fix: no implicit optional (TheAlgorithms#7984)

Author: dhruvmanila

data_structures/binary_tree/fenwick_tree.py

@@ -8,7 +8,7 @@ class FenwickTree:
     More info: https://en.wikipedia.org/wiki/Fenwick_tree
     """
 
-    def __init__(self, arr: list[int] = None, size: int = None) -> None:
+    def __init__(self, arr: list[int] | None = None, size: int | None = None) -> None:
         """
         Constructor for the Fenwick tree
 

fractals/julia_sets.py

@@ -89,7 +89,7 @@ def iterate_function(
     function_params: Any,
     nb_iterations: int,
     z_0: numpy.ndarray,
-    infinity: float = None,
+    infinity: float | None = None,
 ) -> numpy.ndarray:
     """
     Iterate the function "eval_function" exactly nb_iterations times.

linear_algebra/src/schur_complement.py

@@ -7,7 +7,7 @@ def schur_complement(
     mat_a: np.ndarray,
     mat_b: np.ndarray,
     mat_c: np.ndarray,
-    pseudo_inv: np.ndarray = None,
+    pseudo_inv: np.ndarray | None = None,
 ) -> np.ndarray:
     """
     Schur complement of a symmetric matrix X given as a 2x2 block matrix

machine_learning/linear_discriminant_analysis.py

@@ -256,7 +256,7 @@ def valid_input(
     input_msg: str,
     err_msg: str,
     condition: Callable[[num], bool] = lambda x: True,
-    default: str = None,
+    default: str | None = None,
 ) -> num:
     """
     Ask for user value and validate that it fulfill a condition.

project_euler/problem_074/sol1.py

@@ -71,7 +71,7 @@ def sum_digit_factorials(n: int) -> int:
     return ret
 
 
-def chain_length(n: int, previous: set = None) -> int:
+def chain_length(n: int, previous: set | None = None) -> int:
     """
     Calculate the length of the chain of non-repeating terms starting with n.
     Previous is a set containing the previous member of the chain.

sorts/strand_sort.py

@@ -1,7 +1,7 @@
 import operator
 
 
-def strand_sort(arr: list, reverse: bool = False, solution: list = None) -> list:
+def strand_sort(arr: list, reverse: bool = False, solution: list | None = None) -> list:
     """
     Strand sort implementation
     source: https://en.wikipedia.org/wiki/Strand_sort