b: int) -> Tuple[int, int]:
+def extended_euclid(a: int, b: int) -> tuple[int, int]:
     """
     >>> extended_euclid(10, 6)
     (-1, 2)

blockchain/diophantine_equation.py

@@ -1,7 +1,7 @@
-from typing import Tuple
+from __future__ import annotations
 
 
-def diophantine(a: int, b: int, c: int) -> Tuple[float, float]:
+def diophantine(a: int, b: int, c: int) -> tuple[float, float]:
     """
     Diophantine Equation : Given integers a,b,c ( at least one of a and b != 0), the
     diophantine equation a*x + b*y = c has a solution (where x and y are integers)
@@ -95,7 +95,7 @@ def greatest_common_divisor(a: int, b: int) -> int:
     return b
 
 
-def extended_gcd(a: int, b: int) -> Tuple[int, int, int]:
+def extended_gcd(a: int, b: int) -> tuple[int, int, int]:
     """
     Extended Euclid's Algorithm : If d divides a and b and d = a*x + b*y for integers
     x and y, then d = gcd(a,b)

blockchain/modular_division.py

@@ -1,4 +1,4 @@
-from typing import Tuple
+from __future__ import annotations
 
 
 def modular_division(a: int, b: int, n: int) -> int:
@@ -73,7 +73,7 @@ def modular_division2(a: int, b: int, n: int) -> int:
     return x
 
 
-def extended_gcd(a: int, b: int) -> Tuple[int, int, int]:
+def extended_gcd(a: int, b: int) -> tuple[int, int, int]:
     """
     Extended Euclid's Algorithm : If d divides a and b and d = a*x + b*y for integers x
     and y, then d = gcd(a,b)
@@ -101,7 +101,7 @@ def extended_gcd(a: int, b: int) -> Tuple[int, int, int]:
     return (d, x, y)
 
 
-def extended_euclid(a: int, b: int) -> Tuple[int, int]:
+def extended_euclid(a: int, b: int) -> tuple[int, int]:
     """
     Extended Euclid
     >>> extended_euclid(10, 6)

boolean_algebra/quine_mc_cluskey.py

@@ -1,4 +1,4 @@
-from typing import List
+from __future__ import annotations
 
 
 def compare_string(string1: str, string2: str) -> str:
@@ -22,7 +22,7 @@ def compare_string(string1: str, string2: str) -> str:
         return "".join(l1)
 
 
-def check(binary: List[str]) -> List[str]:
+def check(binary: list[str]) -> list[str]:
     """
     >>> check(['0.00.01.5'])
     ['0.00.01.5']
@@ -46,7 +46,7 @@ def check(binary: List[str]) -> List[str]:
         binary = list(set(temp))
 
 
-def decimal_to_binary(no_of_variable: int, minterms: List[float]) -> List[str]:
+def decimal_to_binary(no_of_variable: int, minterms: list[float]) -> list[str]:
     """
     >>> decimal_to_binary(3,[1.5])
     ['0.00.01.5']
@@ -82,7 +82,7 @@ def is_for_table(string1: str, string2: str, count: int) -> bool:
         return False
 
 
-def selection(chart: List[List[int]], prime_implicants: List[str]) -> List[str]:
+def selection(chart: list[list[int]], prime_implicants: list[str]) -> list[str]:
     """
     >>> selection([[1]],['0.00.01.5'])
     ['0.00.01.5']
@@ -130,8 +130,8 @@ def selection(chart: List[List[int]], prime_implicants: List[str]) -> List[str]:
 
 
 def prime_implicant_chart(
-    prime_implicants: List[str], binary: List[str]
+    prime_implicants: list[str], binary: list[str]
-) -> List[List[int]]:
+) -> list[list[int]]:
     """
     >>> prime_implicant_chart(['0.00.01.5'],['0.00.01.5'])
     [[1]]

cellular_automata/conways_game_of_life.py

@@ -2,11 +2,8 @@
 Conway's Game of Life implemented in Python.
 https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
 """
-
 from __future__ import annotations
 
-from typing import List
-
 from PIL import Image
 
 # Define glider example
@@ -25,7 +22,7 @@ GLIDER = [
 BLINKER = [[0, 1, 0], [0, 1, 0], [0, 1, 0]]
 
 
-def new_generation(cells: List[List[int]]) -> List[List[int]]:
+def new_generation(cells: list[list[int]]) -> list[list[int]]:
     """
     Generates the next generation for a given state of Conway's Game of Life.
     >>> new_generation(BLINKER)

ciphers/caesar_cipher.py

@@ -1,8 +1,9 @@
+from __future__ import annotations
+
 from string import ascii_letters
-from typing import Dict, Optional
 
 
-def encrypt(input_string: str, key: int, alphabet: Optional[str] = None) -> str:
+def encrypt(input_string: str, key: int, alphabet: str | None = None) -> str:
     """
     encrypt
     =======
@@ -80,7 +81,7 @@ def encrypt(input_string: str, key: int, alphabet: Optional[str] = None) -> str:
     return result
 
 
-def decrypt(input_string: str, key: int, alphabet: Optional[str] = None) -> str:
+def decrypt(input_string: str, key: int, alphabet: str | None = None) -> str:
     """
     decrypt
     =======
@@ -145,7 +146,7 @@ def decrypt(input_string: str, key: int, alphabet: Optional[str] = None) -> str:
     return encrypt(input_string, key, alphabet)
 
 
-def brute_force(input_string: str, alphabet: Optional[str] = None) -> Dict[int, str]:
+def brute_force(input_string: str, alphabet: str | None = None) -> dict[int, str]:
     """
     brute_force
     ===========

ciphers/decrypt_caesar_with_chi_squared.py

@@ -1,12 +1,11 @@
 #!/usr/bin/env python3
-
+from __future__ import annotations
-from typing import Optional
 
 
 def decrypt_caesar_with_chi_squared(
     ciphertext: str,
-    cipher_alphabet: Optional[list[str]] = None,
+    cipher_alphabet: list[str] | None = None,
-    frequencies_dict: Optional[dict[str, float]] = None,
+    frequencies_dict: dict[str, float] | None = None,
     case_sensetive: bool = False,
 ) -> tuple[int, float, str]:
     """

ciphers/diffie.py

@@ -1,7 +1,7 @@
-from typing import Optional
+from __future__ import annotations
 
 
-def find_primitive(n: int) -> Optional[int]:
+def find_primitive(n: int) -> int | None:
     for r in range(1, n):
         li = []
         for x in range(n - 1):

ciphers/shuffled_shift_cipher.py

@@ -1,6 +1,7 @@
+from __future__ import annotations
+
 import random
 import string
-from typing import Optional
 
 
 class ShuffledShiftCipher:
@@ -27,7 +28,7 @@ class ShuffledShiftCipher:
     cip2 = ShuffledShiftCipher()
     """
 
-    def __init__(self, passcode: Optional[str] = None) -> None:
+    def __init__(self, passcode: str | None = None) -> None:
         """
         Initializes a cipher object with a passcode as it's entity
         Note: No new passcode is generated if user provides a passcode

compression/huffman.py

@@ -30,7 +30,7 @@ def parse_file(file_path):
             if not c:
                 break
             chars[c] = chars[c] + 1 if c in chars.keys() else 1
-    return sorted([Letter(c, f) for c, f in chars.items()], key=lambda l: l.freq)
+    return sorted((Letter(c, f) for c, f in chars.items()), key=lambda l: l.freq)
 
 
 def build_tree(letters):

conversions/molecular_chemistry.py

@@ -20,7 +20,7 @@ def molarity_to_normality(nfactor: int, moles: float, volume: float) -> float:
       >>> molarity_to_normality(4, 11.4, 5.7)
       8
     """
-    return round((float(moles / volume) * nfactor))
+    return round(float(moles / volume) * nfactor)
 
 
 def moles_to_pressure(volume: float, moles: float, temperature: float) -> float:

conversions/prefix_conversions.py

@@ -1,8 +1,9 @@
 """
 Convert International System of Units (SI) and Binary prefixes
 """
+from __future__ import annotations
+
 from enum import Enum
-from typing import Union
 
 
 class SI_Unit(Enum):
@@ -41,8 +42,8 @@ class Binary_Unit(Enum):
 
 def convert_si_prefix(
     known_amount: float,
-    known_prefix: Union[str, SI_Unit],
+    known_prefix: str | SI_Unit,
-    unknown_prefix: Union[str, SI_Unit],
+    unknown_prefix: str | SI_Unit,
 ) -> float:
     """
     Wikipedia reference: https://en.wikipedia.org/wiki/Binary_prefix
@@ -70,8 +71,8 @@ def convert_si_prefix(
 
 def convert_binary_prefix(
     known_amount: float,
-    known_prefix: Union[str, Binary_Unit],
+    known_prefix: str | Binary_Unit,
-    unknown_prefix: Union[str, Binary_Unit],
+    unknown_prefix: str | Binary_Unit,
 ) -> float:
     """
     Wikipedia reference: https://en.wikipedia.org/wiki/Metric_prefix

data_structures/binary_tree/avl_tree.py

@@ -5,15 +5,16 @@ python3 -m doctest -v avl_tree.py
 For testing run:
 python avl_tree.py
 """
+from __future__ import annotations
 
 import math
 import random
-from typing import Any, List, Optional
+from typing import Any
 
 
 class my_queue:
     def __init__(self) -> None:
-        self.data: List[Any] = []
+        self.data: list[Any] = []
         self.head: int = 0
         self.tail: int = 0
 
