how to do binary serch recursively in a list python code example

Example 1: iterative binary search python

def binary_search(a, key):
	low = 0
	high = len(a) - 1
	while low < high:
		mid = (low + high) // 2
		if key == a[mid]:
			return True
		elif key < mid:
			high = mid - 1
		else:
			low = mid + 1

	return False

Example 2: binary search algorithm in python code

def binarySearchAppr (arr, start, end, x):
# check condition
if end >= start:
   mid = start + (end- start)//2
   # If element is present at the middle
   if arr[mid] == x:
      return mid
   # If element is smaller than mid
   elif arr[mid] > x:
      return binarySearchAppr(arr, start, mid-1, x)
   # Else the element greator than mid
   else:
      return binarySearchAppr(arr, mid+1, end, x)
   else:
   # Element is not found in the array
      return -1
arr = sorted(['t','u','t','o','r','i','a','l'])
x ='r'
result = binarySearchAppr(arr, 0, len(arr)-1, x)
if result != -1:
   print ("Element is present at index "+str(result))
else:
print ("Element is not present in array")