leecode/problems/90.subsets-ii.md

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

## 题目描述
```
Given a collection of integers that might contain duplicates, nums, return all possible subsets (the power set).

Note: The solution set must not contain duplicate subsets.

Example:

Input: [1,2,2]
Output:
[
  [2],
  [1],
  [1,2,2],
  [2,2],
  [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++，Python3

JavaScript Code：

```js


/*
 * @lc app=leetcode id=90 lang=javascript
 *
 * [90] Subsets II
 *
 * https://leetcode.com/problems/subsets-ii/description/
 *
 * algorithms
 * Medium (41.53%)
 * Total Accepted:    197.1K
 * Total Submissions: 469.1K
 * Testcase Example:  '[1,2,2]'
 *
 * Given a collection of integers that might contain duplicates, nums, return
 * all possible subsets (the power set).
 * 
 * Note: The solution set must not contain duplicate subsets.
 * 
 * Example:
 * 
 * 
 * Input: [1,2,2]
 * Output:
 * [
 * ⁠ [2],
 * ⁠ [1],
 * ⁠ [1,2,2],
 * ⁠ [2,2],
 * ⁠ [1,2],
 * ⁠ []
 * ]
 * 
 * 
 */
function backtrack(list, tempList, nums, start) {
    list.push([...tempList]);
    for(let i = start; i < nums.length; i++) {
        // 和78.subsets的区别在于这道题nums可以有重复
        // 因此需要过滤这种情况
        if (i > start && nums[i] === nums[i - 1]) continue;
        tempList.push(nums[i]);
        backtrack(list, tempList, nums, i + 1)
        tempList.pop();
    }
}
/**
 * @param {number[]} nums
 * @return {number[][]}
 */
var subsetsWithDup = function(nums) {
    const list = [];
    backtrack(list, [], nums.sort((a, b) => a - b), 0, [])
    return list;
};
```
C++ Code：

```C++
class Solution {
private:
    void subsetsWithDup(vector<int>& nums, size_t start, vector<int>& tmp, vector<vector<int>>& res) {
        res.push_back(tmp);
        for (auto i = start; i < nums.size(); ++i) {
            if (i > start && nums[i] == nums[i - 1]) continue;
            tmp.push_back(nums[i]);
            subsetsWithDup(nums, i + 1, tmp, res);
            tmp.pop_back();
        }
    }
public:
    vector<vector<int>> subsetsWithDup(vector<int>& nums) {
        auto tmp = vector<int>();
        auto res = vector<vector<int>>();
        sort(nums.begin(), nums.end());
        subsetsWithDup(nums, 0, tmp, res);
        return res;
    }
};
```
Python Code:

```Python
class Solution:
    def subsetsWithDup(self, nums: List[int], sorted: bool=False) -> List[List[int]]:
        """回溯法，通过排序参数避免重复排序"""
        if not nums:
            return [[]]
        elif len(nums) == 1:
            return [[], nums]
        else:
            # 先排序，以便去重
            # 注意，这道题排序花的时间比较多
            # 因此，增加一个参数，使后续过程不用重复排序，可以大幅提高时间效率
            if not sorted:
                nums.sort()
            # 回溯法
            pre_lists = self.subsetsWithDup(nums[:-1], sorted=True)
            all_lists = [i+[nums[-1]] for i in pre_lists] + pre_lists
            # 去重
            result = []
            for i in all_lists:
                if i not in result:
                    result.append(i)
            return result
```

## 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)
- [78.subsets](./78.subsets.md)
- [113.path-sum-ii](./113.path-sum-ii.md)
- [131.palindrome-partitioning](./131.palindrome-partitioning.md)