Logical thinking for calculating the square root

Question

Hey guys, so I tried to decrypt this problem in the last hour right now, and there are problems here. This is problem

This method of calculating the square root of n starts with doing (zero) guessing at the square root. He then uses the original hunch to calculate a new guess, according to the formula

newGuess = ((n / oldGuess) + oldGuess) / 2.0; 

They have two variables oldGuess and newGuess . Initialize oldGuess to n / 2.0 and compute newGuess according to the above formula. using a while loop to iterate until the absolute value of the difference between oldGuess and newGuess greater than 1.0E-06 . Remember to reset the oldGuess value for newGuess in the while loop.

In your program, you ask the user to enter a positive number. If the number is negative, print an error message and ask the user to try again. For a positive number, calculate the square root using the method above. Find the difference between the resulting square root and the value obtained from using the exponentiation operator. Write from the value entered by the user, the calculated square root and the difference (your square root is n ** 0.5 )

This is my program so far

 def main(): n = eval(input("Enter a positive number: ")) while (n <= 0): print ("Error please re-input") n = eval(input("Enter a positive number: ")) oldGuess = n / 2.0 newGuess = ((n / oldGuess) + oldGuess) / 2.0; difference = n - n ** 0.5 while (difference < 1 * 10 ** -6): print ("Error") difference = abs(n - n ** 0.5) print ("Difference:", difference) main() 

So, I do not quite understand how we can tell the program to make an assumption, and then calculate the square root of the variable n. I do not even think that my statements in this context are right. I don’t use the squareroot built-in function built into python so I have to do it manually, I believe that it’s still lost what this means with the guessing function.

Answer 1

 while True: n = float(input("Enter a positive number: ")) if n > 0: break print ("Error please re-input") oldGuess = n / 2.0 while True: newGuess = ((n / oldGuess) + oldGuess) / 2.0; oldGuess = newGuess if -1e-6 < n - newGuess * newGuess < 1e-6: break print ("Difference:", abs(n ** .5 - newGuess)) 

Answer 2

Change those eval() to float() s. eval() executes any code it passes, so your user may type something malicious there.

Now, use this for the second part:

 oldGuess = n / 2.0 newGuess = ((n / oldGuess) + oldGuess) / 2.0 while (abs(oldGuess - newGuess) > 1e-06): oldGuess, newGuess = newGuess, ((n / oldGuess) + oldGuess) / 2.0 print("Guess: " + str(n)) print("My root: " + str(newGuess)) print("Accuracy: " + str(newGuess - (n**0.5))) 

This comma syntax is a Python idiom, useful for replacing values ​​unnecessarily:

 temp = new new = old * something old = temp 

Your condition for the while loop tends to end the loop when your difference is less than this (very small) value. This way, you will loop until it is bigger.

Note. You can also use math.sqrt(n) instead of n ** 0.5 . You need import math .

If you want to see what your program does, try print to enter the values ​​of oldGuess and newGuess in a while . You will see how this will change them until you come to an answer.

Edit

I notice that you seem to have stumbled over why you should do oldGuess = newGuess . Let me explain: the = operator does not match the equal sign in mathematics. The equal sign says that the thing on the left is the same as the thing on the right; that is, they are equivalent. In Python, the = operator says: "Give the left side the same value as the thing on the right." It is called an assignment operator. You are thinking of the == operator, which checks for equivalence (mostly).

 >>> a = 10 >>> b = 4 >>> b = a >>> b 10 >>> a == b True >>> c = 6 >>> b = c >>> b 6 >>> a == b False >>> b == c True >>> a == c False >>> a,b,c (10, 6, 6) 

As you can see, when you use the = operator, you do not bind these variables together, saying that they are now one and the same. If you set b = a and then set b = c , b == a will become false, because b no longer has the same value as a . a also does not change, because b its value was assigned, and not vice versa. Think about what instead of the = operator it looks like <- (I think some languages ​​actually use this as an assignment operator).

Why does it matter? Well, you assign something new to a variable, you forget the old value. If you do not have another variable storing the same value, it is lost forever. Your job is to update oldGuess to the previous newGuess . In other words, if your guesses were "a", "b", "c", "d", you start with oldGuess as "a" and from there calculate newGuess as "b". Since this obviously was not the right guess, you say that oldGuess now what only newGuess was - “b”, and you newGuess next newGuess , which is “c”.

You need the oldGuess value to calculate the newGuess value. But you need the newGuess value (before the change) to update the oldGuess value. This is catch-22 unless you save the previous value of newGuess , as I showed above (as an example of swap). That is why you need it.

Answer 3

So, I understand, thanks to the guys for their help. I didn’t know that we cannot post home questions here, but I am trying to definitely learn how to code so that I can get better. Here is my final decision.

 def main(): n = float(input("Enter a positive number: ")) while (n <= 0): print ("Error please re-input") n = eval(input("Enter a positive number: ")) oldGuess = n / 2.0 newGuess = 0 difference = 10 while (difference >= 1 * 10 ** -6): newGuess = ((n / oldGuess) + oldGuess) / 2.0 difference = abs(newGuess - oldGuess) oldGuess = newGuess print ("Square Root is: ", newGuess) differenceSqrt = newGuess - n ** 0.5 print ("Difference is: ", differenceSqrt) main() 

I still don't know how to use breaks effectively, so thanks gnibbler, but couldn't follow your code too well. (New to this, sorry)