leecode/problems/78.subsets.md

## 题目地址
https://leetcode.com/problems/subsets/description/

## 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],
  []
]


```

## 思路

这道题目是求集合，并不是`求极值`，因此动态规划不是特别切合，因此我们需要考虑别的方法。

这种题目其实有一个通用的解法，就是回溯法。
网上也有大神给出了这种回溯法解题的
[通用写法](https://leetcode.com/problems/combination-sum/discuss/16502/A-general-approach-to-backtracking-questions-in-Java-(Subsets-Permutations-Combination-Sum-Palindrome-Partitioning))，这里的所有的解法使用通用方法解答。
除了这道题目还有很多其他题目可以用这种通用解法，具体的题目见后方相关题目部分。

我们先来看下通用解法的解题思路，我画了一张图：

![backtrack](../assets/problems/backtrack.png)

通用写法的具体代码见下方代码区。

## 关键点解析

- 回溯法
- backtrack 解题公式


## 代码

* 语言支持：JS，C++

JavaScript Code:
```js

/*
 * @lc app=leetcode id=78 lang=javascript
 *
 * [78] Subsets
 *
 * https://leetcode.com/problems/subsets/description/
 *
 * algorithms
 * Medium (51.19%)
 * Total Accepted:    351.6K
 * Total Submissions: 674.8K
 * Testcase Example:  '[1,2,3]'
 *
 * 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],
 * []
 * ]
 * 
 */
function backtrack(list, tempList, nums, start) {
    list.push([...tempList]);
    for(let i = start; i < nums.length; i++) {
        tempList.push(nums[i]);
        backtrack(list, tempList, nums, i + 1);
        tempList.pop();
    }
}
/**
 * @param {number[]} nums
 * @return {number[][]}
 */
var subsets = function(nums) {
    const list = [];
    backtrack(list, [], nums, 0);
    return list;
};
```
C++ Code：
```C++
class Solution {
public:
    vector<vector<int>> subsets(vector<int>& nums) {
        auto ret = vector<vector<int>>();
        auto tmp = vector<int>();
        backtrack(ret, tmp, nums, 0);
        return ret;
    }
    
    void backtrack(vector<vector<int>>& list, vector<int>& tempList, vector<int>& nums, int start) {
        list.push_back(tempList);
        for (auto i = start; i < nums.size(); ++i) {
            tempList.push_back(nums[i]);
            backtrack(list, tempList, nums, i + 1);
            tempList.pop_back();
        }
    }
};
```

## 相关题目

- [39.combination-sum](./39.combination-sum.md)
- [40.combination-sum-ii](./40.combination-sum-ii.md)
- [46.permutations](./46.permutations.md)
- [47.permutations-ii](./47.permutations-ii.md)
- [90.subsets-ii](./90.subsets-ii.md)
- [113.path-sum-ii](./113.path-sum-ii.md)
- [131.palindrome-partitioning](./131.palindrome-partitioning.md)