Question

You must use recursion to solve each problem. You cannot use loops in this homework. You cannot import any module. A couple of the tasks have individual restrictions; note them, as we will remove points for any task that does not follow the requirements.

def factorial_evens(num): Implement a function to calculate and return the product of all even numbers from 1 up to num (inclusive if num is even).
o Assumption: num will be an integer greater than or equal to 1.
o Examples:
▪ factorial_evens(4) → 8 # 2*4 = 8
▪ factorial_evens(7) → 48 # 2*4*6 = 48
▪ factorial_evens(1) → 1

def power_of_three(num): Implement a function that determines whether or not a number is a power of three, and returns True or False accordingly
o Assumption: num will be an integer greater than or equal to 1.
o Examples:
▪ power_of_three(1) → True # 3 ** 0
▪ power_of_three(5) → False # not a power of 3
▪ power_of_three(9) → True # 3 ** 2

def snake(grid, row, col): Implement a function to calculate the longest "snake" of ones that can be made from a starting position in a grid. A snake is made by moving right and down from a starting position as far as possible.
o Assumption: grid will be at least 1x1, row and col will each be valid indexes in grid
o Restrictions: You may not use the max() or min() functions.
o Examples: (cells is a 2D list below)

▪ snake(cells,0,0) → 1 # can't move in either direction
▪ snake(cells,0,2) → 2 # can go down one, then no more moves
▪ snake(cells,1,1) → 5 # all the way down, and then right

Answer 1

Thanks for the question, here are the first two functions in python, in the 3rd question the question does not states what is the initial dimension of the cells 2D array, hencce its not very clear to write the logic.

The other two functions is working fine.
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def factorial_evens(num):
    if num<=1:
        return 1
    else:
        if num%2==1:
            return factorial_evens(num-1)
        else:
            return num*factorial_evens(num-1)

a=factorial_evens(1)
print(a)

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import math
def power_of_three(num):
    exp=math.log(num,3)
    exp_int=int(exp)
    return exp-exp_int==0


print(power_of_three(5))

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