Sub sets

class Solution {
private:
    // Recursive function to generate subsets
    void solve(vector<int> nums, vector<int> output, int index, vector<vector<int>>& ans) {
        // Base case: If index reaches the size of nums, store the current subset (output)
        if (index >= nums.size()) {
            ans.push_back(output); // Store the generated subset
            return;
        }

        // Exclude the current element and move to the next index
        solve(nums, output, index + 1, ans);

        // Include the current element in the subset
        int element = nums[index];
        output.push_back(element);

        // Recur with the included element
        solve(nums, output, index + 1, ans);
    }

public:
    // Function to return all subsets of nums
    vector<vector<int>> subsets(vector<int>& nums) {
        vector<vector<int>> ans;  // Stores all subsets
        vector<int> output;  // Temporary list to store the current subset
        int index = 0;  // Start index for recursion
        solve(nums, output, index, ans);
        return ans;  // Return the list of all subsets
    }
};

1. he function subsets(nums) initializes an empty vector ans to store the subsets.

2. It calls the recursive function solve(nums, output, index, ans) to generate all subsets.

3. Base Case: If the index reaches the size of nums, we add the current output (subset) to ans and return.

   • Recursive Calls:

   • Exclude the current element: Move to the next index without adding nums[index] to output.

4. Include the current element: Add nums[index] to output and move to the next index.

5. This process ensures that all possible subsets are generated.

Example Execution with Input {1, 2, 3}

Recursive Call	Current output	Action
solve({1,2,3}, {}, 0, ans)	{}	Start
solve({1,2,3}, {}, 1, ans)	{}	Exclude 1
solve({1,2,3}, {}, 2, ans)	{}	Exclude 2
solve({1,2,3}, {}, 3, ans)	{}	Base Case (Add {})
solve({1,2,3}, {3}, 3, ans)	{3}	Include 3
solve({1,2,3}, {2}, 2, ans)	{2}	Include 2
solve({1,2,3}, {2,3}, 3, ans)	{2,3}	Include 3
solve({1,2,3}, {1}, 1, ans)	{1}	Include 1
solve({1,2,3}, {1,3}, 3, ans)	{1,3}	Include 3
solve({1,2,3}, {1,2}, 2, ans)	{1,2}	Include 2
solve({1,2,3}, {1,2,3}, 3, ans)	{1,2,3}	Include 3

Final Output Subsets:

{
    {}, {3}, {2}, {2,3}, {1}, {1,3}, {1,2}, {1,2,3}
}