# Analyzing space complexity of passing data to function by reference

I have some difficulties with understanding the space complexity of the following algorithm. I’ve solved this problem subsets on leetcode. I understand why solutions’ space complexity would be O(N * 2^N), where N – the length of the initial vector. In all those cases all the subsets (vectors) are passed by value, so we contain every subset in the recursion stack. But i passed everything by reference. This is my code:

``class Solution { public: vector<vector<int>> result; void rec(vector<int>& nums, int &position, vector<int> &currentSubset) {     if (position == nums.size()) {         result.push_back(currentSubset);         return;     }          currentSubset.push_back(nums[position]);     position++;     rec(nums, position, currentSubset);     currentSubset.pop_back();     rec(nums, position, currentSubset);     position--; }  vector<vector<int>> subsets(vector<int>& nums) {     vector <int> currentSubset;     int position = 0;     rec(nums, position, currentSubset);     return result; } }; ``

Would the space complexity be O(N)? As far as i know, passing by reference doesn’t allocate new memory, so every possible subset would be contained in the same vector, which was created before the recursion calls.

I would also appreciate, if you told me how to estimate the space complexity, when working with references in general. Those are the only cases, where i hesitate about the correctness of my reasonings.

Thank you.