What is recursive binary search in python?

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In a nutshell, this search algorithm takes advantage of a collection of elements that is already sorted by ignoring half of the elements after just one comparison. 

1. Compare x with the middle element.
2. If x matches with the middle element, we return the mid index.
3. Else if x is greater than the mid element, then x can only lie in the right [greater] half subarray after the mid element. Then we apply the algorithm again for the right half.
4. Else if x is smaller, the target x must lie in the left [lower] half. So we apply the algorithm for the left half.

Recursive :

Python3

def binary_search[arr, low, high, x]:

    if high >= low:

        mid = [high + low] // 2

        if arr[mid] == x:

            return mid

        elif arr[mid] > x:

            return binary_search[arr, low, mid - 1, x]

        else:

            return binary_search[arr, mid + 1, high, x]

    else:

        return -1

arr = [ 2, 3, 4, 10, 40 ]

x = 10

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"]

Output:  

Element is present at index 3

Time Complexity: O[log n]

Auxiliary Space: O[logn]     [NOTE: Recursion creates Call Stack]

Iterative:
 

Python3

def binary_search[arr, x]:

    low = 0

    high = len[arr] - 1

    mid = 0

    while low x:

            high = mid - 1

        else:

            return mid

    return -1

arr = [ 2, 3, 4, 10, 40 ]

x = 10

result = binary_search[arr, x]

if result != -1:

    print["Element is present at index", str[result]]

else:

    print["Element is not present in array"]

Output:  

Element is present at index 3

Time Complexity: O[log n]

Auxiliary Space: O[1]
Please refer to the article Binary Search for more details!