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

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

strings/wildcard_pattern_matching_fft.py

@@ -1,6 +1,7 @@
 import numpy as np
 from numpy.fft import fft, ifft
 
+
 def preprocess_text_and_pattern(text: str, pattern: str) -> tuple[list[int], list[int]]:
     """Preprocesses text and pattern for pattern matching.
 
@@ -11,7 +12,7 @@
     Returns:
         A tuple containing:
             - A list of integers representing the text characters.
             - A list of integers representing the pattern characters, with 0 for wildcards.
 
     Examples:
         >>> preprocess_text_and_pattern("abcabc", "abc*")
@@ -19,12 +20,14 @@
         >>> preprocess_text_and_pattern("hello", "he*o")
         ([3, 2, 4, 4, 5], [3, 2, 0, 5])
     """
-    
+
     unique_chars = set(text + pattern)
-    char_to_int = {char: i + 1 for i, char in enumerate(unique_chars)}  # Unique non-zero integers
+    char_to_int = {
+        char: i + 1 for i, char in enumerate(unique_chars)
+    }  # Unique non-zero integers
 
     # Replace pattern '*' with 0, other characters with their unique integers
-    pattern_int = [char_to_int[char] if char != '*' else 0 for char in pattern]
+    pattern_int = [char_to_int[char] if char != "*" else 0 for char in pattern]
     text_int = [char_to_int[char] for char in text]
 
     return text_int, pattern_int
@@ -44,10 +47,10 @@
         >>> fft_convolution(np.array([1, 2, 3]), np.array([0, 1, 0.5]))
         array([0. , 1. , 2.5, 3. , 1.5])
     """
-    
+
     n = len(input_seq_a) + len(input_seq_b) - 1
     A = fft(input_seq_a, n)
     B = fft(input_seq_b, n)
     return np.real(ifft(A * B))
 
 
@@ -65,29 +68,30 @@
         >>> compute_a_fft([1, 2, 3, 1, 2, 3], [1, 2, 3, 0])
         array([...])  # Replace with the expected output based on your implementation
     """
-    
+
     n = len(text_int)
     m = len(pattern_int)
 
     # Power transforms of the pattern and text based on the formula
     p1 = np.array(pattern_int)
-    p2 = np.array([p ** 2 for p in pattern_int])
-    p3 = np.array([p ** 3 for p in pattern_int])
+    p2 = np.array([p**2 for p in pattern_int])
+    p3 = np.array([p**3 for p in pattern_int])
 
     t1 = np.array(text_int)
-    t2 = np.array([t ** 2 for t in text_int])
-    t3 = np.array([t ** 3 for t in text_int])
+    t2 = np.array([t**2 for t in text_int])
+    t3 = np.array([t**3 for t in text_int])
 
     # Convolution to calculate the terms for A[i]
     sum1 = fft_convolution(p3[::-1], t1)
     sum2 = fft_convolution(p2[::-1], t2)
     sum3 = fft_convolution(p1[::-1], t3)
 
     # Calculate A[i] using the convolution results
-    A = sum1[:n - m + 1] - 2 * sum2[:n - m + 1] + sum3[:n - m + 1]
+    A = sum1[: n - m + 1] - 2 * sum2[: n - m + 1] + sum3[: n - m + 1]
 
     return A
 
+
 # Main function to run the matching
 if __name__ == "__main__":
     # Example test case