def binary_search_recursion(lst, val, start, end):
  if start > end:
    return None
  mid = (start + end) // 2
  if lst[mid] < val:
    return binary_search_recursion(lst, val, mid + 1, end)
  if lst[mid] > val:
    return binary_search_recursion(lst, val, start, mid - 1)
  return mid
 
 
def binary_search_loop(lst, val):
  start, end = 0, len(lst) - 1
  while start <= end:
    mid = (start + end) // 2
    if lst[mid] < val:
      start = mid + 1
    elif lst[mid] > val:
      end = mid - 1
    else:
      return mid
  return None

> import random
> from random import randint
> from random import choice
> random.seed(5)
> lst = [randint(1, 100) for _ in range(500000)]
> lst.sort()
> val = choice(lst)
> val
6
> def test_recursion():
...   return binary_search_recursion(lst, val, 0, len(lst) - 1)
...
> def test_loop():
...   return binary_search_loop(lst, val)
...
> import timeit
> t1 = timeit.timeit("test_recursion()", setup="from __main__ import test_recursion")
> t1
3.9838006450511045
> t2 = timeit.timeit("test_loop()", setup="from __main__ import test_loop")
> t2
2.749765167240339

> import bisect
> def binary_search_bisect(lst, val):
...   i = bisect.bisect(lst, val)
...   if i != len(lst) and lst[i] == val:
...     return i
...   return None
...
> def test_bisect():
...   return binary_search_bisect(lst, val)
...
> t3 = timeit.timeit("test_bisect()", setup="from __main__ import test_bisect")
> t3
1.3453236258177412

> def test_index():
...   return lst.index(val)
...
> t4 = timeit.timeit("test_index()", setup="from __main__ import test_index")
> t4
518.1656223725007

import random
from random import randint
import bisect
 
lst = []
SIZE = 10
random.seed(5)
for _ in range(SIZE):
  item = randint(1, SIZE)
  bisect.insort(lst, item)
  print('%2d ->' % item, lst)