Help with Implement Bisection Method challenge

Python
1

Hi, I am in the midst of doing the new Beta Full Stack Developer Python course, I am encountering a problem understanding what is wrong with my code in this challenge.

def square_root_bisection(number,tolerance=1e-6,max_iterations=100):

    if number < 0:
        raise ValueError('Square root of negative number is not defined in real numbers')

    elif number == 0 or number == 1:
        print(f'The square root of {number} is {number}')
        return number

    else:
        iterations = 0
        if number < 1:
            upper_bound = 1
        else:
            upper_bound = number
        lower_bound = 0
        while iterations < max_iterations:
            iterations += 1
            mid = (upper_bound + lower_bound)/2
            mid_square = mid ** 2
            if abs(mid_square - number) <= tolerance:
                print(f'The square root of {number} is approximately {mid}')
                return mid
            elif mid_square > number:
                upper_bound = mid
            else:
                lower_bound = mid

        print(f'Failed to converge within {max_iterations} iterations')
        return None


if __name__ == '__main__':
    import math

    test = 0.001
    tolerance = 1e-7
    max_iterations = 50
    root = square_root_bisection(test,tolerance,max_iterations)
    print(math.sqrt(test))
    print(root)
    print(root**2)

My code is failing these test cases

  • 8. square_root_bisection(0.001, 1e-7, 50) should return a number between 0.03162267660168379 and 0.031622876601683794.

  • 9. square_root_bisection(0.001, 1e-7, 50) should print The square root of 0.001 is approximately X, where X is a number between 0.03162267660168379 and 0.031622876601683794.

I understand there could be a issue when you compare abs(mid_square - number) <= tolerance, because the intended tolerance would be changed when you square the mid number to compare with the original number, but how would the math change and how to account for it in my code?

Any feedback on how to improve is appreciated, thanks!

Edit: My code passes when I change abs(mid_square - number) <= tolerance to abs(mid - number**0.5) <= tolerance, but that just defeats the purpose of using this algorithm, so how would I calculate this properly? Thanks for any help!

2

the tolerance is the max accepted difference between the actual square root and the calculated number

you may want to read again the text above the user stories, it says what else you can consider for the tolerance

3

Oh, after rechecking the problem description it says the tolerance is the maximum difference between the upper and lower bound of the square root. After changing one of my lines of code to reflect this, the test cases passed fully. Thanks for your help!

1 Like
4

@chuqingyan123 what did you change?

5

please create your own topic to ask for help, don’t ask others to give you the solution

If you have a question about a specific challenge as it relates to your written code for that challenge and need some help, click the Get Help > Ask for Help button located on the challenge.

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The Ask for Help button will create a new topic with all code you have written and include a link to the challenge also. You will still be able to ask any questions in the post before submitting it to the forum.

Thank you.