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

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

Author: pre-commit-ci[bot]

randomized_algorithms/miller_rabin_primality test.py

@@ -1,5 +1,6 @@
 import random
 
+
 def miller_rabin_primality_test(n: int, k: int = 5) -> bool:
     """
     Probabilistic primality test using Miller-Rabin algorithm.
@@ -46,6 +47,8 @@ def miller_rabin_primality_test(n: int, k: int = 5) -> bool:
             return False
     return True
 
+
 if __name__ == "__main__":
     import doctest
-    doctest.testmod()
+
+    doctest.testmod()

randomized_algorithms/randomized_quicksort.py

@@ -1,6 +1,7 @@
 import random
 from typing import List
 
+
 def randomized_quicksort(arr: List[int]) -> List[int]:
     """
     Sorts a list of integers using randomized QuickSort algorithm.
@@ -25,6 +26,8 @@ def randomized_quicksort(arr: List[int]) -> List[int]:
     greater = [x for x in arr if x > pivot]
     return randomized_quicksort(less) + equal + randomized_quicksort(greater)
 
+
 if __name__ == "__main__":
     import doctest
-    doctest.testmod()
+
+    doctest.testmod()

randomized_algorithms/reservoir_sampling.py

@@ -3,6 +3,7 @@
 
 T = TypeVar("T")
 
+
 def reservoir_sampling(stream: Iterator[T], k: int) -> List[T]:
     """
     Randomly select k items from a stream of unknown length using reservoir sampling.
@@ -29,6 +30,8 @@ def reservoir_sampling(stream: Iterator[T], k: int) -> List[T]:
                 reservoir[j] = item
     return reservoir
 
+
 if __name__ == "__main__":
     import doctest
-    doctest.testmod()
+
+    doctest.testmod()