0077. Combinations.md

• 77- Combinations
• 难度：Medium｜ 中等
• 相关知识点：Array, Backtracking
• 题目链接：https://leetcode.com/problems/combinations/description/

Given two integers n and k, return all possible combinations of k numbers chosen from the range [1, n].

You may return the answer in any order.

Input: n = 4, k = 2
Output: [[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]
Explanation: There are 4 choose 2 = 6 total combinations.
Note that combinations are unordered, i.e., [1,2] and [2,1] are considered to be the same combination.
Example 2:

Input: n = 1, k = 1
Output: [[1]]
Explanation: There is 1 choose 1 = 1 total combination.


Constraints:

1 <= n <= 20
1 <= k <= n```

### solution 1
```python
class Solution:
   def combine(self, n: int, k: int) -> List[List[int]]:
       result = []
       lst = list(range(1, n+1))

       ans = []
       def  backtracking(lst):
           if len(ans) == k:
               result.append(ans[:])
           
           for i in range(len(lst)):
               ans.append(lst[i])
               backtracking(lst[i+1:])
               ans.pop()
               
       backtracking(lst)
       return result

class Solution {
public:
    void helper(int n, int k, int i, vector<int>& curr, vector<vector<int>>& res) {
        if(curr.size() == k) {
            res.push_back(curr);
            return;
        }

        for(int j = i; j <= n; j++) {
            curr.push_back(j);
            helper(n, k, j + 1, curr, res);
            curr.pop_back();
        }
    }

    vector<vector<int>> combine(int n, int k) {
        vector<vector<int>> res;
        vector<int> curr;
        helper(n, k, 1, curr, res);
        return res;
    }
};