Find all subsets - c++

Question

I already managed to make me of all the subsets but I do not know how to make their values add up and identify what I want. If someone could explain to me please.
#include <iostream>
#include <math.h>
using namespace std;
int main()
{
int n=3;
int arr[]={1,2,3};
int v;
int count = pow(2,n);
int acum=0;
cout << "Enter a value: ";
cin >> v;
for (int i = 0; i < count; i++) {
for (int j = 0; j < n; j++) {
if ((i & (1 << j)) != 0){
cout << arr[j] << " ";
}
}
cout << "\n";
}
return 0;
}

Answer 1

For your problem domain, is it valid to assume that all of the elements will be positive integers? If so, then you might want to consider using a "Dynamic Programming" (DP) solution (instead of the "Generate and Test" approach that you had begun).
The DP approach would solve your example as follows:
The initial task was to identify a subset whose sum is v=5.
DP makes one single pass through your arr[] data (my implementation's for i loop)
For the first element arr[0], that addition term (1) is either used or not used. If that 1 addition term is not used, then the problem arr[]={1,2,3},v=5 recursively becomes the sub-problem arr[]={2,3},v=5. But if that 1 term is used, then the problem arr[]={1,2,3},v=5 recursively becomes the sub-problem arr[]={2,3},v=4. We "memoize" this possibility by recording the used term (the 1 value) in memory at term[4] (term[] is a utility array that had been allocated for this very "DP memoization" purpose).
For the next element arr[1], again that term (2) is either used or not used. If that term is used, then the v=5 problem becomes a v=3 sub-problem, whereas the v=4 problem (if it exists) becomes a v=2 sub-problem. Again, any such sub-problem is recorded via "memoization" (in the same term[] utility array).
Finally, this pattern repeats for the final arr[2] element.
Once that single pass through arr[] is finished, the solution can be "back-traced" through the "memoization", by an iteration that starts at term[0].
This is a C++ implementation of the DP approach:
#include <iostream>
int main()
{
int n = 3;
int arr[n] = {1, 2, 3}; // All elements must be positive
int v;
std::cout << "Enter a value: ";
std::cin >> v;
int* term = new int[v];
for (int init = 0; init < v; init++) {
term[init] = 0;
}
for (int i = 0; i < n; i++) {
for (int before = 0; before < v; before++) {
if (term[before] == 0) {
int after = before + arr[i];
// This tests the "(if it exists)" condition in my verbal description:
if (after == v || (after < v && term[after] != 0)) {
// This assignment performs the "memoization":
term[before] = arr[i];
}
}
}
}
if (term[0] == 0) {
std::cout << "No such subset exists";
}
else {
int partialSum = 0;
while (partialSum < v) {
std::cout << term[partialSum];
partialSum += term[partialSum];
if (partialSum < v) {
std::cout << "+";
}
else {
std::cout << "=" << v;
}
}
}
delete[] term;
}