@@ -41,17 +42,17 @@ class my_queue:
 class my_node:
     def __init__(self, data: Any) -> None:
         self.data = data
-        self.left: Optional[my_node] = None
+        self.left: my_node | None = None
-        self.right: Optional[my_node] = None
+        self.right: my_node | None = None
         self.height: int = 1
 
     def get_data(self) -> Any:
         return self.data
 
-    def get_left(self) -> Optional["my_node"]:
+    def get_left(self) -> my_node | None:
         return self.left
 
-    def get_right(self) -> Optional["my_node"]:
+    def get_right(self) -> my_node | None:
         return self.right
 
     def get_height(self) -> int:
@@ -61,11 +62,11 @@ class my_node:
         self.data = data
         return
 
-    def set_left(self, node: Optional["my_node"]) -> None:
+    def set_left(self, node: my_node | None) -> None:
         self.left = node
         return
 
-    def set_right(self, node: Optional["my_node"]) -> None:
+    def set_right(self, node: my_node | None) -> None:
         self.right = node
         return
 
@@ -74,7 +75,7 @@ class my_node:
         return
 
 
-def get_height(node: Optional["my_node"]) -> int:
+def get_height(node: my_node | None) -> int:
     if node is None:
         return 0
     return node.get_height()
@@ -149,7 +150,7 @@ def rl_rotation(node: my_node) -> my_node:
     return left_rotation(node)
 
 
-def insert_node(node: Optional["my_node"], data: Any) -> Optional["my_node"]:
+def insert_node(node: my_node | None, data: Any) -> my_node | None:
     if node is None:
         return my_node(data)
     if data < node.get_data():
@@ -197,7 +198,7 @@ def get_leftMost(root: my_node) -> Any:
     return root.get_data()
 
 
-def del_node(root: my_node, data: Any) -> Optional["my_node"]:
+def del_node(root: my_node, data: Any) -> my_node | None:
     left_child = root.get_left()
     right_child = root.get_right()
     if root.get_data() == data:
@@ -275,7 +276,7 @@ class AVLtree:
     """
 
     def __init__(self) -> None:
-        self.root: Optional[my_node] = None
+        self.root: my_node | None = None
 
     def get_height(self) -> int:
         return get_height(self.root)

data_structures/binary_tree/basic_binary_tree.py

@@ -1,4 +1,4 @@
-from typing import Optional
+from __future__ import annotations
 
 
 class Node:
@@ -8,11 +8,11 @@ class Node:
 
     def __init__(self, data: int) -> None:
         self.data = data
-        self.left: Optional[Node] = None
+        self.left: Node | None = None
-        self.right: Optional[Node] = None
+        self.right: Node | None = None
 
 
-def display(tree: Optional[Node]) -> None:  # In Order traversal of the tree
+def display(tree: Node | None) -> None:  # In Order traversal of the tree
     """
     >>> root = Node(1)
     >>> root.left = Node(0)
@@ -30,7 +30,7 @@ def display(tree: Optional[Node]) -> None:  # In Order traversal of the tree
         display(tree.right)
 
 
-def depth_of_tree(tree: Optional[Node]) -> int:
+def depth_of_tree(tree: Node | None) -> int:
     """
     Recursive function that returns the depth of a binary tree.
 

data_structures/binary_tree/binary_search_tree_recursive.py

@@ -7,21 +7,23 @@ python -m unittest binary_search_tree_recursive.py
 To run an example:
 python binary_search_tree_recursive.py
 """
+from __future__ import annotations
+
 import unittest
-from typing import Iterator, Optional
+from typing import Iterator
 
 
 class Node:
-    def __init__(self, label: int, parent: Optional["Node"]) -> None:
+    def __init__(self, label: int, parent: Node | None) -> None:
         self.label = label
         self.parent = parent
-        self.left: Optional[Node] = None
+        self.left: Node | None = None
-        self.right: Optional[Node] = None
+        self.right: Node | None = None
 
 
 class BinarySearchTree:
     def __init__(self) -> None:
-        self.root: Optional[Node] = None
+        self.root: Node | None = None
 
     def empty(self) -> None:
         """
@@ -66,9 +68,7 @@ class BinarySearchTree:
         """
         self.root = self._put(self.root, label)
 
-    def _put(
+    def _put(self, node: Node | None, label: int, parent: Node | None = None) -> Node:
-        self, node: Optional[Node], label: int, parent: Optional[Node] = None
-    ) -> Node:
         if node is None:
             node = Node(label, parent)
         else:
@@ -98,7 +98,7 @@ class BinarySearchTree:
         """
         return self._search(self.root, label)
 
-    def _search(self, node: Optional[Node], label: int) -> Node:
+    def _search(self, node: Node | None, label: int) -> Node:
         if node is None:
             raise Exception(f"Node with label {label} does not exist")
         else:
@@ -140,7 +140,7 @@ class BinarySearchTree:
         else:
             self._reassign_nodes(node, None)
 
-    def _reassign_nodes(self, node: Node, new_children: Optional[Node]) -> None:
+    def _reassign_nodes(self, node: Node, new_children: Node | None) -> None:
         if new_children:
             new_children.parent = node.parent
 
@@ -244,7 +244,7 @@ class BinarySearchTree:
         """
         return self._inorder_traversal(self.root)
 
-    def _inorder_traversal(self, node: Optional[Node]) -> Iterator[Node]:
+    def _inorder_traversal(self, node: Node | None) -> Iterator[Node]:
         if node is not None:
             yield from self._inorder_traversal(node.left)
             yield node
@@ -266,7 +266,7 @@ class BinarySearchTree:
         """
         return self._preorder_traversal(self.root)
 
-    def _preorder_traversal(self, node: Optional[Node]) -> Iterator[Node]:
+    def _preorder_traversal(self, node: Node | None) -> Iterator[Node]:
         if node is not None:
             yield node
             yield from self._preorder_traversal(node.left)

data_structures/binary_tree/binary_tree_traversals.py

@@ -1,13 +1,14 @@
 # https://en.wikipedia.org/wiki/Tree_traversal
+from __future__ import annotations
+
 from dataclasses import dataclass
-from typing import Optional
 
 
 @dataclass
 class Node:
     data: int
-    left: Optional["Node"] = None
+    left: Node | None = None
-    right: Optional["Node"] = None
+    right: Node | None = None
 
 
 def make_tree() -> Node:

data_structures/binary_tree/lazy_segment_tree.py

@@ -1,7 +1,6 @@
 from __future__ import annotations
 
 import math
-from typing import List, Union
 
 
 class SegmentTree:
@@ -38,7 +37,7 @@ class SegmentTree:
         return idx * 2 + 1
 
     def build(
-        self, idx: int, left_element: int, right_element: int, A: List[int]
+        self, idx: int, left_element: int, right_element: int, A: list[int]
     ) -> None:
         if left_element == right_element:
             self.segment_tree[idx] = A[left_element - 1]
@@ -89,7 +88,7 @@ class SegmentTree:
     # query with O(lg n)
     def query(
         self, idx: int, left_element: int, right_element: int, a: int, b: int
-    ) -> Union[int, float]:
+    ) -> int | float:
         """
         query(1, 1, size, a, b) for query max of [a,b]
         >>> A = [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]

data_structures/binary_tree/merge_two_binary_trees.py

@@ -5,7 +5,7 @@ The rule for merging is that if two nodes overlap, then put the value sum of
 both nodes to the new value of the merged node. Otherwise, the NOT null node
 will be used as the node of new tree.
 """
-from typing import Optional
+from __future__ import annotations
 
 
 class Node:
@@ -15,11 +15,11 @@ class Node:
 
     def __init__(self, value: int = 0) -> None:
         self.value = value
-        self.left: Optional[Node] = None
+        self.left: Node | None = None
-        self.right: Optional[Node] = None
+        self.right: Node | None = None
 
 
-def merge_two_binary_trees(tree1: Optional[Node], tree2: Optional[Node]) -> Node:
+def merge_two_binary_trees(tree1: Node | None, tree2: Node | None) -> Node:
     """
     Returns root node of the merged tree.
 
