为什么发生“RecursionError：超出最大递归深度”

Question

I am looking at this code challenge:

Define a function cycle that takes in three functions f1 , f2 , f3 , as arguments. cycle will return another function that should take in an integer argument n and return another function. That final function should take in an argument x and cycle through applying f1 , f2 , and f3 to x , depending on what n was.

Here's what the final function should do to x for a few values of n :

• n = 0, return x

• n = 1, apply f1 to x , or return f1(x)

• n = 2, apply f1 to x and then f2 to the result of that, or return f2(f1(x))

• n = 3, apply f1 to x , f2 to the result of applying f1 , and then f3 to the result of applying f2 , or f3(f2(f1(x)))

• n = 4, start the cycle again applying f1 , then f2 , then f3 , then f1 again, or f1(f3(f2(f1(x)))) And so forth.

Below is my code, but the following error occurs for the case add_one_then_double :

RecursionError: maximum recursion depth exceeded

Could anybody help me on this? Thank you!

def cycle(f1, f2, f3):

    """
    >>> def add1(x):
    ...     return x + 1
    >>> def times2(x):
    ...     return x * 2
    >>> def add3(x):
    ...     return x + 3
    >>> my_cycle = cycle(add1, times2, add3)
    >>> identity = my_cycle(0)
    >>> identity(5)
    5
    >>> add_one_then_double = my_cycle(2)
    >>> add_one_then_double(1)
    4
    >>> do_all_functions = my_cycle(3)
    >>> do_all_functions(2)
    9
    >>> do_more_than_a_cycle = my_cycle(4)
    >>> do_more_than_a_cycle(2)
    10
    >>> do_two_cycles = my_cycle(6)
    >>> do_two_cycles(1)
    19
    """
    def cycle_func(n):
        i=1
        result=lambda x:x
        while i<n+1:
            if i%3==1:
                result=lambda x: f1(result(x))
            elif i%3==2:
                result=lambda x: f2(result(x))
            else:
                result=lambda x: f3(result(x))
            i=i+1
        return result

    return cycle_func

Answer 1

The problem is statements like this one:

result=lambda x: f1(result(x))

When this assignment is executed, result will be assigned this new lambda function. When later it is executed , result(x) will be a reference to this same function, and thus there is an infinite recursion. Here you intended to have a reference to the previous value of result , but as you can see, that was lost at the moment this assignment took place.

The solution, is to not create those "little" lambda functions there, but to create one inner function that gets the value of x , and will then go through this logic of determining what to execute next.

Here is the corrected code:

def cycle(f1, f2, f3):
    def cycle_func(n):
        def inner(x):
            i = 1
            result = x
            while i < n + 1:
                if i % 3 == 1:
                    result = f1(result)
                elif i % 3 == 2:
                    result = f2(result)
                else:
                    result = f3(result)
                i = i + 1
            return result

        return inner

    return cycle_func

def add1(x):
    return x + 1

def times2(x):
    return x * 2

def add3(x):
    return x + 3

my_cycle = cycle(add1, times2, add3)
identity = my_cycle(0)
print(identity(5)) # 5
add_one_then_double = my_cycle(2)
print(add_one_then_double(1)) # 4
do_all_functions = my_cycle(3)
print(do_all_functions(2)) # 9
do_more_than_a_cycle = my_cycle(4)
print(do_more_than_a_cycle(2)) # 10
do_two_cycles = my_cycle(6)
print(do_two_cycles(1)) # 19