Problem description:

Given two integers n and k, return all possible combinations of k numbers out of 1 … n.

Example:

Input: n = 4, k = 2
Output:

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[
  [2,4],
  [3,4],
  [2,3],
  [1,2],
  [1,3],
  [1,4],
]

Solution:

This is a very basic backtracking problem. We can use a helper function to do the work. The only input is start, which denotes where is current position in the 1...n sequence.

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class Solution {
public:
    vector<vector<int>> combine(int n, int k) {
        /*
        use backtracking, when a temp vector<int> have size k, store then backtracking
        another input is start pos.
        */
        vector<vector<int>> res;
        vector<int> tmp;
        helper(res, tmp, n, k, 1);
        return res;
    }
    void helper(vector<vector<int>>& res, vector<int>& tmp, int n, int k, int start){
        if(k== 0){
            res.push_back(tmp);
            return;
        }
        
        for(int i= start; i<= n; i++){
            tmp.push_back(i);
            helper(res, tmp, n, k-1, i+1);
            tmp.pop_back();
        }
        
    }
};

reference: