We are given a set of integers and we have to find all the possible subsets of this set of integers. The following example elaborates on this further.

- Guess the number of subsets for a set of size ‘n’
- Combinations

void get_all_subsets(vector<int>& v, vector<unordered_set<int>>& sets) {//TODO: Write - Your - Code}

int get_bit(int num, int bit) {int temp = (1 << bit);temp = temp & num;if (temp == 0) {return 0;}return 1;}void get_all_subsets(vector<int>& v, vector<unordered_set<int>>& sets) {int subsets_count = pow((double)2, (double)v.size());for (int i = 0; i < subsets_count; ++i) {unordered_set<int> set;for (int j = 0; j < v.size(); ++j) {if (get_bit(i, j)) {set.insert(v[j]);}}sets.push_back(set);}}int main() {int myints[] = {8,13,3,22, 17, 39, 87, 45, 36};std::vector<int> v (myints, myints + sizeof(myints) / sizeof(int) );vector<unordered_set<int>> subsets;get_all_subsets(v, subsets);cout << "****Total*****" << subsets.size() << endl;for (int i = 0; i < subsets.size(); ++i) {cout << "{";for (unordered_set<int>::iterator it = subsets[i].begin(); it != subsets[i].end(); ++it) {cout << *it << ",";}cout << "}" << endl;}cout << "****Total***** = " << subsets.size() << endl;return 0;}

Exponential, $O(2^{n}* n)$ - where ‘n’ is number of integers in the given set.

Exponential, $O(2^{n}* n)$

There are several ways to solve this problem. We will discuss the one that is neat and easier to understand. We know that for a set of ‘n’ elements there are $2^{n}$ subsets. For example, a set with 3 elements will have 8 subsets. Here is the algorithm we will use:

```
n = size of given integer set
subsets_count = 2^n
for i = 0 to subsets_count
form a subset using the value of 'i' as following:
bits in number 'i' represent index of elements to choose from original set,
if a specific bit is 1 choose that number from original set and add it to current subset,
e.g. if i = 6 i.e 110 in binary means that 1st and 2nd elements in original array need to be picked.
add current subset to list of all subsets
```

Note that the ordering of bits for picking integers from the set does not matter; picking integers from left to right would produce the same output as picking integers from right to left.

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