Combination

1. Combinations

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.

Example 1: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.

Solution

class Solution {
public:
    vector<vector<int>> combine(int n, int k) {
        vector<vector<int>> ans;
        vector<int> combination;
         solve(n, k, 1, ans, combination);
        
        return ans;
    }
   
    void solve(int n, int k,int index, vector<vector<int>> &ans, vector<int> &combination){
        // cout << index << " ";
      //base case
       // if(index > n) return;
       // if(combination.size() > k) return;
        if(combination.size() == k) {
            ans.push_back(combination);
            return;
        }
        
        if(index > n) return;
      //recursive case
        // 1. inclusion
        combination.push_back(index);
        solve(n, k, index + 1, ans, combination);
        combination.pop_back(); // backtracking
        // 2. exclusion
        solve(n, k, index + 1, ans, combination);
    }
};