Recursive backtracking to find all subsets

Question

I have tried to solve a problem of generating all subsets of an array which contains no duplicates from leetcode : https://leetcode.com/problems/subsets/ . e.g if input is [1,2,3], output should be [[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]].

Since we need to generate all subsets, its a backtracking problem. I figured the states, decisions and base cases. Decision will be that we have to include the current element and move forward and next time exclude it and move forward. The code will look like :

vector<vector<int>> subsets(vector<int>& nums) { // nums is our input array
        vector<int> res;
        vector<vector<int>> final_res;
        
        if(nums.empty())
            return {};
        
        subsetsUtil(nums, 0, nums.size(), res, final_res);
        return final_res;
    }
    
    void subsetsUtil(vector<int> &nums, int i, int n, vector<int> res, vector<vector<int>> &final_res) {
        
      if (i == n) {
            final_res.push_back(res);
             return;
        }
        
        res.push_back(nums[i]);
        subsetsUtil(nums, i+1, n, res, final_res); // include
        res.pop_back();
        subsetsUtil(nums, i+1, n, res, final_res);   // exclude
       
    }
};

Now I have changed the implementation of susbsetsUtil and The same problem can be implemented using the for loop in the below code snippet. Is the same approach of include/exclude is used in the for loop ? If yes, I am not able to visualize that how is include/exclude approach is translated to the for loop below. Also are there some good resources to learn about the backtracking patterns and to master it. Thanks !

 void subsetsUtil(vector<int> &nums, int i, int n, vector<int> res, vector<vector<int>> &final_res) {
        
        final_res.push_back(res);
               
        for (int index = i; index < n; index++) {
            res.push_back(nums[index]);
            subsetsUtil(nums, index+1, n, res, final_res);
            res.pop_back();
        }
    }