Added static typing to backtracking algorithms

DIRECTORY.md

@@ -667,6 +667,7 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_071/sol1.py)
   * Problem 072
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_072/sol1.py)
+    * [Sol2](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_072/sol2.py)
   * Problem 074
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_074/sol1.py)
   * Problem 076
@@ -689,6 +690,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_125/sol1.py)
   * Problem 173
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_173/sol1.py)
+  * Problem 174
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_174/sol1.py)
   * Problem 191
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_191/sol1.py)
   * Problem 234

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)
 

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.

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.
     """

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.

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