@@ -52,7 +52,7 @@ def merge_two_binary_trees(tree1: Optional[Node], tree2: Optional[Node]) -> Node
     return tree1
 
 
-def print_preorder(root: Optional[Node]) -> None:
+def print_preorder(root: Node | None) -> None:
     """
     Print pre-order traversal of the tree.
 

data_structures/binary_tree/red_black_tree.py

@@ -2,7 +2,9 @@
 python/black : true
 flake8 : passed
 """
-from typing import Iterator, Optional
+from __future__ import annotations
+
+from typing import Iterator
 
 
 class RedBlackTree:
@@ -21,11 +23,11 @@ class RedBlackTree:
 
     def __init__(
         self,
-        label: Optional[int] = None,
+        label: int | None = None,
         color: int = 0,
-        parent: Optional["RedBlackTree"] = None,
+        parent: RedBlackTree | None = None,
-        left: Optional["RedBlackTree"] = None,
+        left: RedBlackTree | None = None,
-        right: Optional["RedBlackTree"] = None,
+        right: RedBlackTree | None = None,
     ) -> None:
         """Initialize a new Red-Black Tree node with the given values:
         label: The value associated with this node
@@ -42,7 +44,7 @@ class RedBlackTree:
 
     # Here are functions which are specific to red-black trees
 
-    def rotate_left(self) -> "RedBlackTree":
+    def rotate_left(self) -> RedBlackTree:
         """Rotate the subtree rooted at this node to the left and
         returns the new root to this subtree.
         Performing one rotation can be done in O(1).
@@ -62,7 +64,7 @@ class RedBlackTree:
         right.parent = parent
         return right
 
-    def rotate_right(self) -> "RedBlackTree":
+    def rotate_right(self) -> RedBlackTree:
         """Rotate the subtree rooted at this node to the right and
         returns the new root to this subtree.
         Performing one rotation can be done in O(1).
@@ -82,7 +84,7 @@ class RedBlackTree:
         left.parent = parent
         return left
 
-    def insert(self, label: int) -> "RedBlackTree":
+    def insert(self, label: int) -> RedBlackTree:
         """Inserts label into the subtree rooted at self, performs any
         rotations necessary to maintain balance, and then returns the
         new root to this subtree (likely self).
@@ -139,7 +141,7 @@ class RedBlackTree:
                 self.grandparent.color = 1
                 self.grandparent._insert_repair()
 
-    def remove(self, label: int) -> "RedBlackTree":
+    def remove(self, label: int) -> RedBlackTree:
         """Remove label from this tree."""
         if self.label == label:
             if self.left and self.right:
@@ -337,7 +339,7 @@ class RedBlackTree:
         """
         return self.search(label) is not None
 
-    def search(self, label: int) -> "RedBlackTree":
+    def search(self, label: int) -> RedBlackTree:
         """Search through the tree for label, returning its node if
         it's found, and None otherwise.
         This method is guaranteed to run in O(log(n)) time.
@@ -411,7 +413,7 @@ class RedBlackTree:
             return self.label
 
     @property
-    def grandparent(self) -> "RedBlackTree":
+    def grandparent(self) -> RedBlackTree:
         """Get the current node's grandparent, or None if it doesn't exist."""
         if self.parent is None:
             return None
@@ -419,7 +421,7 @@ class RedBlackTree:
             return self.parent.parent
 
     @property
-    def sibling(self) -> "RedBlackTree":
+    def sibling(self) -> RedBlackTree:
         """Get the current node's sibling, or None if it doesn't exist."""
         if self.parent is None:
             return None

data_structures/binary_tree/treap.py

@@ -1,9 +1,6 @@
-# flake8: noqa
-
 from __future__ import annotations
 
 from random import random
-from typing import Optional, Tuple
 
 
 class Node:
@@ -12,11 +9,11 @@ class Node:
     Treap is a binary tree by value and heap by priority
     """
 
-    def __init__(self, value: Optional[int] = None):
+    def __init__(self, value: int | None = None):
         self.value = value
         self.prior = random()
-        self.left: Optional[Node] = None
+        self.left: Node | None = None
-        self.right: Optional[Node] = None
+        self.right: Node | None = None
 
     def __repr__(self) -> str:
         from pprint import pformat
@@ -35,7 +32,7 @@ class Node:
         return value + left + right
 
 
-def split(root: Optional[Node], value: int) -> Tuple[Optional[Node], Optional[Node]]:
+def split(root: Node | None, value: int) -> tuple[Node | None, Node | None]:
     """
     We split current tree into 2 trees with value:
 
@@ -64,7 +61,7 @@ def split(root: Optional[Node], value: int) -> Tuple[Optional[Node], Optional[No
             return root, right
 
 
-def merge(left: Optional[Node], right: Optional[Node]) -> Optional[Node]:
+def merge(left: Node | None, right: Node | None) -> Node | None:
     """
     We merge 2 trees into one.
     Note: all left tree's values must be less than all right tree's
@@ -86,7 +83,7 @@ def merge(left: Optional[Node], right: Optional[Node]) -> Optional[Node]:
         return right
 
 
-def insert(root: Optional[Node], value: int) -> Optional[Node]:
+def insert(root: Node | None, value: int) -> Node | None:
     """
     Insert element
 
@@ -99,7 +96,7 @@ def insert(root: Optional[Node], value: int) -> Optional[Node]:
     return merge(merge(left, node), right)
 
 
-def erase(root: Optional[Node], value: int) -> Optional[Node]:
+def erase(root: Node | None, value: int) -> Node | None:
     """
     Erase element
 
@@ -112,7 +109,7 @@ def erase(root: Optional[Node], value: int) -> Optional[Node]:
     return merge(left, right)
 
 
-def inorder(root: Optional[Node]) -> None:
+def inorder(root: Node | None) -> None:
     """
     Just recursive print of a tree
     """
@@ -124,7 +121,7 @@ def inorder(root: Optional[Node]) -> None:
         inorder(root.right)
 
 
-def interactTreap(root: Optional[Node], args: str) -> Optional[Node]:
+def interactTreap(root: Node | None, args: str) -> Node | None:
     """
     Commands:
     + value to add value into treap

data_structures/binary_tree/wavelet_tree.py

@@ -7,8 +7,7 @@ such as the with segment trees or fenwick trees. You can read more about them he
 2. https://www.youtube.com/watch?v=4aSv9PcecDw&t=811s
 3. https://www.youtube.com/watch?v=CybAgVF-MMc&t=1178s
 """
-
+from __future__ import annotations
-from typing import Optional
 
 test_array = [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]
 
@@ -18,8 +17,8 @@ class Node:
         self.minn: int = -1
         self.maxx: int = -1
         self.map_left: list[int] = [-1] * length
-        self.left: Optional[Node] = None
+        self.left: Node | None = None
-        self.right: Optional[Node] = None
+        self.right: Node | None = None
 
     def __repr__(self) -> str:
         """

data_structures/hashing/hash_table.py

@@ -19,7 +19,7 @@ class HashTable:
         return self._keys
 
     def balanced_factor(self):
-        return sum([1 for slot in self.values if slot is not None]) / (
+        return sum(1 for slot in self.values if slot is not None) / (
             self.size_table * self.charge_factor
         )
 

data_structures/hashing/hash_table_with_linked_list.py

@@ -14,7 +14,7 @@ class HashTableWithLinkedList(HashTable):
 
     def balanced_factor(self):
         return (
-            sum([self.charge_factor - len(slot) for slot in self.values])
+            sum(self.charge_factor - len(slot) for slot in self.values)
             / self.size_table
             * self.charge_factor
         )

data_structures/heap/heap.py

@@ -1,4 +1,6 @@
-from typing import Iterable, List, Optional
+from __future__ import annotations
+
+from typing import Iterable
 
 
 class Heap:
@@ -25,19 +27,19 @@ class Heap:
     """
 
     def __init__(self) -> None:
-        self.h: List[float] = []
+        self.h: list[float] = []
         self.heap_size: int = 0
 
     def __repr__(self) -> str:
         return str(self.h)
 
-    def parent_index(self, child_idx: int) -> Optional[int]:
+    def parent_index(self, child_idx: int) -> int | None:
         """return the parent index of given child"""
         if child_idx > 0:
             return (child_idx - 1) // 2
         return None
 
-    def left_child_idx(self, parent_idx: int) -> Optional[int]:
+    def left_child_idx(self, parent_idx: int) -> int | None:
         """
         return the left child index if the left child exists.
         if not, return None.
@@ -47,7 +49,7 @@ class Heap:
             return left_child_index
         return None
 
-    def right_child_idx(self, parent_idx: int) -> Optional[int]:
+    def right_child_idx(self, parent_idx: int) -> int | None:
         """
         return the right child index if the right child exists.
         if not, return None.

data_structures/heap/randomized_heap.py

@@ -3,7 +3,7 @@
 from __future__ import annotations
 
 import random
-from typing import Generic, Iterable, List, Optional, TypeVar
+from typing import Generic, Iterable, TypeVar
 
 T = TypeVar("T")
 
