Binary Search

Recursive : 

Compare x with the middle element. 
If x matches with the middle element, we return the mid index.
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. Else if x is smaller, the target x must lie in the left (lower) half. So we apply the algorithm for the left half.

# 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")

Iterative:

# Iterative Binary Search Function

# It returns index of x in given array arr if present,

# else returns -1

def binary_search(arr, x):

    low = 0

    high = len(arr) - 1

    mid = 0

    while low <= high:

        mid = (high + low) // 2

        # If x is greater, ignore left half

        if arr[mid] < x:

            low = mid + 1

        # If x is smaller, ignore right half

        elif arr[mid] > x:

            high = mid - 1

        # means x is present at mid

        else:

            return mid

    # If we reach here, then the element was not present

    return -1

# Test array

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

x = 10

# Function call

result = binary_search(arr, x)

if result != -1:

    print("Element is present at index", str(result))

else:

    print("Element is not present in array")