Number guessing using recursion

Question

I've got some homework on recursion, and I'm really stuck. The task is to create a program where we enter upper and lower boundaries and a number within those boundaries. The program should compute the middle number of those boundaries. If the middle number is bigger than the number, the middle number becomes the lower boundary, if lower, the upper one. It does it till it picks the right number. The moment it is the same, the program stops and returns it.

Here is the code that I've already written, but it only works when the 1st guess of the number is right:

def number_guess(number ,upper_boundary, lower_boundary):
    boundary_dif = upper_boundary - lower_boundary
    middle_number = boundary_dif/2 + lower_boundary
    if middle_number == number:
        return middle_number
    if middle_number > number:
        middle_number = lower_boundary
        number_guess(number, upper_boundary, lower_boundary)
    if middle_number < number:
        middle_number = upper_boundary
        number_guess(number, upper_boundary, lower_boundary)

PS It must be done only with recursion.

Answer 1

Recursion can take awhile to get a hold of. I would look into binary search to see how this works:

def number_guess(number, lower, upper):
    middle = ((upper - lower) // 2) + lower
    if middle == number:
        return middle
    if number > middle:
        return number_guess(number, middle, upper)
    return number_guess(number, lower, middle)

print(number_guess(57, 0, 100))

Answer 2

There are lots of issues with this small piece of code. First is a common recursion programming error. Your recursive function returns a value:

if middle_number == number:
    return middle_number

But when you call it recursively, you ignore that returned value:

if middle_number > number:
    middle_number = lower_boundary
    number_guess(number, upper_boundary, lower_boundary)

If you return a value, you have to deal with it. In this case, the solution is simple, simply return it in turn:

    return number_guess(number, upper_boundary, lower_boundary)

The next problem is the two limit tests are backwards:

if middle_number > number:
    middle_number = lower_boundary

if the middle number is greater than the number, then it should be the new upper boundary, not lower. Ditto for the upper_boundary test. Next, this assignment is backward:

middle_number = lower_boundary
return number_guess(number, upper_boundary, lower_boundary)

We don't use middle_number again after this, we recurse using lower_boundary so we should either do:

lower_boundary = middle_number
return number_guess(number, upper_boundary, lower_boundary)

or, we can simply do:

return number_guess(number, upper_boundary, middle_number)

ditto for the upper_boundary code. Next, you tagged this as Python 3 so this code:

boundary_dif/2

will generate a floating point number, which you don't want! You need:

boundary_dif // 2

Finally, although this works:

boundary_dif = upper_boundary - lower_boundary
middle_number = boundary_dif // 2 + lower_boundary

it can also be expressed as simply:

middle_number = (upper_boundary + lower_boundary) // 2