Implement the Bisection Method - Implement the Bisection Method

Python
1

Tell us what’s happening:

Hi, obviously, my code does not work, and I do not understand why. Normally, when I type square_root_bisection(225, 1e-7, 10), it should give me None because it should not be able to find 15 in 10 iterations, but it gives me 15. Can you please put me in the right direction?

Your code so far

def square_root_bisection(number, tolerance=0.1, max_iterations=100):
    
    if number < 0:
        raise ValueError("Square root of negative number is not defined in real numbers")
    
    if number == 0 or number == 1:
        print(f'The square root of {number} is {number}')
        return number
    
    if number < 1:
        Min = 0
        Max = 1
    
        for i in range(max_iterations): 
            Mid = (Min+Max)/2
            square = Mid **2
            if square > number:
                Max = Mid
            elif square < number:
                Min = Mid
        if square == number or abs(Max-Min) <= tolerance:
            print(f'The square root of {number} is approximately {Mid}')
            return Mid
        else:
            print(f"Failed to converge within {max_iterations} iterations")
            return None

    Min = 1
    Max = number
    
    for i in range(max_iterations):
        Mid = (Min + Max)/2
        square = Mid **2
        if square > number:
            Max = Mid
        elif square < number:
            Min = Mid  
    if square == number or abs(Max - Min) < tolerance:
        print(f'The square root of {number} is approximately {Mid}')
        return Mid 
    else:
        print(f"Failed to converge within {max_iterations} iterations")
        return None
    

print(square_root_bisection(0))
square_root_bisection(225, 1e-7, 10)
print(square_root_bisection(225, 1e-7, 10))

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Challenge Information:

Implement the Bisection Method - Implement the Bisection Method

2

have you tried any debugging (you didn’t say if you had).
Debugging like: adding print statements to your code to investigate the values of various variables at different points and trace how they change as the program runs.

3

In addition to debugging with print statements, you can also step through your code to see what it’s doing with this Python Code Visualizer.

4

Tell us what’s happening:

I do not get it. While other tests pass, tests 8-9 do not and actually, the iterations should continue but they do not. Can you please guide me?

Your code so far

def square_root_bisection(number, tolerance=0.1, max_iterations=10):
    
    if number < 0:
        raise ValueError("Square root of negative number is not defined in real numbers")
    if number == 0 or number == 1:
        print(f"The square root of {number} is {number}")
        return number
       
    low = 0.0
    high = max(1.0, number)
       
    for _ in range(max_iterations):
        mid = (low + high) / 2.0
        print(f"{_} {mid}")
        square_target = mid * mid
        if abs(square_target - number) <= tolerance:
            print(f"square_target {square_target}")
            print(f"The square root of {number} is approximately {mid}")
            return mid
        if square_target > number:
            high = mid
        else:
            low = mid
       
    print(f"Failed to converge within {max_iterations} iterations")
    return None


    

print(square_root_bisection(0))

square_root_bisection(0.001, 1e-7, 50)
print(square_root_bisection(0.001, 1e-7, 50))

square_root_bisection(0.25, 1e-7, 50)
print(square_root_bisection(0.25, 1e-7, 50))

print(square_root_bisection(1))

square_root_bisection(81, 1e-3, 50)
print(square_root_bisection(81, 1e-3, 50))

square_root_bisection(225, 1e-3, 100)
print(square_root_bisection(225, 1e-3, 100))

square_root_bisection(225, 1e-5, 100)
print(square_root_bisection(225, 1e-5, 100))

square_root_bisection(225, 1e-7, 100)
print(square_root_bisection(225, 1e-7, 100))

square_root_bisection(225, 1e-7, 10)
print(square_root_bisection(225, 1e-7, 10))

Your browser information:

User Agent is: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/605.1.15 (KHTML, like Gecko) Version/18.3.1 Safari/605.1.15

Challenge Information:

Implement the Bisection Method - Implement the Bisection Method

5

I went ahead and combined your posts for you. In the future, just reply to the original thread to add further updates.

6

Yes sorry. Looking forward to your help.

7

Hi @BPCJ ,

For example, if the tolerance is 0.01 , the bisection method will keep halving the interval until the difference between the upper and lower bounds is less than or equal to 0.01 .

Is your code doing what this instruction says it should?

Happy coding!

8

No, the code does not do that, but the thing is I do not understand why. Can you help?

9

Actually, what I do not understand is why square_root_bisection(0.001, 1e-7, 50) stops after 16 iterations while it should iterate 50 times. Can you please explain what I did wrong?

10

Why do you think it should iterate 50 times?

Please review the instructions until you understand what the function is supposed to do:

image
image407×387 23.4 KB

11

I still do not get it. It should iterate 50 times (or less) until it coverages to a value within the specified tolerance. Here it stops iterating while it is not yet within the specified tolerance. I am stuck.

12

Have you tried checking the difference between the high and low bounds against the tolerance?

13

Yes, as you can see, I tested different cases, and in one case (square root bisection 0.001), iterations stop after 16 iterations while it is not yet within the specified tolerance. I do not understand why. Normally, it should continue iterating until it gets within the tolerance or issue a message that it failed to converge within the max number of iterations.

14

Can you please reply. I am stuck at this point and have been stuck for 2 weeks now. But you have not really helped.

15

I managed to find the solution by looking at other posts.

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