@@ -16,8 +16,8 @@ class RandomizedHeapNode(Generic[T]):
 
     def __init__(self, value: T) -> None:
         self._value: T = value
-        self.left: Optional[RandomizedHeapNode[T]] = None
+        self.left: RandomizedHeapNode[T] | None = None
-        self.right: Optional[RandomizedHeapNode[T]] = None
+        self.right: RandomizedHeapNode[T] | None = None
 
     @property
     def value(self) -> T:
@@ -26,8 +26,8 @@ class RandomizedHeapNode(Generic[T]):
 
     @staticmethod
     def merge(
-        root1: Optional[RandomizedHeapNode[T]], root2: Optional[RandomizedHeapNode[T]]
+        root1: RandomizedHeapNode[T] | None, root2: RandomizedHeapNode[T] | None
-    ) -> Optional[RandomizedHeapNode[T]]:
+    ) -> RandomizedHeapNode[T] | None:
         """Merge 2 nodes together."""
         if not root1:
             return root2
@@ -69,13 +69,13 @@ class RandomizedHeap(Generic[T]):
     [-1, 0, 1]
     """
 
-    def __init__(self, data: Optional[Iterable[T]] = ()) -> None:
+    def __init__(self, data: Iterable[T] | None = ()) -> None:
         """
         >>> rh = RandomizedHeap([3, 1, 3, 7])
         >>> rh.to_sorted_list()
         [1, 3, 3, 7]
         """
-        self._root: Optional[RandomizedHeapNode[T]] = None
+        self._root: RandomizedHeapNode[T] | None = None
         for item in data:
             self.insert(item)
 
@@ -151,7 +151,7 @@ class RandomizedHeap(Generic[T]):
         """
         self._root = None
 
-    def to_sorted_list(self) -> List[T]:
+    def to_sorted_list(self) -> list[T]:
         """
         Returns sorted list containing all the values in the heap.
 

data_structures/heap/skew_heap.py

@@ -2,7 +2,7 @@
 
 from __future__ import annotations
 
-from typing import Generic, Iterable, Iterator, Optional, TypeVar
+from typing import Generic, Iterable, Iterator, TypeVar
 
 T = TypeVar("T")
 
@@ -15,8 +15,8 @@ class SkewNode(Generic[T]):
 
     def __init__(self, value: T) -> None:
         self._value: T = value
-        self.left: Optional[SkewNode[T]] = None
+        self.left: SkewNode[T] | None = None
-        self.right: Optional[SkewNode[T]] = None
+        self.right: SkewNode[T] | None = None
 
     @property
     def value(self) -> T:
@@ -25,8 +25,8 @@ class SkewNode(Generic[T]):
 
     @staticmethod
     def merge(
-        root1: Optional[SkewNode[T]], root2: Optional[SkewNode[T]]
+        root1: SkewNode[T] | None, root2: SkewNode[T] | None
-    ) -> Optional[SkewNode[T]]:
+    ) -> SkewNode[T] | None:
         """Merge 2 nodes together."""
         if not root1:
             return root2
@@ -69,13 +69,13 @@ class SkewHeap(Generic[T]):
     [-1, 0, 1]
     """
 
-    def __init__(self, data: Optional[Iterable[T]] = ()) -> None:
+    def __init__(self, data: Iterable[T] | None = ()) -> None:
         """
         >>> sh = SkewHeap([3, 1, 3, 7])
         >>> list(sh)
         [1, 3, 3, 7]
         """
-        self._root: Optional[SkewNode[T]] = None
+        self._root: SkewNode[T] | None = None
         for item in data:
             self.insert(item)
 

data_structures/linked_list/merge_two_lists.py

@@ -5,7 +5,6 @@ from __future__ import annotations
 
 from collections.abc import Iterable, Iterator
 from dataclasses import dataclass
-from typing import Optional
 
 test_data_odd = (3, 9, -11, 0, 7, 5, 1, -1)
 test_data_even = (4, 6, 2, 0, 8, 10, 3, -2)
@@ -14,12 +13,12 @@ test_data_even = (4, 6, 2, 0, 8, 10, 3, -2)
 @dataclass
 class Node:
     data: int
-    next: Optional[Node]
+    next: Node | None
 
 
 class SortedLinkedList:
     def __init__(self, ints: Iterable[int]) -> None:
-        self.head: Optional[Node] = None
+        self.head: Node | None = None
         for i in reversed(sorted(ints)):
             self.head = Node(i, self.head)
 

data_structures/linked_list/print_reverse.py

@@ -1,4 +1,4 @@
-from typing import List
+from __future__ import annotations
 
 
 class Node:
@@ -16,7 +16,7 @@ class Node:
         return "->".join(string_rep)
 
 
-def make_linked_list(elements_list: List):
+def make_linked_list(elements_list: list):
     """Creates a Linked List from the elements of the given sequence
     (list/tuple) and returns the head of the Linked List.
     >>> make_linked_list([])

data_structures/linked_list/skip_list.py

@@ -2,11 +2,10 @@
 Based on "Skip Lists: A Probabilistic Alternative to Balanced Trees" by William Pugh
 https://epaperpress.com/sortsearch/download/skiplist.pdf
 """
-
 from __future__ import annotations
 
 from random import random
-from typing import Generic, Optional, TypeVar
+from typing import Generic, TypeVar
 
 KT = TypeVar("KT")
 VT = TypeVar("VT")
@@ -124,7 +123,7 @@ class SkipList(Generic[KT, VT]):
 
         return level
 
-    def _locate_node(self, key) -> tuple[Optional[Node[KT, VT]], list[Node[KT, VT]]]:
+    def _locate_node(self, key) -> tuple[Node[KT, VT] | None, list[Node[KT, VT]]]:
         """
         :param key: Searched key,
         :return: Tuple with searched node (or None if given key is not present)
@@ -222,7 +221,7 @@ class SkipList(Generic[KT, VT]):
                 else:
                     update_node.forward[i] = new_node
 
-    def find(self, key: VT) -> Optional[VT]:
+    def find(self, key: VT) -> VT | None:
         """
         :param key: Search key.
         :return: Value associated with given key or None if given key is not present.

data_structures/stacks/evaluate_postfix_notations.py

@@ -1,5 +1,3 @@
-from typing import Any, List
-
 """
 The Reverse Polish Nation also known as Polish postfix notation
 or simply postfix notation.
@@ -8,6 +6,9 @@ Classic examples of simple stack implementations
 Valid operators are +, -, *, /.
 Each operand may be an integer or another expression.
 """
+from __future__ import annotations
+
+from typing import Any
 
 
 def evaluate_postfix(postfix_notation: list) -> int:
@@ -23,7 +24,7 @@ def evaluate_postfix(postfix_notation: list) -> int:
         return 0
 
     operations = {"+", "-", "*", "/"}
-    stack: List[Any] = []
+    stack: list[Any] = []
 
     for token in postfix_notation:
         if token in operations:

data_structures/stacks/linked_stack.py

@@ -1,5 +1,7 @@
 """ A Stack using a linked list like structure """
-from typing import Any, Optional
+from __future__ import annotations
+
+from typing import Any
 
 
 class Node:
@@ -42,7 +44,7 @@ class LinkedStack:
     """
 
     def __init__(self) -> None:
-        self.top: Optional[Node] = None
+        self.top: Node | None = None
 
     def __iter__(self):
         node = self.top

data_structures/stacks/stack.py

@@ -1,4 +1,4 @@
-from typing import List
+from __future__ import annotations
 
 
 class StackOverflowError(BaseException):
@@ -15,7 +15,7 @@ class Stack:
     """
 
     def __init__(self, limit: int = 10):
-        self.stack: List[int] = []
+        self.stack: list[int] = []
         self.limit = limit
 
     def __bool__(self) -> bool:

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_of_tuples: list[Point] | list[list[float]] | Iterable[list[float]],
-) -> List[Point]:
+) -> 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

divide_and_conquer/kth_order_statistic.py

@@ -8,8 +8,9 @@ This is a divide and conquer algorithm that can find a solution in O(n) time.
 For more information of this algorithm:
 https://web.stanford.edu/class/archive/cs/cs161/cs161.1138/lectures/08/Small08.pdf
 """
+from __future__ import annotations
+
 from random import choice
-from typing import List
 
 
 def random_pivot(lst):
@@ -21,7 +22,7 @@ def random_pivot(lst):
     return choice(lst)
 
 
-def kth_number(lst: List[int], k: int) -> int:
+def kth_number(lst: list[int], k: int) -> int:
     """
     Return the kth smallest number in lst.
     >>> kth_number([2, 1, 3, 4, 5], 3)

divide_and_conquer/mergesort.py

@@ -1,7 +1,7 @@
-from typing import List
+from __future__ import annotations
 
 
-def merge(left_half: List, right_half: List) -> List:
+def merge(left_half: list, right_half: list) -> list:
     """Helper function for mergesort.
 
