> For the complete documentation index, see [llms.txt](https://wentao-shao.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://wentao-shao.gitbook.io/leetcode/permutation-and-combination/78.subsets.md).

# 78.Subsets

## 78. Subsets

## 题目地址

<https://leetcode.com/problems/subsets/>

<http://www.lintcode.com/en/problem/subsets/>

## 题目描述

```
Given a set of distinct integers, nums, return all possible subsets (the power set).

Note: The solution set must not contain duplicate subsets.

Example:

Input: nums = [1,2,3]
Output:
[
  [3],
  [1],
  [2],
  [1,2,3],
  [1,3],
  [2,3],
  [1,2],
  []
]
```

## 代码

### Approach #1 DFS

数组排序的算法复杂度 $$O(nlogn)$$

结果数为 $$2^n$$ 个，所以时间复杂度为: $$O(2^n)$$

使用临时数组list保存中间结果，所以空间复杂度为 $$O(n)$$

```java
class Solution {
    public List<List<Integer>> subsets(int[] nums) {
    List<List<Integer>> result = new ArrayList<List<Integer>>();
    if (nums == null || nums.length == 0) return result;

    // dfs
    List<Integer> list = new ArrayList<Integer>();
    dfs(nums, 0, list, result);

    return result;
  }

  private void dfs(int[] nums, int pos, List<Integer> list, List<List<Integer>> ret) {
    // Put it first,  let's make it have an empty set
    ret.add(new ArrayList<Integer>(list));

    for (int i = pos; i < nums.length; i++) {
      list.add(nums[i]);
      dfs(nums, i + 1, list, ret);
      list.remove(list.size() - 1);
    }
  }

}
```

### Approach 2: Recursion

```java
class Solution {
  public List<List<Integer>> subsets(int[] nums) {
    List<List<Integer>> output = new ArrayList();
    output.add(new ArrayList<Integer>());

    for (int num: nums) {
      List<List<Integer>> newSubsets = new ArrayList();
      for (List<Integer> curr: output) {
        newSubsets.add(new ArrayList<Integer>(curr){{add(num);}});
      }
      for (List<Integer> curr: newSubsets) {
        output.add(curr);
      }
    }
    return output;
  }
}
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://wentao-shao.gitbook.io/leetcode/permutation-and-combination/78.subsets.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.