离散数学课后作业1-17的Python实现

题目要求：编写一个程序，输入任意一个自然数$n$，输出$P(\lbrace 1,2,…,n \rbrace )$的所有元素！

使用了例1.2.4中提及的递归算法

def add_to_list(mylist,myset):
    """直接调用append方法会导致集合重复出现，因此编写此函数在添加前检查是否重复"""
    if myset not in mylist:
        mylist.append(myset)

def make_set(a,B):
    """进行集合运算new_set(a,B)={{a} union x|x belongs to P(B)}"""
    mylist=[]
    add_to_list(mylist,a)
    for element in B:
        newset=a|element
        add_to_list(mylist,newset)
    return mylist

def power_set(myset):
    """递归函数"""
    mylist=[]
    if not myset:
        mylist.append(set())
        return mylist
    else:
        for element in myset:
            a = set((element,))
            B = myset - a
            newset = power_set(B)
            for element1 in newset:
                add_to_list(mylist, element1)
            for element1 in make_set(a, newset):
                add_to_list(mylist, element1)
    return mylist

num = int(input("Input a number:"))
myset = set(range(1, num + 1))
for element in power_set(myset):
    if element == set():
        print("Ø")
    else:
        print(element)