     >>> left_half = [-2]
@@ -57,7 +57,7 @@ def merge(left_half: List, right_half: List) -> List:
     return sorted_array
 
 
-def merge_sort(array: List) -> List:
+def merge_sort(array: list) -> list:
     """Returns a list of sorted array elements using merge sort.
 
     >>> from random import shuffle

divide_and_conquer/peak.py

@@ -7,10 +7,10 @@ to find the maximum of the array.
 (From Kleinberg and Tardos. Algorithm Design.
 Addison Wesley 2006: Chapter 5 Solved Exercise 1)
 """
-from typing import List
+from __future__ import annotations
 
 
-def peak(lst: List[int]) -> int:
+def peak(lst: list[int]) -> int:
     """
     Return the peak value of `lst`.
     >>> peak([1, 2, 3, 4, 5, 4, 3, 2, 1])

electronics/electric_power.py

@@ -1,9 +1,10 @@
 # https://en.m.wikipedia.org/wiki/Electric_power
+from __future__ import annotations
+
 from collections import namedtuple
-from typing import Tuple
 
 
-def electric_power(voltage: float, current: float, power: float) -> Tuple:
+def electric_power(voltage: float, current: float, power: float) -> tuple:
     """
     This function can calculate any one of the three (voltage, current, power),
     fundamental value of electrical system.

electronics/ohms_law.py

@@ -1,8 +1,8 @@
 # https://en.wikipedia.org/wiki/Ohm%27s_law
-from typing import Dict
+from __future__ import annotations
 
 
-def ohms_law(voltage: float, current: float, resistance: float) -> Dict[str, float]:
+def ohms_law(voltage: float, current: float, resistance: float) -> dict[str, float]:
     """
     Apply Ohm's Law, on any two given electrical values, which can be voltage, current,
     and resistance, and then in a Python dict return name/value pair of the zero value.

graphs/basic_graphs.py

@@ -13,7 +13,7 @@ def initialize_unweighted_directed_graph(
         graph[i + 1] = []
 
     for e in range(edge_count):
-        x, y = [int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> ")]
+        x, y = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> "))
         graph[x].append(y)
     return graph
 
@@ -26,7 +26,7 @@ def initialize_unweighted_undirected_graph(
         graph[i + 1] = []
 
     for e in range(edge_count):
-        x, y = [int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> ")]
+        x, y = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> "))
         graph[x].append(y)
         graph[y].append(x)
     return graph
@@ -40,14 +40,14 @@ def initialize_weighted_undirected_graph(
         graph[i + 1] = []
 
     for e in range(edge_count):
-        x, y, w = [int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> <weight> ")]
+        x, y, w = (int(i) for i in _input(f"Edge {e + 1}: <node1> <node2> <weight> "))
         graph[x].append((y, w))
         graph[y].append((x, w))
     return graph
 
 
 if __name__ == "__main__":
-    n, m = [int(i) for i in _input("Number of nodes and edges: ")]
+    n, m = (int(i) for i in _input("Number of nodes and edges: "))
 
     graph_choice = int(
         _input(

graphs/bellman_ford.py

@@ -11,7 +11,7 @@ def check_negative_cycle(
     graph: list[dict[str, int]], distance: list[float], edge_count: int
 ):
     for j in range(edge_count):
-        u, v, w = [graph[j][k] for k in ["src", "dst", "weight"]]
+        u, v, w = (graph[j][k] for k in ["src", "dst", "weight"])
         if distance[u] != float("inf") and distance[u] + w < distance[v]:
             return True
     return False
@@ -38,7 +38,7 @@ def bellman_ford(
 
     for i in range(vertex_count - 1):
         for j in range(edge_count):
-            u, v, w = [graph[j][k] for k in ["src", "dst", "weight"]]
+            u, v, w = (graph[j][k] for k in ["src", "dst", "weight"])
 
             if distance[u] != float("inf") and distance[u] + w < distance[v]:
                 distance[v] = distance[u] + w
@@ -62,10 +62,10 @@ if __name__ == "__main__":
 
     for i in range(E):
         print("Edge ", i + 1)
-        src, dest, weight = [
+        src, dest, weight = (
             int(x)
             for x in input("Enter source, destination, weight: ").strip().split(" ")
-        ]
+        )
         graph[i] = {"src": src, "dst": dest, "weight": weight}
 
     source = int(input("\nEnter shortest path source:").strip())

graphs/bfs_zero_one_shortest_path.py

@@ -1,13 +1,13 @@
-from collections import deque
-from collections.abc import Iterator
-from dataclasses import dataclass
-from typing import Optional, Union
-
 """
 Finding the shortest path in 0-1-graph in O(E + V) which is faster than dijkstra.
 0-1-graph is the weighted graph with the weights equal to 0 or 1.
 Link: https://codeforces.com/blog/entry/22276
 """
+from __future__ import annotations
+
+from collections import deque
+from collections.abc import Iterator
+from dataclasses import dataclass
 
 
 @dataclass
@@ -59,7 +59,7 @@ class AdjacencyList:
 
         self._graph[from_vertex].append(Edge(to_vertex, weight))
 
-    def get_shortest_path(self, start_vertex: int, finish_vertex: int) -> Optional[int]:
+    def get_shortest_path(self, start_vertex: int, finish_vertex: int) -> int | None:
         """
         Return the shortest distance from start_vertex to finish_vertex in 0-1-graph.
               1                  1         1
@@ -107,7 +107,7 @@ class AdjacencyList:
         ValueError: No path from start_vertex to finish_vertex.
         """
         queue = deque([start_vertex])
-        distances: list[Union[int, None]] = [None] * self.size
+        distances: list[int | None] = [None] * self.size
         distances[start_vertex] = 0
 
         while queue:

graphs/bidirectional_a_star.py

@@ -1,15 +1,12 @@
 """
 https://en.wikipedia.org/wiki/Bidirectional_search
 """
-
 from __future__ import annotations
 
 import time
 from math import sqrt
 
 # 1 for manhattan, 0 for euclidean
-from typing import Optional
-
 HEURISTIC = 0
 
 grid = [
@@ -50,7 +47,7 @@ class Node:
         goal_x: int,
         goal_y: int,
         g_cost: int,
-        parent: Optional[Node],
+        parent: Node | None,
     ) -> None:
         self.pos_x = pos_x
         self.pos_y = pos_y
@@ -157,7 +154,7 @@ class AStar:
             )
         return successors
 
-    def retrace_path(self, node: Optional[Node]) -> list[TPosition]:
+    def retrace_path(self, node: Node | None) -> list[TPosition]:
         """
         Retrace the path from parents to parents until start node
         """

graphs/bidirectional_breadth_first_search.py

@@ -1,11 +1,9 @@
 """
 https://en.wikipedia.org/wiki/Bidirectional_search
 """
-
 from __future__ import annotations
 
 import time
-from typing import Optional
 
 Path = list[tuple[int, int]]
 
@@ -24,7 +22,7 @@ delta = [[-1, 0], [0, -1], [1, 0], [0, 1]]  # up, left, down, right
 
 class Node:
     def __init__(
-        self, pos_x: int, pos_y: int, goal_x: int, goal_y: int, parent: Optional[Node]
+        self, pos_x: int, pos_y: int, goal_x: int, goal_y: int, parent: Node | None
     ):
         self.pos_x = pos_x
         self.pos_y = pos_y
@@ -57,7 +55,7 @@ class BreadthFirstSearch:
         self.node_queue = [self.start]
         self.reached = False
 
-    def search(self) -> Optional[Path]:
+    def search(self) -> Path | None:
         while self.node_queue:
             current_node = self.node_queue.pop(0)
 
@@ -93,7 +91,7 @@ class BreadthFirstSearch:
             )
         return successors
 
-    def retrace_path(self, node: Optional[Node]) -> Path:
+    def retrace_path(self, node: Node | None) -> Path:
         """
         Retrace the path from parents to parents until start node
         """
@@ -125,7 +123,7 @@ class BidirectionalBreadthFirstSearch:
         self.bwd_bfs = BreadthFirstSearch(goal, start)
         self.reached = False
 
-    def search(self) -> Optional[Path]:
+    def search(self) -> Path | None:
         while self.fwd_bfs.node_queue or self.bwd_bfs.node_queue:
             current_fwd_node = self.fwd_bfs.node_queue.pop(0)
             current_bwd_node = self.bwd_bfs.node_queue.pop(0)

graphs/breadth_first_search.py

@@ -1,13 +1,12 @@
 #!/usr/bin/python
 
 """ Author: OMKAR PATHAK """
-
+from __future__ import annotations
-from typing import Dict, List, Set
 
 
 class Graph:
     def __init__(self) -> None:
-        self.vertices: Dict[int, List[int]] = {}
+        self.vertices: dict[int, list[int]] = {}
 
     def print_graph(self) -> None:
         """
@@ -35,7 +34,7 @@ class Graph:
         else:
             self.vertices[from_vertex] = [to_vertex]
 
