137 lines
3.2 KiB
Markdown
137 lines
3.2 KiB
Markdown
## Problem Link
|
||
https://leetcode.com/problems/subsets/description/
|
||
|
||
## Description
|
||
```
|
||
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],
|
||
[]
|
||
]
|
||
|
||
|
||
```
|
||
|
||
## Solution
|
||
|
||
Since this problem is seeking `Subset` not `Extreme Value`, dynamic programming is not an ideal solution. Other approaches should be taken into our consideration.
|
||
|
||
Actually, there is a general approach to solve problems similar to this one -- backtracking. Given a [Code Template](https://leetcode.com/problems/combination-sum/discuss/16502/A-general-approach-to-backtracking-questions-in-Java-(Subsets-Permutations-Combination-Sum-Palindrome-Partitioning)) here, it demonstrates how backtracking works with varieties of problems. Apart from current one, many problems can be solved by such a general approach. For more details, please check the `Related Problems` section below.
|
||
|
||
Given a picture as followed, let's start with problem-solving ideas of this general solution.
|
||
|
||
|
||
|
||
See Code Template details below.
|
||
|
||
## Key Points
|
||
|
||
- Backtrack Approach
|
||
- Backtrack Code Template/ Formula
|
||
|
||
|
||
## Code
|
||
|
||
* Supported Language：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();
|
||
}
|
||
}
|
||
};
|
||
```
|
||
|
||
## Related Problems
|
||
|
||
- [39.combination-sum](./39.combination-sum.md)(chinese)
|
||
- [40.combination-sum-ii](./40.combination-sum-ii.md)(chinese)
|
||
- [46.permutations](./46.permutations.md)(chinese)
|
||
- [47.permutations-ii](./47.permutations-ii.md)(chinese)
|
||
- [90.subsets-ii](./90.subsets-ii-en.md)
|
||
- [113.path-sum-ii](./113.path-sum-ii.md)(chinese)
|
||
- [131.palindrome-partitioning](./131.palindrome-partitioning.md)(chinese)
|