递归原理求证：Python阶乘递归代码执行逻辑疑问

API 探路者

2026-5-15

Hey there! Let's break this down clearly to confirm your understanding and fill in any small gaps:

原始递归阶乘代码

def factorial(n):
    print("factorial has been called with n = " + str(n))
    if n == 1:
        return 1
    else:
        res = n * factorial(n-1)
        print("intermediate result for ", n, " * factorial(" ,n-1, "): ",res)
        return res
print(factorial(5))

控制台输出

factorial has been called with n = 5
factorial has been called with n = 4
factorial has been called with n = 3
factorial has been called with n = 2
factorial has been called with n = 1
intermediate result for 2 * factorial( 1 ): 2
intermediate result for 3 * factorial( 2 ): 6
intermediate result for 4 * factorial( 3 ): 24
intermediate result for 5 * factorial( 4 ): 120
120

你的理解确认与补充

你的核心理解完全正确！不过我们可以补充几个细节让整个流程更精准：

关于调用栈：每次调用factorial(n)时，Python会为该函数创建一个独立的栈帧（包含当前n值、局部变量、返回地址等信息）。从factorial(5)到factorial(1)，栈里一共压入了5个栈帧——factorial(1)虽然触发了基准条件直接返回，但它也是栈中的一个有效帧，只是没有进入else分支。
回溯阶段的执行逻辑：当factorial(1)返回1后，程序回到factorial(2)的else分支，此时factorial(n-1)的返回值是1，计算得到res=2*1=2，打印中间结果后返回2给factorial(3)；以此类推，直到factorial(5)计算出5*24=120，最终被外层的print语句输出。
你提到的“弹出n=1时无输出”是准确的，因为factorial(1)走的是if分支，没有执行else块里的打印语句，自然不会产生中间结果输出。