-    def bfs(self, start_vertex: int) -> Set[int]:
+    def bfs(self, start_vertex: int) -> set[int]:
         """
         >>> g = Graph()
         >>> g.add_edge(0, 1)

graphs/breadth_first_search_shortest_path.py

@@ -3,8 +3,6 @@ from a given source node to a target node in an unweighted graph.
 """
 from __future__ import annotations
 
-from typing import Optional
-
 graph = {
     "A": ["B", "C", "E"],
     "B": ["A", "D", "E"],
@@ -24,7 +22,7 @@ class Graph:
         """
         self.graph = graph
         # mapping node to its parent in resulting breadth first tree
-        self.parent: dict[str, Optional[str]] = {}
+        self.parent: dict[str, str | None] = {}
         self.source_vertex = source_vertex
 
     def breath_first_search(self) -> None:

graphs/depth_first_search.py

@@ -1,11 +1,8 @@
 """Non recursive implementation of a DFS algorithm."""
-
 from __future__ import annotations
 
-from typing import Set
 
-
+def depth_first_search(graph: dict, start: str) -> set[str]:
-def depth_first_search(graph: dict, start: str) -> Set[str]:
     """Depth First Search on Graph
     :param graph: directed graph in dictionary format
     :param start: starting vertex as a string

graphs/greedy_best_first.py

@@ -4,8 +4,6 @@ https://en.wikipedia.org/wiki/Best-first_search#Greedy_BFS
 
 from __future__ import annotations
 
-from typing import Optional
-
 Path = list[tuple[int, int]]
 
 grid = [
@@ -44,7 +42,7 @@ class Node:
         goal_x: int,
         goal_y: int,
         g_cost: float,
-        parent: Optional[Node],
+        parent: Node | None,
     ):
         self.pos_x = pos_x
         self.pos_y = pos_y
@@ -93,7 +91,7 @@ class GreedyBestFirst:
 
         self.reached = False
 
-    def search(self) -> Optional[Path]:
+    def search(self) -> Path | None:
         """
         Search for the path,
         if a path is not found, only the starting position is returned
@@ -156,7 +154,7 @@ class GreedyBestFirst:
             )
         return successors
 
-    def retrace_path(self, node: Optional[Node]) -> Path:
+    def retrace_path(self, node: Node | None) -> Path:
         """
         Retrace the path from parents to parents until start node
         """

graphs/minimum_spanning_tree_kruskal.py

@@ -40,7 +40,7 @@ if __name__ == "__main__":  # pragma: no cover
     edges = []
 
     for _ in range(num_edges):
-        node1, node2, cost = [int(x) for x in input().strip().split()]
+        node1, node2, cost = (int(x) for x in input().strip().split())
         edges.append((node1, node2, cost))
 
     kruskal(num_nodes, edges)

graphs/minimum_spanning_tree_prims2.py

@@ -6,9 +6,10 @@ edges in the tree is minimized. The algorithm operates by building this tree one
 at a time, from an arbitrary starting vertex, at each step adding the cheapest possible
 connection from the tree to another vertex.
 """
+from __future__ import annotations
 
 from sys import maxsize
-from typing import Generic, Optional, TypeVar
+from typing import Generic, TypeVar
 
 T = TypeVar("T")
 
@@ -219,7 +220,7 @@ class GraphUndirectedWeighted(Generic[T]):
 
 def prims_algo(
     graph: GraphUndirectedWeighted[T],
-) -> tuple[dict[T, int], dict[T, Optional[T]]]:
+) -> tuple[dict[T, int], dict[T, T | None]]:
     """
     >>> graph = GraphUndirectedWeighted()
 
@@ -240,7 +241,7 @@ def prims_algo(
     """
     # prim's algorithm for minimum spanning tree
     dist: dict[T, int] = {node: maxsize for node in graph.connections}
-    parent: dict[T, Optional[T]] = {node: None for node in graph.connections}
+    parent: dict[T, T | None] = {node: None for node in graph.connections}
 
     priority_queue: MinPriorityQueue[T] = MinPriorityQueue()
     for node, weight in dist.items():

graphs/page_rank.py

@@ -43,7 +43,7 @@ def page_rank(nodes, limit=3, d=0.85):
         print(f"======= Iteration {i + 1} =======")
         for j, node in enumerate(nodes):
             ranks[node.name] = (1 - d) + d * sum(
-                [ranks[ib] / outbounds[ib] for ib in node.inbound]
+                ranks[ib] / outbounds[ib] for ib in node.inbound
             )
         print(ranks)
 

graphs/scc_kosaraju.py

@@ -1,4 +1,4 @@
-from typing import List
+from __future__ import annotations
 
 
 def dfs(u):
@@ -39,16 +39,16 @@ if __name__ == "__main__":
     # n - no of nodes, m - no of edges
     n, m = list(map(int, input().strip().split()))
 
-    graph: List[List[int]] = [[] for i in range(n)]  # graph
+    graph: list[list[int]] = [[] for i in range(n)]  # graph
-    reversedGraph: List[List[int]] = [[] for i in range(n)]  # reversed graph
+    reversedGraph: list[list[int]] = [[] for i in range(n)]  # reversed graph
     # input graph data (edges)
     for i in range(m):
         u, v = list(map(int, input().strip().split()))
         graph[u].append(v)
         reversedGraph[v].append(u)
 
-    stack: List[int] = []
+    stack: list[int] = []
-    visit: List[bool] = [False] * n
+    visit: list[bool] = [False] * n
-    scc: List[int] = []
+    scc: list[int] = []
-    component: List[int] = []
+    component: list[int] = []
     print(kosaraju())

hashes/luhn.py

@@ -1,5 +1,5 @@
 """ Luhn Algorithm """
-from typing import List
+from __future__ import annotations
 
 
 def is_luhn(string: str) -> bool:
@@ -17,9 +17,9 @@ def is_luhn(string: str) -> bool:
     [False, False, False, True, False, False, False, False, False, False]
     """
     check_digit: int
-    _vector: List[str] = list(string)
+    _vector: list[str] = list(string)
     __vector, check_digit = _vector[:-1], int(_vector[-1])
-    vector: List[int] = [int(digit) for digit in __vector]
+    vector: list[int] = [int(digit) for digit in __vector]
 
     vector.reverse()
     for i, digit in enumerate(vector):

knapsack/knapsack.py

@@ -1,11 +1,10 @@
-from typing import List
-
 """ A naive recursive implementation of 0-1 Knapsack Problem
     https://en.wikipedia.org/wiki/Knapsack_problem
 """
+from __future__ import annotations
 
 
-def knapsack(capacity: int, weights: List[int], values: List[int], counter: int) -> int:
+def knapsack(capacity: int, weights: list[int], values: list[int], counter: int) -> int:
     """
     Returns the maximum value that can be put in a knapsack of a capacity cap,
     whereby each weight w has a specific value val.

linear_algebra/src/lib.py

@@ -18,11 +18,11 @@ Overview:
 - function squareZeroMatrix(N)
 - function randomMatrix(W,H,a,b)
 """
-
+from __future__ import annotations
 
 import math
 import random
-from typing import Collection, Optional, Union, overload
+from typing import Collection, overload
 
 
 class Vector:
@@ -46,7 +46,7 @@ class Vector:
     TODO: compare-operator
     """
 
-    def __init__(self, components: Optional[Collection[float]] = None) -> None:
+    def __init__(self, components: Collection[float] | None = None) -> None:
         """
         input: components or nothing
         simple constructor for init the vector
@@ -97,7 +97,7 @@ class Vector:
             summe += c ** 2
         return math.sqrt(summe)
 
-    def __add__(self, other: "Vector") -> "Vector":
+    def __add__(self, other: Vector) -> Vector:
         """
         input: other vector
         assumes: other vector has the same size
@@ -110,7 +110,7 @@ class Vector:
         else:
             raise Exception("must have the same size")
 
-    def __sub__(self, other: "Vector") -> "Vector":
+    def __sub__(self, other: Vector) -> Vector:
         """
         input: other vector
         assumes: other vector has the same size
@@ -124,14 +124,14 @@ class Vector:
             raise Exception("must have the same size")
 
     @overload
-    def __mul__(self, other: float) -> "Vector":
+    def __mul__(self, other: float) -> Vector:
         ...
 
     @overload
-    def __mul__(self, other: "Vector") -> float:
+    def __mul__(self, other: Vector) -> float:
         ...
 
-    def __mul__(self, other: Union[float, "Vector"]) -> Union[float, "Vector"]:
+    def __mul__(self, other: float | Vector) -> float | Vector:
         """
         mul implements the scalar multiplication
         and the dot-product
@@ -148,7 +148,7 @@ class Vector:
         else:  # error case
             raise Exception("invalid operand!")
 
-    def copy(self) -> "Vector":
+    def copy(self) -> Vector:
         """
         copies this vector and returns it.
         """
@@ -313,14 +313,14 @@ class Matrix:
             raise Exception("matrix is not square")
 
     @overload
-    def __mul__(self, other: float) -> "Matrix":
+    def __mul__(self, other: float) -> Matrix:
         ...
 
