Fix all Ruff warnings and formatting issues

Author: CuTyche

backtracking/all_permutations.py

@@ -5,12 +5,11 @@
 """
 
 from __future__ import annotations
-from typing import List, Union
 
-Element = Union[int, str]
+Element = int | str
 
 
-def generate_all_permutations(sequence: List[Element]) -> List[List[Element]]:
+def generate_all_permutations(sequence: list[Element]) -> list[list[Element]]:
     """
     Generate and return all permutations of the given sequence.
 
@@ -19,11 +18,21 @@ def generate_all_permutations(sequence: List[Element]) -> List[List[Element]]:
 
     Example 1 (integers):
     >>> generate_all_permutations([1, 2, 3])
-    [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
+    [[1, 2, 3],
+    [1, 3, 2],
+    [2, 1, 3],
+    [2, 3, 1],
+    [3, 1, 2],
+    [3, 2, 1]]
 
     Example 2 (strings):
     >>> generate_all_permutations(["A", "B", "C"])
-    [['A', 'B', 'C'], ['A', 'C', 'B'], ['B', 'A', 'C'], ['B', 'C', 'A'], ['C', 'A', 'B'], ['C', 'B', 'A']]
+    [['A', 'B', 'C'],
+    ['A', 'C', 'B'],
+    ['B', 'A', 'C'],
+    ['B', 'C', 'A'],
+    ['C', 'A', 'B'],
+    ['C', 'B', 'A']]
 
     Example 3 (single element):
     >>> generate_all_permutations([1])
@@ -33,18 +42,18 @@ def generate_all_permutations(sequence: List[Element]) -> List[List[Element]]:
     >>> generate_all_permutations([])
     [[]]
     """
-    result: List[List[Element]] = []
+    result: list[list[Element]] = []
     index_used = [False] * len(sequence)
     create_state_space_tree(sequence, [], 0, index_used, result)
     return result
 
 
 def create_state_space_tree(
-    sequence: List[Element],
-    current_sequence: List[Element],
+    sequence: list[Element],
+    current_sequence: list[Element],
     index: int,
-    index_used: List[bool],
-    result: List[List[Element]],
+    index_used: list[bool],
+    result: list[list[Element]],
 ) -> None:
     """
     Backtracking helper that appends permutations into result.
@@ -64,7 +73,11 @@ def create_state_space_tree(
         if not index_used[i]:
             current_sequence.append(sequence[i])
             index_used[i] = True
-            create_state_space_tree(sequence, current_sequence, index + 1, index_used, result)
+            create_state_space_tree(sequence,
+                                    current_sequence,
+                                    index + 1,
+                                    index_used,
+                                    result)
             current_sequence.pop()
             index_used[i] = False