Correct binary-search algorithm

You have to specify low and high when you work with the only array/list. At every iteration you treat a part of list in low..high range.

Your implementation makes sublists, so it does not need explicit range definition (but is this sublist formation free of cost?)

Compare these two implementations of binarySearch. The first is yours, the second is mine.

In your version, you are passing "slices", ie, entire copies of subarrays, to the recursive call. In my version, all recursive calls access the same array without copying it, and instead only low and high are passed as parameters.

# using slices, ie, copies of subarrays
def binarySearching(sortedArr,v):
    # print(sortedArr)
    if len(sortedArr)>=1:
        mid = len(sortedArr)//2
        if v<sortedArr[mid]:
            return binarySearching(sortedArr[:mid],v)
        elif v>sortedArr[mid]:
            return binarySearching(sortedArr[mid+1:],v)
        else:
            return mid
    else:
        return None

# using low and high indices
def otherBinarySearching(sortedArr, v):
    def auxiliary(low, high, v):
        #print(low, high, sortedArr[low:high])
        if high > low:
            mid = (high + low) // 2
            if v < sortedArr[mid]:
                return auxiliary(low, mid, v)
            elif v > sortedArr[mid]:
                return auxiliary(mid+1, high, v)
            else:
                return mid
        elif high == low:
            return (low if v == sortedArr[low] else None)
    return auxiliary(0, len(sortedArr), v)

# add some tests to make sure implementations are correct
if __name__=='__main__':
    a = [x for x in range(0, 101, 2)]
    b = [x for x in range(1, 100, 2)]
    print('a: ', a)
    print('b: ', b)
    print('binarySearching:      ', all(isinstance(binarySearching(a, x), int) for x in a) and all(binarySearching(a, x) is None for x in b))
    print('otherBinarySearching: ', all(otherBinarySearching(a, x) == x / 2 for x in a) and all(otherBinarySearching(a, x) is None for x in b))

In addition, your version returns the wrong indices: the line return mid returns the index of v in the subarray binarySearching is currently looking at, instead of the index in the original array.