接口和多态

def factorial(n):
    if n <= 1:
        return 1
    else:
        return n* factorial(n-1)
print(factorial(6))
print(factorial(5))

# 1 * 2 * 3 * 4 * 5 * 6


def sum_naturals(n):
    if n in [0, 1]:
        return n
    else:
        return n + sum_naturals(n-1)
print(sum_naturals(0))
print(sum_naturals(1))
print(sum_naturals(5))



def remeber_fact(n0, product):
    if n0 <= 1:
        return product
    else:
        return remeber_fact(n0-1, product*n0)

print(remeber_fact(0, 1))
print(remeber_fact(0, 10))
print(remeber_fact(1, 1))
# 第一个数是 0， 1 返回第二个数
# 第一个数大于 1 返回的是
print(remeber_fact(4, 5))
# remeber_fact(n0-1, product*n0)
# remeber_fact(4, 5)
# remeber_fact(3, 5*4)
# remeber_fact(2, 5*4*3)
# remeber_fact(1, 5*4*3*2)


def factorial2(n):
    return remeber_fact(n, 1)

print(factorial2(6))
# remeber_fact(n0-1, product*n0)
# remeber_fact(6, 1)
# remeber_fact(5, 1*6)
# remeber_fact(4, 1*6*5)
# remeber_fact(3, 1*6*5*4)
# remeber_fact(2, 1*6*5*4*3)
# remeber_fact(1, 1*6*5*4*3*2)

# 求列表中所有的偶数累加和
def sum_acc(s, r):
    if r == []:
        return s
    elif r[0] % 2 == 0:

        return sum_acc(s + r[0], r[1:])
    else:
        return sum_acc(s, r[1:])
def sum_evens(L):
    return sum_acc(0, L)

print(sum_evens([3, 4, 5, 4]))
print(sum_evens([]))



def count(s, char):
    if s == '':
        return 0
    else:
        is_char = 0
        if s.find(char) ==0 and char != '' :
            is_char += 1
        return count(s[1:], char) + is_char
print(count("", ""))     # 0
print('"',count("banana", ""))  # 0
print(count("banana", "a"))    # 3
print(count("banana", "z"))       #0



def count_acc(s, char, acc):
    if s == '':
        return acc
    else:
        is_char = 0
        if s.find(char) ==0 and char != '' :
            is_char += 1
        return count_acc(s[1:], char, acc+is_char)
def count_letters(s, char):
    return count_acc(s, char, 0)
print(count_letters("", ""))     # 0
print('"',count_letters("banana", ""))  # 0
print(count_letters("banana", "a"))    # 3
print(count_letters("banana", "z"))       #0



print("+++++++++++++++++++++++++++++++++++++++++++++++++++++++")
# 奇数和
def sum_odd(L):
    if L == []:
        return 0
    else:
        if L[0]%2== 1:
            return L[0] + sum_odd(L[1:])
    return sum_odd(L[1:])

print(sum_odd([]))   # 0
print(sum_odd([1]))     # 1
print(sum_odd([1, 2, 3]))   # 4

print("+++++++++++++++++++++++++++++++++++++++++++++++++++++++")
def filter_odd(L):
    if L==[]:
        return []
    else:
        if L[0]%2 !=0:
            return [L[0]] + filter_odd(L[1:])
        else:
            return  filter_odd(L[1:])

print(filter_odd([]))
print(filter_odd([1, 2, 3]))
print(filter_odd([2, 4, 6, 8]))


print("+++++++++++++++++++++++++++++++++++++++++++++++++++++++")
def inverse(L):
    if L == []:
        return []
    else:
        return  [L[-1]] + inverse(L[:-1])
    pass
print(inverse([]))
print(inverse([1, 2, 3]))

print("+++++++++++++++++++++++++++++++++++++++++++++++++++++++")
def product(L):
    if L ==[]:
        return 1
    else:
        return L[0]*product(L[1:])
print(product([]))
print(product([3]))
print(product([2, 3, 5]))

print("+++++++++++++++++++++++++++++++++++++++++++++++++++++++")
def mul_table(n):
    if n <= 0 :
        return [[0]]
    else:
        return [[mul_table(n-1)]]


print(mul_table(0))
print(mul_table(1))
print(mul_table(2))