binary search in 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

def binary_search(item_list,item):
	first = 0
	last = len(item_list)-1
	found = False
	while( first<=last and not found):
		mid = (first + last)//2
		if item_list[mid] == item :
			found = True
		else:
			if item < item_list[mid]:
				last = mid - 1
			else:
				first = mid + 1	
	return found

# Python 3 program for recursive binary search. 
# Modifications needed for the older Python 2 are found in comments. 
  
# Returns index of x in arr if present, else -1 
def binary_search(arr, low, high, x): 
  
    # Check base case 
    if high >= low: 
  
        mid = (high + low) // 2
  
        # If element is present at the middle itself 
        if arr[mid] == x: 
            return mid 
  
        # If element is smaller than mid, then it can only 
        # be present in left subarray 
        elif arr[mid] > x: 
            return binary_search(arr, low, mid - 1, x) 
  
        # Else the element can only be present in right subarray 
        else: 
            return binary_search(arr, mid + 1, high, x) 
  
    else: 
        # Element is not present in the array 
        return -1
  
# Test array 
arr = [ 2, 3, 4, 10, 40 ] 
x = 10
  
# Function call 
result = binary_search(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") 

def binary_search_recursive(A, key, low, high):
	if low > high:
		return False
	else:
		mid = (low + high) // 2
		if key == A[mid]:
			return True
		elif key < A[mid]:
			return binary_search_recursive(A, key, low, mid - 1)
		else:
			return binary_search_recursive(A, key, mid + 1, high)

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")

def binary_search(group, suspect):
  group.sort()
  midpoint = len(group)//2
  while(True):
    if(group[midpoint] == suspect):
      return midpoint
    if(suspect > group[midpoint]):
            group = group[midpoint]
    if(suspect < group[midpoint]):
      group = group[0: midpoint]
    midpoint = (len(group)//2)