[pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Author: pre-commit-ci[bot]

maths/lucas_series.py

@@ -25,7 +25,7 @@ def recursive_lucas_number(n_th_number: int) -> int:
     """
     if not isinstance(n_th_number, int):
         raise TypeError("recursive_lucas_number accepts only integer arguments.")
-    
+
     # Use memoization to cache results and avoid redundant calculations
     @functools.lru_cache(maxsize=None)
     def _recursive_lucas(n: int) -> int:
@@ -34,7 +34,7 @@ def _recursive_lucas(n: int) -> int:
         if n == 1:
             return 1
         return _recursive_lucas(n - 1) + _recursive_lucas(n - 2)
-    
+
     return _recursive_lucas(n_th_number)
 
 
@@ -56,16 +56,16 @@ def dynamic_lucas_number(n_th_number: int) -> int:
     """
     if not isinstance(n_th_number, int):
         raise TypeError("dynamic_lucas_number accepts only integer arguments.")
-    
+
     if n_th_number == 0:
         return 2
     if n_th_number == 1:
         return 1
-    
+
     a, b = 2, 1
     for _ in range(2, n_th_number + 1):
         a, b = b, a + b
-    
+
     return b
 
 
@@ -87,35 +87,41 @@ def matrix_power_lucas_number(n_th_number: int) -> int:
     """
     if not isinstance(n_th_number, int):
         raise TypeError("matrix_power_lucas_number accepts only integer arguments.")
-    
+
     if n_th_number == 0:
         return 2
     if n_th_number == 1:
         return 1
-    
+
     def matrix_mult(a: list[list[int]], b: list[list[int]]) -> list[list[int]]:
         return [
-            [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
-            [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
+            [
+                a[0][0] * b[0][0] + a[0][1] * b[1][0],
+                a[0][0] * b[0][1] + a[0][1] * b[1][1],
+            ],
+            [
+                a[1][0] * b[0][0] + a[1][1] * b[1][0],
+                a[1][0] * b[0][1] + a[1][1] * b[1][1],
+            ],
         ]
-    
+
     def matrix_power(matrix: list[list[int]], power: int) -> list[list[int]]:
         # Start with identity matrix
         result: list[list[int]] = [[1, 0], [0, 1]]
         base = matrix
-        
+
         while power > 0:
             if power % 2 == 1:
                 result = matrix_mult(result, base)
             base = matrix_mult(base, base)
             power //= 2
-        
+
         return result
-    
+
     # Lucas number matrix form: [[1, 1], [1, 0]]
     base_matrix = [[1, 1], [1, 0]]
     powered_matrix = matrix_power(base_matrix, n_th_number - 1)
-    
+
     # L(n) = powered_matrix[0][0] * L(1) + powered_matrix[0][1] * L(0)
     # Where L(1) = 1, L(0) = 2
     return powered_matrix[0][0] * 1 + powered_matrix[0][1] * 2
@@ -139,17 +145,17 @@ def closed_form_lucas_number(n_th_number: int) -> int:
     """
     if not isinstance(n_th_number, int):
         raise TypeError("closed_form_lucas_number accepts only integer arguments.")
-    
+
     if n_th_number == 0:
         return 2
     if n_th_number == 1:
         return 1
-    
+
     # Golden ratio
     phi = (1 + math.sqrt(5)) / 2
     # Conjugate of golden ratio
     psi = (1 - math.sqrt(5)) / 2
-    
+
     # Lucas number closed form: L(n) = phi^n + psi^n
     return round(phi**n_th_number + psi**n_th_number)
 
@@ -158,7 +164,6 @@ def closed_form_lucas_number(n_th_number: int) -> int:
 _lucas_cache: Dict[int, int] = {0: 2, 1: 1}
 
 
-
 def cached_lucas_number(n_th_number: int) -> int:
     """
     Returns the nth lucas number using a cached approach for optimal performance
@@ -177,16 +182,16 @@ def cached_lucas_number(n_th_number: int) -> int:
     """
     if not isinstance(n_th_number, int):
         raise TypeError("cached_lucas_number accepts only integer arguments.")
-    
+
     if n_th_number in _lucas_cache:
         return _lucas_cache[n_th_number]
-    
+
     # Calculate using the fastest method for uncached values
     if n_th_number < 70:  # For smaller values, closed form is efficient
         result = closed_form_lucas_number(n_th_number)
     else:  # For larger values, matrix exponentiation is more stable
         result = matrix_power_lucas_number(n_th_number)
-    
+
     _lucas_cache[n_th_number] = result
     return result
 
@@ -205,4 +210,4 @@ def cached_lucas_number(n_th_number: int) -> int:
     print("\nUsing closed-form formula to calculate lucas series:")
     print(" ".join(str(closed_form_lucas_number(i)) for i in range(n)))
     print("\nUsing cached function to calculate lucas series:")
-    print(" ".join(str(cached_lucas_number(i)) for i in range(n)))
+    print(" ".join(str(cached_lucas_number(i)) for i in range(n)))