     @overload
     def __mul__(self, other: Vector) -> Vector:
         ...
 
-    def __mul__(self, other: Union[float, Vector]) -> Union[Vector, "Matrix"]:
+    def __mul__(self, other: float | Vector) -> Vector | Matrix:
         """
         implements the matrix-vector multiplication.
         implements the matrix-scalar multiplication
@@ -347,7 +347,7 @@ class Matrix:
             ]
             return Matrix(matrix, self.__width, self.__height)
 
-    def __add__(self, other: "Matrix") -> "Matrix":
+    def __add__(self, other: Matrix) -> Matrix:
         """
         implements the matrix-addition.
         """
@@ -362,7 +362,7 @@ class Matrix:
         else:
             raise Exception("matrix must have the same dimension!")
 
-    def __sub__(self, other: "Matrix") -> "Matrix":
+    def __sub__(self, other: Matrix) -> Matrix:
         """
         implements the matrix-subtraction.
         """

machine_learning/similarity_search.py

@@ -7,8 +7,9 @@ returns a list containing two data for each vector:
     1. the nearest vector
     2. distance between the vector and the nearest vector (float)
 """
+from __future__ import annotations
+
 import math
-from typing import List, Union
 
 import numpy as np
 
@@ -33,7 +34,7 @@ def euclidean(input_a: np.ndarray, input_b: np.ndarray) -> float:
 
 def similarity_search(
     dataset: np.ndarray, value_array: np.ndarray
-) -> List[List[Union[List[float], float]]]:
+) -> list[list[list[float] | float]]:
     """
     :param dataset: Set containing the vectors. Should be ndarray.
     :param value_array: vector/vectors we want to know the nearest vector from dataset.

maths/area_under_curve.py

@@ -1,14 +1,15 @@
 """
 Approximates the area under the curve using the trapezoidal rule
 """
+from __future__ import annotations
 
-from typing import Callable, Union
+from typing import Callable
 
 
 def trapezoidal_area(
-    fnc: Callable[[Union[int, float]], Union[int, float]],
+    fnc: Callable[[int | float], int | float],
-    x_start: Union[int, float],
+    x_start: int | float,
-    x_end: Union[int, float],
+    x_end: int | float,
     steps: int = 100,
 ) -> float:
     """

maths/average_mean.py

@@ -1,7 +1,7 @@
-from typing import List
+from __future__ import annotations
 
 
-def mean(nums: List) -> float:
+def mean(nums: list) -> float:
     """
     Find mean of a list of numbers.
     Wiki: https://en.wikipedia.org/wiki/Mean

maths/average_median.py

@@ -1,7 +1,7 @@
-from typing import Union
+from __future__ import annotations
 
 
-def median(nums: list) -> Union[int, float]:
+def median(nums: list) -> int | float:
     """
     Find median of a list of numbers.
     Wiki: https://en.wikipedia.org/wiki/Median

maths/entropy.py

@@ -68,7 +68,7 @@ def calculate_prob(text: str) -> None:
             my_fir_sum += prob * math.log2(prob)  # entropy formula.
 
     # print entropy
-    print("{:.1f}".format(round(-1 * my_fir_sum)))
+    print(f"{round(-1 * my_fir_sum):.1f}")
 
     # two len string
     all_sum = sum(two_char_strings.values())
@@ -83,10 +83,10 @@ def calculate_prob(text: str) -> None:
                 my_sec_sum += prob * math.log2(prob)
 
     # print second entropy
-    print("{:.1f}".format(round(-1 * my_sec_sum)))
+    print(f"{round(-1 * my_sec_sum):.1f}")
 
     # print the difference between them
-    print("{:.1f}".format(round((-1 * my_sec_sum) - (-1 * my_fir_sum))))
+    print(f"{round((-1 * my_sec_sum) - (-1 * my_fir_sum)):.1f}")
 
 
 def analyze_text(text: str) -> tuple[dict, dict]:

maths/euclidean_distance.py

@@ -1,3 +1,5 @@
+from __future__ import annotations
+
 from typing import Iterable, Union
 
 import numpy as np

maths/extended_euclidean_algorithm.py

@@ -12,12 +12,12 @@ https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
 # @Email:  silentcat@protonmail.com
 # @Last modified by:   pikulet
 # @Last modified time: 2020-10-02
+from __future__ import annotations
 
 import sys
-from typing import Tuple
 
 
-def extended_euclidean_algorithm(a: int, b: int) -> Tuple[int, int]:
+def extended_euclidean_algorithm(a: int, b: int) -> tuple[int, int]:
     """
     Extended Euclidean Algorithm.
 

maths/hardy_ramanujanalgo.py

@@ -37,7 +37,7 @@ def exactPrimeFactorCount(n):
 if __name__ == "__main__":
     n = 51242183
     print(f"The number of distinct prime factors is/are {exactPrimeFactorCount(n)}")
-    print("The value of log(log(n)) is {:.4f}".format(math.log(math.log(n))))
+    print(f"The value of log(log(n)) is {math.log(math.log(n)):.4f}")
 
     """
     The number of distinct prime factors is/are 3

maths/line_length.py

@@ -1,11 +1,13 @@
+from __future__ import annotations
+
 import math
-from typing import Callable, Union
+from typing import Callable
 
 
 def line_length(
-    fnc: Callable[[Union[int, float]], Union[int, float]],
+    fnc: Callable[[int | float], int | float],
-    x_start: Union[int, float],
+    x_start: int | float,
-    x_end: Union[int, float],
+    x_end: int | float,
     steps: int = 100,
 ) -> float:
 

maths/max_sum_sliding_window.py

@@ -6,10 +6,10 @@ Instead of using a nested for loop, in a Brute force approach we will use a tech
 called 'Window sliding technique' where the nested loops can be converted to a single
 loop to reduce time complexity.
 """
-from typing import List
+from __future__ import annotations
 
 
-def max_sum_in_array(array: List[int], k: int) -> int:
+def max_sum_in_array(array: list[int], k: int) -> int:
     """
     Returns the maximum sum of k consecutive elements
     >>> arr = [1, 4, 2, 10, 2, 3, 1, 0, 20]

maths/median_of_two_arrays.py

@@ -1,7 +1,7 @@
-from typing import List
+from __future__ import annotations
 
 
-def median_of_two_arrays(nums1: List[float], nums2: List[float]) -> float:
+def median_of_two_arrays(nums1: list[float], nums2: list[float]) -> float:
     """
     >>> median_of_two_arrays([1, 2], [3])
     2

maths/numerical_integration.py

@@ -1,14 +1,15 @@
 """
 Approximates the area under the curve using the trapezoidal rule
 """
+from __future__ import annotations
 
-from typing import Callable, Union
+from typing import Callable
 
 
 def trapezoidal_area(
-    fnc: Callable[[Union[int, float]], Union[int, float]],
+    fnc: Callable[[int | float], int | float],
-    x_start: Union[int, float],
+    x_start: int | float,
-    x_end: Union[int, float],
+    x_end: int | float,
     steps: int = 100,
 ) -> float:
 

maths/sieve_of_eratosthenes.py

@@ -10,13 +10,12 @@ Reference: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
 doctest provider: Bruno Simas Hadlich (https://github.com/brunohadlich)
 Also thanks to Dmitry (https://github.com/LizardWizzard) for finding the problem
 """
-
+from __future__ import annotations
 
 import math
-from typing import List
 
 
-def prime_sieve(num: int) -> List[int]:
+def prime_sieve(num: int) -> list[int]:
     """
     Returns a list with all prime numbers up to n.
 

maths/volume.py

@@ -3,11 +3,12 @@ Find Volumes of Various Shapes.
 
