def removeMultiples(x, arr) - directly remove the multiples of prime numbers (instead of just marking them) by creating a helper function. This recursive function takes in a number, n, and a list and returns a list that doesn’t contain the multiples of n. def createList(n) - a recursive function, createList(), that takes in the user input n and returns an array of integers from 2 through n (i.e. [2, 3, 4, …, n]). def Sieve_of_Eratosthenes(list) - a recursive function that takes in a list and returns a list of prime numbers from the input list. Template below: def createList(n): #Base Case/s #ToDo: Add conditions here for base case/s #if : #return #Recursive Case/s #ToDo: Add conditions here for your recursive case/s #else: #return #remove the line after this once all ToDo is completed return [] def removeMultiples(x, arr): #Base Case/s #TODO: Add conditions here for your base case/s #if : #return #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return #remove the line after this once you've completed all ToDo return [] def Sieve_of_Eratosthenes(list): #Base Case/s if len(list) < 1 : return list #Recursive Case/s else: return [list[0]] + Sieve_of_Eratosthenes(removeMultiples(list[0], list[1:])) if __name__ == "__main__": n = int(input("Enter n: ")) print(n) list = createList(n) #Solution 1 primes = Sieve_of_Eratosthenes(list) print(primes)
def removeMultiples(x, arr) - directly remove the multiples of prime numbers (instead of just marking them) by creating a helper function. This recursive function takes in a number, n, and a list and returns a list that doesn’t contain the multiples of n.
def createList(n) - a recursive function, createList(), that takes in the user input n and returns an array of integers from 2 through n (i.e. [2, 3, 4, …, n]).
def Sieve_of_Eratosthenes(list) - a recursive function that takes in a list and returns a list of prime numbers from the input list.
Template below:
def createList(n):
#Base Case/s
#ToDo: Add conditions here for 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 all ToDo is completed
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 ToDo
return []
def Sieve_of_Eratosthenes(list):
#Base Case/s
if len(list) < 1 :
return list
#Recursive Case/s
else:
return [list[0]] + Sieve_of_Eratosthenes(removeMultiples(list[0], list[1:]))
if __name__ == "__main__":
n = int(input("Enter n: "))
print(n)
list = createList(n)
#Solution 1
primes = Sieve_of_Eratosthenes(list)
print(primes)
![The code is already given above.
Problem: Using PYTHON, create and implement a recursive function that will do the following:
Input #1
Output #1
10
Enter n: 10
[2, 3, 5, 7]
Input #2
Output #2
Enter n: 50
50
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
V The input is a single integer value. This value will be the upper bound of the list of values that will be created using
the createList() function.
V The input is an integer from the range [2,200] (inclusive). Assume that the input is always valid.
Output:
V The output will be a list containing primes within the range of 2 to n (inclusive), where n is the value of the user's input.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3cf655d-3bdc-4013-8c1f-5d6d56ea7228%2Fdefed57d-4976-4e11-866e-496abf17f820%2Fvm3i7lf_processed.png&w=3840&q=75)
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