[ Python ] 递归函数

一、 什么是递归函数

    如果一个函数在内部调用自身本身，这个函数就是递归函数。
    在递归函数中，是一个有去有回的过程。

二、递归函数的说明

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

print(fact(5))

# fact(5)
# ===> 5 * fact(4)
# ===> 5 * (4 * fact(3))
# ===> 5 * (4 * (3 * fact(2)))
# ===> 5 * (4 * (3 * (2 * fact(1))))
# ===> 5 * (4 * (3 * (2 * 1)))
# ===> 5 * (4 * (3 * 2))
# ===> 5 * (4 * 6)
# ===> 5 * 24
# ===> 120

    通过上面的实例，可以总结出：
        递归函数就是在函数内部调用自身本身，直到自身返回的是一个具体的值而不是函数，然后从内向外逐一返回函数的值，因此递归是一个有去有回两个过程组成的；

三、一个递归函数的实例

menu = {
        '陕西省': {
                '西安':{
                        '未央区':{},
                        '莲湖区':{},
                        '高新区':{},
                },
                '咸阳':{
                        '秦都区':{},
                        '渭城区':{}
                }
        },
        '四川省': {
                '成都':{
                        '锦江区':{},
                        '青羊区':{},
                        '金牛区':{},
                },
                '绵阳':{
                        '涪城区': {},
                        '游仙区': {},
                }
        }
}

def threeTL(dic):
        while True:
                for key in dic: print(key)
                choice = input('>>>').strip()
                if choice == 'b' or choice == 'q': return choice
                elif choice in dic and dic[choice]:
                        res = threeTL(dic[choice])
                        if res == 'q': return 'q'
                elif not choice or choice not in dic:
                        continue

threeTL(menu)

该实例是选择省打印城市，输入城市打印区, 当用户输入 b 返回上一层，当用户输入 q 退出整个程序，这里最难理解的就是 b 和 q 的用法；

分析如下：

（1）正常递归深入过程：

# def threeTL(dic):
#     while True:
#         for key in dic: print(key) # 陕西省、四川省
#         choice = input('>>>').strip()   # 用户输入：陕西省
#         if choice == 'b' or choice == 'q': return choice
#         elif choice in dic and dic[choice]:
#             res = threeTL(dic[choice])  # 递归返回 threeTL(dic['陕西省'])
#             if res == 'q': return 'q'
#         elif not choice or choice not in dic:
#             continue
#
# def threeTL(dic): # dic = dic['陕西省']
#     while True:
#         for key in dic: print(key) # 西安、咸阳
#         choice = input('>>>').strip()   # 用户输入：西安
#         if choice == 'b' or choice == 'q': return choice
#         elif choice in dic and dic[choice]:
#             res = threeTL(dic[choice])  # 递归返回 threeTL(dic['陕西省']['西安'])
#             if res == 'q': return 'q'
#         elif not choice or choice not in dic:
#             continue
#
# def threeTL(dic): # dic = dic['陕西省']['西安']
#     while True:
#         for key in dic: print(key) # 未央莲湖高新
#         choice = input('>>>').strip()   # # 用户输入：未央区
#         if choice == 'b' or choice == 'q': return choice
#         elif choice in dic and dic[choice]:
#             res = threeTL(dic[choice])  
#             if res == 'q': return 'q'
#         elif not choice or choice not in dic: # 因为未央区没有值，进入下一次循环

threeTL(menu)
-->threeTL(menu['陕西省'])
-->threeTL(menu['陕西省'])-->threeTL(menu['陕西省']['西安'])
-->threeTL(menu['陕西省'])-->threeTL(menu['陕西省']['西安'])-->threeTL(menu['陕西省']['西安']['未央区'])

（2）当用户输入 ' b '：

def threeTL(dic): # dic = dic['陕西省']['西安']
        while True:
                for key in dic: print(key) # 未央莲湖高新
                choice = input('>>>').strip()   # # 用户输入：b
                if choice == 'b' or choice == 'q': return choice # 返回'b'，程序退出
                elif choice in dic and dic[choice]:
                        res = threeTL(dic[choice])  
                        if res == 'q': return 'q'
                elif not choice or choice not in dic:
                        continue

def threeTL(dic): # dic = dic['陕西省']
        while True:
                for key in dic: print(key) # 第二次while循环打印 <西安、咸阳>(第一次while循环是在递归函数深入的时候执行)
                choice = input('>>>').strip()   # 第二次while循环到此，用户输入 b
                if choice == 'b' or choice == 'q': return choice # 返回'b'，程序退出
                elif choice in dic and dic[choice]:
                        res = threeTL(dic[choice])  # res = 'b', 本次if循环没有匹配到res退出，进行下一次while循环
                        if res == 'q': return 'q'
                elif not choice or choice not in dic:
                        continue

def threeTL(dic):
        while True:
                for key in dic: print(key) # 第二次while循环打印 <陕西省、四川省>(第一次while循环是在递归函数深入的时候执行)
                choice = input('>>>').strip()   # 第二次while循环到此，用户输入 b
                if choice == 'b' or choice == 'q': return choice # 返回'b'，整个程序退出，递归结束
                elif choice in dic and dic[choice]:
                        res = threeTL(dic[choice])  # 递归返回 threeTL(dic['陕西省'])
                        if res == 'q': return 'q'
                elif not choice or choice not in dic:
                        continue

（3）当用户输入 'q'

def threeTL(dic): # dic = dic['陕西省']['西安']
        while True:
                for key in dic: print(key) # 未央莲湖高新
                choice = input('>>>').strip()   # # 用户输入：q
                if choice == 'b' or choice == 'q': return choice # 返回'q'，程序退出
                elif choice in dic and dic[choice]:
                        res = threeTL(dic[choice])  
                        if res == 'q': return 'q'
                elif not choice or choice not in dic:
                        continue

def threeTL(dic): # dic = dic['陕西省']
        while True:
                for key in dic: print(key) # <西安、咸阳>
                choice = input('>>>').strip()    
                if choice == 'b' or choice == 'q': return choice 
                elif choice in dic and dic[choice]:
                        res = threeTL(dic[choice])  # res = 'q'
                        if res == 'q': return 'q'    # 匹配到 res='q' 返回 'q' 程序退出
                elif not choice or choice not in dic:
                        continue

def threeTL(dic): # dic = dic['陕西省']['西安']
        while True:
                for key in dic: print(key) # 未央莲湖高新
                choice = input('>>>').strip()   # # 用户输入：q
                if choice == 'b' or choice == 'q': return choice # 返回'q'，程序退出
                elif choice in dic and dic[choice]:
                        res = threeTL(dic[choice])  
                        if res == 'q': return 'q'
                elif not choice or choice not in dic:
                        continue