08.04. Power Set

Description

Write a method to return all subsets of a set. The elements in a set are pairwise distinct.

Note: The result set should not contain duplicated subsets.

Example:

 Input:  nums = [1,2,3]

 Output: 

[

  [3],

  [1],

  [2],

  [1,2,3],

  [1,3],

  [2,3],

  [1,2],

  []

]

Solutions

Solution 1: Recursive Enumeration

We design a recursive function $dfs(u, t)$, where $u$ is the index of the current element being enumerated, and $t$ is the current subset.

For the current element with index $u$, we can choose to add it to the subset $t$, or we can choose not to add it to the subset $t$. Recursively making these two choices will yield all subsets.

The time complexity is $O(n \times 2^n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array. Each element in the array has two states, namely chosen or not chosen, for a total of $2^n$ states. Each state requires $O(n)$ time to construct the subset.

Python3JavaC++GoTypeScriptRustJavaScriptSwift

class Solution:
    def subsets(self, nums: List[int]) -> List[List[int]]:
        def dfs(u, t):
            if u == len(nums):
                ans.append(t[:])
                return
            dfs(u + 1, t)
            t.append(nums[u])
            dfs(u + 1, t)
            t.pop()

        ans = []
        dfs(0, [])
        return ans

class Solution {
    private List<List<Integer>> ans = new ArrayList<>();
    private int[] nums;

    public List<List<Integer>> subsets(int[] nums) {
        this.nums