FindDistinctSubsets.cpp

#include <bits/stdc++.h>

using namespace std;

/*
Problem Statement:
Given an integer array nums of unique elements, return all possible
subsets (the power set).

The solution set must not contain duplicate subsets. Return the solution in any
order.
*/

// Using Bit Manipulation
// 1) Traverse all subsets
// 2) Traverse all elements of nums
// 3) Check if jth bit is set in i
// It is like for 3 elements:
// 000, 001, 010, 011, 100, 101, 110, 111
// where 1 means that element is present in the subset
// Time: O(n * 2ⁿ)
// Space: O(1)
vector<vector<int>> subsets(vector<int> &nums) {
  int n = nums.size();
  int total = 1 << n; // 2ⁿ
  vector<vector<int>> ans(total);

  // Traverse all subsets
  for (int i = 0; i < total; i++) // 2ⁿ
  {
    // Traverse elements of nums
    for (int j = 0; j < n; j++) // n
    {
      // Check if jth bit is set in i
      if ((1 << j) & i) {
        ans[i].push_back(nums[j]);
      }
    }
  }

  return ans;
}

int main() {
  vector<int> nums = {1, 2, 3};
  vector<vector<int>> ans = subsets(nums);

  cout << "Subsets are: \n";
  for (auto v : ans) {
    cout << "[ ";
    for (auto i : v) {
      cout << i << " ";
    }
    cout << "]\n";
  }

  return 0;
}