Add static typing to backtracking algorithms (TheAlgorithms#2684)

* Added static typing to backtracking algorithms

* Ran psf/black to fix some minor issues.

* updating DIRECTORY.md

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: John Law <[email protected]>

Author: 3 people

Diff for: DIRECTORY.md

@@ -41,6 +41,7 @@
   * [Quine Mc Cluskey](https://github.com/TheAlgorithms/Python/blob/master/boolean_algebra/quine_mc_cluskey.py)
 
 ## Cellular Automata
+  * [Conways Game Of Life](https://github.com/TheAlgorithms/Python/blob/master/cellular_automata/conways_game_of_life.py)
   * [One Dimensional](https://github.com/TheAlgorithms/Python/blob/master/cellular_automata/one_dimensional.py)
 
 ## Ciphers
@@ -107,6 +108,7 @@
   * [Prefix Conversions](https://github.com/TheAlgorithms/Python/blob/master/conversions/prefix_conversions.py)
   * [Roman To Integer](https://github.com/TheAlgorithms/Python/blob/master/conversions/roman_to_integer.py)
   * [Temperature Conversions](https://github.com/TheAlgorithms/Python/blob/master/conversions/temperature_conversions.py)
+  * [Weight Conversion](https://github.com/TheAlgorithms/Python/blob/master/conversions/weight_conversion.py)
 
 ## Data Structures
   * Binary Tree
@@ -321,10 +323,6 @@
     * [Test Min Spanning Tree Kruskal](https://github.com/TheAlgorithms/Python/blob/master/graphs/tests/test_min_spanning_tree_kruskal.py)
     * [Test Min Spanning Tree Prim](https://github.com/TheAlgorithms/Python/blob/master/graphs/tests/test_min_spanning_tree_prim.py)
 
-## Greedy Method
-  * [Greedy Knapsack](https://github.com/TheAlgorithms/Python/blob/master/greedy_method/greedy_knapsack.py)
-  * [Test Knapsack](https://github.com/TheAlgorithms/Python/blob/master/greedy_method/test_knapsack.py)
-
 ## Hashes
   * [Adler32](https://github.com/TheAlgorithms/Python/blob/master/hashes/adler32.py)
   * [Chaos Machine](https://github.com/TheAlgorithms/Python/blob/master/hashes/chaos_machine.py)
@@ -336,8 +334,11 @@
   * [Sha1](https://github.com/TheAlgorithms/Python/blob/master/hashes/sha1.py)
 
 ## Knapsack
+  * [Greedy Knapsack](https://github.com/TheAlgorithms/Python/blob/master/knapsack/greedy_knapsack.py)
   * [Knapsack](https://github.com/TheAlgorithms/Python/blob/master/knapsack/knapsack.py)
-  * [Test Knapsack](https://github.com/TheAlgorithms/Python/blob/master/knapsack/test_knapsack.py)
+  * Tests
+    * [Test Greedy Knapsack](https://github.com/TheAlgorithms/Python/blob/master/knapsack/tests/test_greedy_knapsack.py)
+    * [Test Knapsack](https://github.com/TheAlgorithms/Python/blob/master/knapsack/tests/test_knapsack.py)
 
 ## Linear Algebra
   * Src
@@ -400,6 +401,7 @@
   * [Combinations](https://github.com/TheAlgorithms/Python/blob/master/maths/combinations.py)
   * [Decimal Isolate](https://github.com/TheAlgorithms/Python/blob/master/maths/decimal_isolate.py)
   * [Entropy](https://github.com/TheAlgorithms/Python/blob/master/maths/entropy.py)
+  * [Euclidean Distance](https://github.com/TheAlgorithms/Python/blob/master/maths/euclidean_distance.py)
   * [Eulers Totient](https://github.com/TheAlgorithms/Python/blob/master/maths/eulers_totient.py)
   * [Explicit Euler](https://github.com/TheAlgorithms/Python/blob/master/maths/explicit_euler.py)
   * [Extended Euclidean Algorithm](https://github.com/TheAlgorithms/Python/blob/master/maths/extended_euclidean_algorithm.py)
@@ -886,6 +888,7 @@
   * [Get Imdbtop](https://github.com/TheAlgorithms/Python/blob/master/web_programming/get_imdbtop.py)
   * [Instagram Crawler](https://github.com/TheAlgorithms/Python/blob/master/web_programming/instagram_crawler.py)
   * [Instagram Pic](https://github.com/TheAlgorithms/Python/blob/master/web_programming/instagram_pic.py)
+  * [Instagram Video](https://github.com/TheAlgorithms/Python/blob/master/web_programming/instagram_video.py)
   * [Recaptcha Verification](https://github.com/TheAlgorithms/Python/blob/master/web_programming/recaptcha_verification.py)
   * [Slack Message](https://github.com/TheAlgorithms/Python/blob/master/web_programming/slack_message.py)
   * [Test Fetch Github Info](https://github.com/TheAlgorithms/Python/blob/master/web_programming/test_fetch_github_info.py)

