An article to help you understand Python recursive functions

1. What is a recursive function?

Within a function, other functions can be called. A function is recursive if it calls itself internally.

2. Principle of recursive calling of functions

• In fact, the recursive function is executed recursively on the stack memory. Each recursive execution will consume some stack memory.

• The size of the stack memory is an important factor in limiting the depth of recursion

##3. Case analysis

1. Find the factorial

Calculate factorial n! = 1 x 2 x 3 x … x n,

can be expressed by the function fact(n).

fact(n) = n! = 1 x 2 x 3 x … x (n-1) x n = (n-1)! x n = fact(n-1) x n

fact(n)可以表示为n x fact(n-1)，只有n=1时需要特殊处理。

So, fact(n) is written recursively:

def fact(n):    if n == 1:        return 1    return n * fact(n - 1)

如果计算fact(6)，可以根据函数定义看到计算过程如下：

def fac(n):    if n==1:        return 1    else:        res=n*fac(n-1)        return  res
print(fac(6))

运行结果：

2. 斐波拉契级数

有这样一个数列：1，1，2，3，5，8，13，21，34…。其第一元素和第二个元素等于 1，其他元素等于其前面两个元素的和。

例：

def fab(n):  # 定义斐波拉契级数    if n in [1, 2]:  # 如果n=1或者2      return 1    return fab(n - 1) + fab(n - 2)  # n>2

print(fab(1))  # 斐波拉契级数的第一个元素
print(fab(2))  # 斐波拉契级数的第二个元素
print(fab(8))  # 斐波拉契级数的第8个元素print(fab(13))  # 斐波拉契级数的第9个元素

运行结果：

3. 递归函数的优点

定义简单，逻辑清晰。理论上，所有的递归函数都可以写成循环的方式，但循环的逻辑不如递归清晰。

递归需要注意递归的深度。由于递归会产生多次函数调用，而函数调用会消耗代码的栈空间，如果递归的深度太大，会导致栈溢出。以上面的阶乘为例，如果计算 100000 的阶乘，在一般机器上都会出现栈溢出的问题。

print(fac(10000))

如下所示：

4. Summary

This article is based on Python basics. Python's standard interpreter is not optimized for tail recursion, and any recursive function will have a stack overflow. This article introduces the advantages and disadvantages of using recursive functions. The advantage is that the logic is simple and clear, but the disadvantage is that excessive calls can cause stack overflow.

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