@@ -130,7 +130,7 @@ def binary_search(sorted_collection: list[int], item: int) -> int:
130130 """
131131 if any (a > b for a , b in pairwise (sorted_collection )):
132132 raise ValueError ("sorted_collection must be sorted in ascending order" )
133-
133+
134134 left = 0
135135 right = len (sorted_collection ) - 1
136136 result = - 1
@@ -187,7 +187,7 @@ def binary_search_by_recursion(
187187 """
188188 if right < 0 :
189189 right = len (sorted_collection ) - 1
190-
190+
191191 # Base case: range is empty
192192 if right < left :
193193 return - 1
@@ -198,10 +198,12 @@ def binary_search_by_recursion(
198198 # We found a match! Now see if there's an earlier one to the left.
199199 # CRITICAL: Only recurse if there is actually space to the left
200200 if midpoint > left :
201- res = binary_search_by_recursion (sorted_collection , item , left , midpoint - 1 )
201+ res = binary_search_by_recursion (
202+ sorted_collection , item , left , midpoint - 1
203+ )
202204 return res if res != - 1 else midpoint
203205 return midpoint
204-
206+
205207 elif sorted_collection [midpoint ] > item :
206208 return binary_search_by_recursion (sorted_collection , item , left , midpoint - 1 )
207209 else :
@@ -251,6 +253,9 @@ def exponential_search(sorted_collection: list[int], item: int) -> int:
251253 print (
252254 f"{ name :>26} :" ,
253255 timeit .timeit (
254- f"{ name } (list(collection), 500)" , setup = setup , number = 5_000 , globals = globals ()
256+ f"{ name } (list(collection), 500)" ,
257+ setup = setup ,
258+ number = 5_000 ,
259+ globals = globals (),
255260 ),
256- )
261+ )
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