Incorrect binary search code in python

View Discussion

Improve Article

Save Article

View Discussion

Improve Article

Save Article

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 <= high:

        mid = (high + low) // 2

        if arr[mid] < x:

            low = mid + 1

        elif arr[mid] > 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!