Question

Write a python program (recursive.py) that contains a main() function. The main() should test the following functions by calling each one with several different values. Here are the functions:

1) rprint - Recursive Printing: Design a recursive function that accepts an integer argument, n, and prints the numbers 1 up through n.

2) rmult - Recursive Multiplication: Design a recursive function that accepts two arguments into the parameters x and y. The function should return the value of x times y. Remember, multiplication can be performed as repeated addition as follows: 7*4=4+4+4+4+4+4+4. (To keep the function simple, assume that x and y will always hold positive nonzero integers.)

3) rlines - Recursive Lines: Write a recursive function that accepts an integer argument, n. The function should display n lines of asterisks on the screen, with the first line showing 1 asterisk, the second line showing 2 asterisks, up to the nth line which shows n asterisks.

4) rLargestList-LargestListItem:Designafunctionthatacceptsalist as an argument, and returns the largest value in the list. The function should use recursion to find the largest item.

5) rMultList - Recursive List Product: Design a function that accepts a list of numbers as an argument. The function should recursively calculate the product of all the numbers in the list and return that value.

6) rSum - Sum of Numbers: Design a function that accepts an integer argument and returns the sum of all the integers from 1 up to the number passed as an argument. For example, if 50 is passed as an argument, the function will return the sum of 1, 2, 3, 4, . . . 50. Use recursion to calculate the sum.

7) rPower - Recursive Power Method: Design a function that uses recursion to raise a number to a power. The function should accept two arguments: the number to be raised and the exponent. Assume that the exponent is a 0 or a positive integer.

Answer 1

def rprint(n):
    if n > 0:
        rprint(n-1)
        print(n)

def rmult(x,y):
    if y == 0:
        return 0
    elif y < 1:
        return -( x - rmult(x, y + 1))
    else:
        return (x + rmult(x, y - 1))

def rlines(n):
    if n > 0:
        rlines(n-1)
        print("*" * n)

def rLargestList(A):
    if len(A) == 1:
        return A[0]
    else:
        return max(A[0], rLargestList(A[1:]))

def rMultList(A):
    if len(A) == 1:
        return A[0]
    else:
        return (rMultList([A[0]]) * rMultList(A[1:]))

def rSum(n):
    if n == 1:
        return 1
    return n + rSum(n-1)  

def rPower(a, b):
    if b == 0:
        return 1
    if b == 1:
        return a
    else:
        return a * rPower(a, b-1)

def main():
    rprint(5)
    print(rmult(7,5))
    rlines(5)
    print(rLargestList([1,5,2,9,7]))
    print(rMultList([1,5,2,9,7]))
    print(rSum(50))
    print(rPower(3,4))

main()