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

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

Author: pre-commit-ci[bot]

algorithms/cryptography/shor_algorithm.py

@@ -1,12 +1,14 @@
 import math
 import random
 
+
 def gcd(a, b):
     """Computes the greatest common divisor using Euclidean algorithm."""
     while b:
         a, b = b, a % b
     return a
 
+
 def modular_exponentiation(base, exp, mod):
     """Computes (base^exp) % mod using fast modular exponentiation."""
     result = 1
@@ -17,6 +19,7 @@ def modular_exponentiation(base, exp, mod):
         exp //= 2
     return result
 
+
 def find_order(a, N):
     """Finds the smallest r such that a^r ≡ 1 (mod N)"""
     r = 1
@@ -26,6 +29,7 @@ def find_order(a, N):
             return None
     return r
 
+
 def shor_algorithm(N):
     """Simulates Shor’s Algorithm classically to factorize N."""
     if N % 2 == 0:
@@ -49,6 +53,7 @@ def shor_algorithm(N):
         if 1 < factor2 < N:
             return factor2, N // factor2
 
+
 # Example usage
 if __name__ == "__main__":
     N = 15  # You can test with 21, 35, 55, etc.