# we want the square root of 17 for example g = 4 # our guess is 4 initially error = 0.0000000001 # we want to stop when we are this close while abs(n - (g**2)) > error: g = g - ((g**2 - n)/(2 * g)) # g holds the square root of n at this point Implement this algorithm in a function sqR
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The following code implements Newton's
n = 17 # we want the square root of 17 for example
g = 4 # our guess is 4 initially
error = 0.0000000001 # we want to stop when we are this close
while abs(n - (g**2)) > error:
g = g - ((g**2 - n)/(2 * g))
# g holds the square root of n at this point
Implement this algorithm in a function sqRoot(n), that returns the square root using recursion.
Assume that the function will be called with positive numbers only.
Note: Your initial guess cannot be zero!
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- The following code implements Newton's algorithm for finding the square root of a number using repetition: n = 17 # we want the square root of 17 for example # our guess is 4 initially # we want to stop when we are this close g = 4 error = 0.0000000001 while abs(n - (g**2)) > error: g = g - ((g**2 - n)/(2 * g)) # g holds the square root of n at this point Implement this algorithm in a function sqRoot (n), that returns the square root using recursion. Assume that the function will be called with positive numbers only. Note: Your initial guess cannot be zero!le.com/forms/d/e/1FAlpQLSc6PlhZGOLJ4LOHo5cCGEf9HDChfQ-tT1bES-BKgkKu44eEnw/formResponse The following iterative sequence is defined for the set of positive integers: Sn/2 3n +1 ifn is odd if n is even Un = Using the rule above and starting with 13, we generate the following sequence: 13 u13 = 40 u40 =20 u20 = 10→ u10 =5 u5 = 16 u16 = 8 ug = 4 → Us =2 u2 =1. It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. The below function takes as input an integer n and returns the number of terms generated by the sequence starting at n. function i-Seq (n) u=n; i=%3; while u =1 if statement 1 u=u/2; else statement 2 end i=i+1; end statement 1 and statement 2 should be replaced by: None of the choices statement 1 is "mod(u,2)=D%3D0" and statement 2 is "u = 3*u+1;" statement 1 is "u%2" and statement 2 is "u = 3*u+1;" O statement 1 is "mod(n,2)=30" and statement 2 is "u = 3*n+1;"Write an algorithm that asks the user to enter a positive integer n and prints the sum of the divisors of n.
- The greatest common divisor of two positive integers, A and B, is the largest number that can be evenly divided into both of them. Euclid's algorithm can be used to find the greatest common divisor (GCD) of two positive integers. You can use this algorithm in the following manner: 1. Compute the remainder of dividing the larger number by the smaller number. 2. Replace the larger number with the smaller number and the smaller number with the remainder. 3. Repeat this process until the smaller number is zero. The larger number at this point is the GCD of A and B. Write a program that lets the user enter two integers and then prints each step in the process of using the Euclidean algorithm to find their GCD. An example of the program input and output is shown below: Enter the smaller number: 5 Enter the larger number: 15 The greatest common divisor is 5Eulers number e is used as the base of natural logarithm. It may be approximated using the formula e=1/0!+1/1!+1/2!…1/(n-1)!+1/n! When n is sufficiently large. Write a program that approximates e using a loop that terminates when the difference between the two successive values of e is less than 0.0000001.use JAVA to write the code. : Euclid’s algorithm for finding the greatest common divisor (gdc) of two numbers The algorithm: given two numbers, n1 and n2: Divide n1 by n2 and let r be the remainder. If the remainder r is 0, the algorithm is finished and the answer is n2. (If the remainder is 1, the numbers are mutually prime and we are done-see below.) Set n1 to the value of n2, set n2 to the value of r, and go back to step 1. Entering 0 for one of the values is bad. It should work for the other value, but you have to figure out which is OK and which is bad. Catch this problem as it happens and make the user enter another value until they enter an acceptable one. Give an appropriate error message if this happens.
- Nuts and bolts You are given a collection of n bolts of different widths and n corresponding nuts. You are allowed to try a nut and bolt together, from which you can determine whether the nut is larger than the bolt, smaller than the bolt, or matches the bolt exactly. However, there is no way to compare two nuts together or two bolts together. The problem is to match each bolt to its nut. Design an algorithm for this problem with average-case efficiency in (n log n).Which one is correct for the following snippet of code? def factorial1(x): if x== 0: return 1 return x *factorial1(x-1) def factorial2 (x,y=1): if x== 0: return y return factorial2 (x-1,x*y) Group of answer choices a) Both factorial1() and factorial2() aren’t tail recursive. b) Both factorial1() and factorial2() are tail recursive. c) factorial1() is tail recursive but factorial2() isn’t. d) factorial2() is tail recursive but factorial1() isn’t.please code in python The bisection code below finds the square root of a number. Try inputting 16 into the code to confirm it works. Next, try inputting 0.25 into the bisection search algorithm below and confirm that it doesn't work. Then correct the algorithm so that it works for all positive numbers, including decimals such as 0.25. # Q4-3 Grading Tag: ## Please fix the code in this cell (that is don't make a new cell)## Bisection Search to Find a Square Root x = float(input("enter a number:")) epsilon = 0.00001num_guesses = 0low = 0.0high = xans = (high + low)/2.0 while high - low >= 2 * epsilon: print("low =",low,"high =", high) num_guesses += 1 if ans ** 2 < x: low = ans else: high = ans ans = (high + low)/2.0 # Do not modify these output statements as the autograder looks for these!print('Number of guesses =', num_guesses)print(ans, 'is close to square root of', x)
- How can I apply this python code in the problem? def createList(n): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once you've completed all the TODO for this function return [] def removeMultiples(x, arr): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once you've completed all the TODO for this function return [] def Sieve_of_Eratosthenes(list): #Base Case/s if len(list) < 1 : return list #Recursive Case/s else: return [list[0]] +…How to solve the problem by FOLLOWING this python code format? def createList(n): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once you've completed all the TODO for this function return [] def removeMultiples(x, arr): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once you've completed all the TODO for this function return [] def Sieve_of_Eratosthenes(list): #Base Case/s if len(list) < 1 : return list #Recursive Case/s else: return [list[0]] +…Problem: In this problem, we would like to implement the algorithm to calculate digit sum of a given natural number that can be used in detecting errors in message transmission or data storage.For example:N = 103509, the digit sum = 1 + 0 + 3 + 5 + 0 + 9 = 18.N = 9512, the digit sum = 9 + 5 + 1 + 2 = 17Exercise 1: Write a pseudo-code to solve the above problem using Iteration. Write a program from the pseudo-code and solve the Problem using Iteration. Calculate the complexity. Justify your answer. Exercise 2: Write a program to solve the Problem using Recursion (with Iteration if necessary). Calculate the complexity. Justify your answer. Exercise 3: Write a program to solve the Problem using a List data structure. Note: Elements in List data structure can be used to store a digit of the given natural number.