How to print power set in order each pair of subset differs only one element?

Question

I want to print a power set in an order such that adjacent subsets will differ by only one element.

For example:

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

Output would be printed like this:

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

or

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

Answer 1

Generate the first 2^N gray codes, where N = len(S). Use the bits of the code to select elements for that set.

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)

Output:

[]
[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]