python - 如何打印幂集以使每对子集仅一个元素不同？

Question

我想按照相邻子集仅相差一个元素的顺序打印幂集。

例如:

Input: S= {1,2,3,4}

输出将像这样打印:

{"",{1},{2}, {3}, {4} ,{4,1}, {4,2} ,{4,3},{3,1}...}

或

{"", {1}, {1,2}, {2}, {2,3}, ...}

Answer 1

生成前2^N gray codes ，其中 N = len(S)。使用代码位来选择该集合的元素。

S = [1, 2, 3, 4]

for i in range(2**len(S)):
    gray_code = i ^ (i >> 1)
    subset = [S[j] for j in range(len(S)) if gray_code & (1 << j) ]
    print(subset)

输出:

[]
[1]
[1, 2]
[2]
[2, 3]
[1, 2, 3]
[1, 3]
[3]
[3, 4]
[1, 3, 4]
[1, 2, 3, 4]
[2, 3, 4]
[2, 4]
[1, 2, 4]
[1, 4]
[4]