Diff for: backtracking/all_combinations.py

@@ -16,7 +16,13 @@ def generate_all_combinations(n: int, k: int) -> [[int]]:
     return result
 
 
-def create_all_state(increment, total_number, level, current_list, total_list):
+def create_all_state(
+    increment: int,
+    total_number: int,
+    level: int,
+    current_list: [int],
+    total_list: [int],
+) -> None:
     if level == 0:
         total_list.append(current_list[:])
         return
@@ -27,7 +33,7 @@ def create_all_state(increment, total_number, level, current_list, total_list):
         current_list.pop()
 
 
-def print_all_state(total_list):
+def print_all_state(total_list: [int]) -> None:
     for i in total_list:
         print(*i)
 

Diff for: backtracking/all_permutations.py

@@ -7,11 +7,13 @@
 """
 
 
-def generate_all_permutations(sequence):
+def generate_all_permutations(sequence: [int]) -> None:
     create_state_space_tree(sequence, [], 0, [0 for i in range(len(sequence))])
 
 
-def create_state_space_tree(sequence, current_sequence, index, index_used):
+def create_state_space_tree(
+    sequence: [int], current_sequence: [int], index: int, index_used: int
+) -> None:
     """
     Creates a state space tree to iterate through each branch using DFS.
     We know that each state has exactly len(sequence) - index children.

Diff for: backtracking/n_queens.py

@@ -10,7 +10,7 @@
 solution = []
 
 
-def isSafe(board, row, column):
+def isSafe(board: [[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.
@@ -38,7 +38,7 @@ def isSafe(board, row, column):
     return True
 
 
-def solve(board, row):
+def solve(board: [[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
@@ -68,7 +68,7 @@ def solve(board, row):
     return False
 
 
-def printboard(board):
+def printboard(board: [[int]]) -> None:
     """
     Prints the boards that have a successful combination.
     """

Diff for: backtracking/rat_in_maze.py

@@ -1,4 +1,4 @@
-def solve_maze(maze: list) -> bool:
+def solve_maze(maze: [[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.
@@ -67,7 +67,7 @@ def solve_maze(maze: list) -> bool:
     return solved
 
 
-def run_maze(maze, i, j, solutions):
+def run_maze(maze: [[int]], i: int, j: int, solutions: [[int]]) -> bool:
     """
     This method is recursive starting from (i, j) and going in one of four directions:
     up, down, left, right.

Diff for: backtracking/sum_of_subsets.py

@@ -8,7 +8,7 @@
 """
 
 
-def generate_sum_of_subsets_soln(nums, max_sum):
+def generate_sum_of_subsets_soln(nums: [int], max_sum: [int]) -> [int]:
     result = []
     path = []
     num_index = 0
@@ -17,7 +17,14 @@ def generate_sum_of_subsets_soln(nums, max_sum):
     return result
 
 
-def create_state_space_tree(nums, max_sum, num_index, path, result, remaining_nums_sum):
+def create_state_space_tree(
+    nums: [int],
+    max_sum: int,
+    num_index: int,
+    path: [int],
+    result: [int],
+    remaining_nums_sum: int,
+) -> None:
     """
     Creates a state space tree to iterate through each branch using DFS.
     It terminates the branching of a node when any of the two conditions