 Wikipedia reference: https://en.wikipedia.org/wiki/Volume
 """
+from __future__ import annotations
+
 from math import pi, pow
-from typing import Union
 
 
-def vol_cube(side_length: Union[int, float]) -> float:
+def vol_cube(side_length: int | float) -> float:
     """
     Calculate the Volume of a Cube.
 

matrix/searching_in_sorted_matrix.py

@@ -1,10 +1,8 @@
 from __future__ import annotations
 
-from typing import Union
-
 
 def search_in_a_sorted_matrix(
-    mat: list[list], m: int, n: int, key: Union[int, float]
+    mat: list[list], m: int, n: int, key: int | float
 ) -> None:
     """
     >>> search_in_a_sorted_matrix(

other/date_to_weekday.py

@@ -14,7 +14,7 @@ def date_to_weekday(inp_date: str) -> str:
     >>> date_to_weekday("1/1/2021")
     'Friday'
     """
-    day, month, year = [int(x) for x in inp_date.split("/")]
+    day, month, year = (int(x) for x in inp_date.split("/"))
     if year % 100 == 0:
         year = "00"
     new_base_date: str = f"{day}/{month}/{year%100} 0:0:0"

other/davisb_putnamb_logemannb_loveland.py

@@ -8,9 +8,9 @@ conjunctive normal form, i.e, for solving the Conjunctive Normal Form SATisfiabi
 
 For more information about the algorithm: https://en.wikipedia.org/wiki/DPLL_algorithm
 """
+from __future__ import annotations
 
 import random
-from typing import Dict, List
 
 
 class Clause:
@@ -27,7 +27,7 @@ class Clause:
     True
     """
 
-    def __init__(self, literals: List[int]) -> None:
+    def __init__(self, literals: list[int]) -> None:
         """
         Represent the literals and an assignment in a clause."
         """
@@ -52,7 +52,7 @@ class Clause:
         """
         return len(self.literals)
 
-    def assign(self, model: Dict[str, bool]) -> None:
+    def assign(self, model: dict[str, bool]) -> None:
         """
         Assign values to literals of the clause as given by model.
         """
@@ -68,7 +68,7 @@ class Clause:
                     value = not value
             self.literals[literal] = value
 
-    def evaluate(self, model: Dict[str, bool]) -> bool:
+    def evaluate(self, model: dict[str, bool]) -> bool:
         """
         Evaluates the clause with the assignments in model.
         This has the following steps:
@@ -97,7 +97,7 @@ class Formula:
         {{A1, A2, A3'}, {A5', A2', A1}} is ((A1 v A2 v A3') and (A5' v A2' v A1))
     """
 
-    def __init__(self, clauses: List[Clause]) -> None:
+    def __init__(self, clauses: list[Clause]) -> None:
         """
         Represent the number of clauses and the clauses themselves.
         """
@@ -146,7 +146,7 @@ def generate_formula() -> Formula:
     return Formula(set(clauses))
 
 
-def generate_parameters(formula: Formula) -> (List[Clause], List[str]):
+def generate_parameters(formula: Formula) -> (list[Clause], list[str]):
     """
     Return the clauses and symbols from a formula.
     A symbol is the uncomplemented form of a literal.
@@ -173,8 +173,8 @@ def generate_parameters(formula: Formula) -> (List[Clause], List[str]):
 
 
 def find_pure_symbols(
-    clauses: List[Clause], symbols: List[str], model: Dict[str, bool]
+    clauses: list[Clause], symbols: list[str], model: dict[str, bool]
-) -> (List[str], Dict[str, bool]):
+) -> (list[str], dict[str, bool]):
     """
     Return pure symbols and their values to satisfy clause.
     Pure symbols are symbols in a formula that exist only
@@ -225,8 +225,8 @@ def find_pure_symbols(
 
 
 def find_unit_clauses(
-    clauses: List[Clause], model: Dict[str, bool]
+    clauses: list[Clause], model: dict[str, bool]
-) -> (List[str], Dict[str, bool]):
+) -> (list[str], dict[str, bool]):
     """
     Returns the unit symbols and their values to satisfy clause.
     Unit symbols are symbols in a formula that are:
@@ -273,8 +273,8 @@ def find_unit_clauses(
 
 
 def dpll_algorithm(
-    clauses: List[Clause], symbols: List[str], model: Dict[str, bool]
+    clauses: list[Clause], symbols: list[str], model: dict[str, bool]
-) -> (bool, Dict[str, bool]):
+) -> (bool, dict[str, bool]):
     """
     Returns the model if the formula is satisfiable, else None
     This has the following steps:

other/lfu_cache.py

@@ -1,4 +1,6 @@
-from typing import Callable, Optional
+from __future__ import annotations
+
+from typing import Callable
 
 
 class DoubleLinkedListNode:
@@ -119,7 +121,7 @@ class LFUCache:
         """
         return key in self.cache
 
-    def get(self, key: int) -> Optional[int]:
+    def get(self, key: int) -> int | None:
         """
         Returns the value for the input key and updates the Double Linked List. Returns
         None if key is not present in cache

other/lru_cache.py

@@ -1,4 +1,6 @@
-from typing import Callable, Optional
+from __future__ import annotations
+
+from typing import Callable
 
 
 class DoubleLinkedListNode:
@@ -125,7 +127,7 @@ class LRUCache:
 
         return key in self.cache
 
-    def get(self, key: int) -> Optional[int]:
+    def get(self, key: int) -> int | None:
         """
         Returns the value for the input key and updates the Double Linked List. Returns
         None if key is not present in cache

project_euler/problem_001/sol1.py

@@ -26,7 +26,7 @@ def solution(n: int = 1000) -> int:
     0
     """
 
-    return sum([e for e in range(3, n) if e % 3 == 0 or e % 5 == 0])
+    return sum(e for e in range(3, n) if e % 3 == 0 or e % 5 == 0)
 
 
 if __name__ == "__main__":

project_euler/problem_001/sol5.py

@@ -25,7 +25,7 @@ def solution(n: int = 1000) -> int:
     83700
     """
 
-    return sum([i for i in range(n) if i % 3 == 0 or i % 5 == 0])
+    return sum(i for i in range(n) if i % 3 == 0 or i % 5 == 0)
 
 
 if __name__ == "__main__":

project_euler/problem_006/sol3.py

@@ -33,7 +33,7 @@ def solution(n: int = 100) -> int:
     1582700
     """
 
-    sum_of_squares = sum([i * i for i in range(1, n + 1)])
+    sum_of_squares = sum(i * i for i in range(1, n + 1))
     square_of_sum = int(math.pow(sum(range(1, n + 1)), 2))
     return square_of_sum - sum_of_squares
 

project_euler/problem_008/sol2.py

@@ -70,10 +70,7 @@ def solution(n: str = N) -> int:
     """
 
     return max(
-        [
+        reduce(lambda x, y: int(x) * int(y), n[i : i + 13]) for i in range(len(n) - 12)
-            reduce(lambda x, y: int(x) * int(y), n[i : i + 13])
-            for i in range(len(n) - 12)
-        ]
     )
 
 

project_euler/problem_012/sol2.py

@@ -29,7 +29,7 @@ def triangle_number_generator():
 
 
 def count_divisors(n):
-    return sum([2 for i in range(1, int(n ** 0.5) + 1) if n % i == 0 and i * i != n])
+    return sum(2 for i in range(1, int(n ** 0.5) + 1) if n % i == 0 and i * i != n)
 
 
 def solution():

project_euler/problem_013/sol1.py

@@ -18,7 +18,7 @@ def solution():
     """
     file_path = os.path.join(os.path.dirname(__file__), "num.txt")
     with open(file_path) as file_hand:
-        return str(sum([int(line) for line in file_hand]))[:10]
+        return str(sum(int(line) for line in file_hand))[:10]
 
 
 if __name__ == "__main__":

project_euler/problem_014/sol2.py

@@ -25,10 +25,10 @@ that all starting numbers finish at 1.
 
 Which starting number, under one million, produces the longest chain?
 """
-from typing import List
+from __future__ import annotations
 
 
-def collatz_sequence(n: int) -> List[int]:
+def collatz_sequence(n: int) -> list[int]:
     """Returns the Collatz sequence for n."""
     sequence = [n]
     while n != 1:
@@ -54,7 +54,7 @@ def solution(n: int = 1000000) -> int:
     13255
     """
 
-    result = max([(len(collatz_sequence(i)), i) for i in range(1, n)])
+    result = max((len(collatz_sequence(i)), i) for i in range(1, n))
     return result[1]
 
 

project_euler/problem_020/sol2.py

@@ -28,7 +28,7 @@ def solution(num: int = 100) -> int:
     >>> solution(1)
     1
     """
-    return sum([int(x) for x in str(factorial(num))])
+    return sum(int(x) for x in str(factorial(num)))
 
 
 if __name__ == "__main__":

project_euler/problem_021/sol1.py

@@ -41,11 +41,9 @@ def solution(n: int = 10000) -> int:
     0
     """
     total = sum(
-        [
+        i
-            i
+        for i in range(1, n)
-            for i in range(1, n)
+        if sum_of_divisors(sum_of_divisors(i)) == i and sum_of_divisors(i) != i
-            if sum_of_divisors(sum_of_divisors(i)) == i and sum_of_divisors(i) != i
-        ]
     )
     return total
 

project_euler/problem_033/sol1.py

@@ -14,8 +14,9 @@ and denominator.
 If the product of these four fractions is given in its lowest common
 terms, find the value of the denominator.
 """
+from __future__ import annotations
+
 from fractions import Fraction
-from typing import List
 
 
 def is_digit_cancelling(num: int, den: int) -> bool:
@@ -26,7 +27,7 @@ def is_digit_cancelling(num: int, den: int) -> bool:
     return False
 
 
-def fraction_list(digit_len: int) -> List[str]:
+def fraction_list(digit_len: int) -> list[str]:
     """
     >>> fraction_list(2)
     ['16/64', '19/95', '26/65', '49/98']