factorial(0) = 1
factorial(n) = n * factorial(n-1)

factorial(3) = 3 * factorial(2)
             = 3 * 2 * factorial(1)
             = 3 * 2 * 1 * factorial(0)
             = 3 * 2 * 1 * 1
             = 6

factorial(n) = 1 * 2 * ... * (n-1) * n
In [4]:
def factorial(n):
    if n < 0:
        return None
    elif (n == 0):
        return 1
    return n * factorial(n-1)
In [6]:
print(factorial(-5))

None
In [9]:
def my_sum(nums):
    answer = 0
    for num in nums:
        answer = answer + num
    return answer
In [10]:
my_sum([1,2,3])
Out[10]:
6
In [11]:
# my_sum2([]) = 0
# my_sum2(xs) = xs[0] + my_sum2(xs[1:])

def my_sum2(nums):
    if nums == []:
        return 0
    return nums[0] + my_sum2(nums[1:])
In [12]:
my_sum2([1,2,3,4])
Out[12]:
10
my_sum2([1,2,3,4]) = 1 + my_sum2([2,3,4])
                   = 1 + 2 + my_sum2([3,4])
                   = 1 + 2 + 3 + my_sum2([4])
                   = 1 + 2 + 3 + 4 + my_sum2([])
                   = 1 + 2 + 3 + 4 + 0
                   = 10
In [15]:
def my_max(nums):
    if nums == []:
        return None
    answer = nums[0]
    for num in nums[1:]:
        if num > answer:
            answer = num
    return answer
In [16]:
my_max([10,5,16,24,2])
Out[16]:
24
In [ ]:
def my_max2(nums):
    if nums == []:
        return None
    if len(nums) == 1:
        return nums[0]
    return max(nums[0],my_max2(nums[1:]))
In [17]:
max(10,20)
Out[17]:
20
In [19]:
max([10,20])
Out[19]:
20
  my_max([10,5,16,24,2])
= max(10,my_max([5,16,24,2]))
= max(10,max(5,my_max([16,24,2])))
= max(10,max(5,max(16,my_max([24,2]))))
= max(10,max(5,max(16,max(24,my_max([2])))))
= max(10,max(5,max(16,max(24,2))))
= max(10,max(5,max(16,24)))
= max(10,max(5,24))
= max(10,24)
= 24