Print Sum of int > 0 - c++

Question

Given a number S ( int > 0 ) and n (int > 0), print all the different subsets of len n which sum to S.
For S = 7 and n = 3, the output is the following, the output must be descending order:
5 + 1 + 1
4 + 2 + 1
3 + 3 + 1
3 + 2 + 2
Here is what I've tried so far:
vector<vector<int> > partitions(int X, int Y)
{
vector<vector<int> > v;
if (X <= 1 && X <= X - Y + 1)
{
v.resize(1);
v[0].push_back(X);
return v;
}
for (int y = min(X - 1, Y); y >= 1; y--)
{
vector<vector<int> > w = partitions(X - y, y);
for (int i = 0; i<w.size(); i++)
{
w[i].push_back(y);
v.push_back(w[i]);
}
}
return v;
}
int main()
{
vector<vector<int> > v = partitions(7, 3);
int i;
for (i = 0; i<v.size(); i++)
{
int x;
for (x = 0; x<v[i].size(); x++)
printf("%d ", v[i][x]);
printf("\n");
}
}
the first element in the matrix is s- n + 1 and full of 1 till the sum is reached, or if the s-n+1 is equal to s, then n is 1, so only s will be the solution.
p.s.: I don t know if this problem has a particular name

Answer 1

This may not be the best solution for your problem, since it's not a dynamic programming based solution. In this case, I'm using recursion to fill an array until I reduce the desired number to 0. In this solution, every combination will be stored in the increasing order of the elements so we prevent permutations of a already calculated solution.
#include <iostream>
void findCombinationGivenSize(int numbersArray[], int index, int num, int reducedNum, int maxNum){
if (reducedNum < 0)
return; // this is our base case
if (reducedNum == 0 && index == maxNum){ // both criteria were attended:
//the sum is up to num, and the subset contain maxNum numbers
for (int i = index - 1; i>=0; i--)
std::cout<< numbersArray[i] << " + ";
// here we will have a problem with an extra '+' on the end, but you can figure out easily how to remove it :)
std::cout<<std::endl;
return;
}
// Find the previous number stored in arrayNumber[]
int prev;
if(index == 0)
prev = 1;
else
prev = numbersArray[index-1];
for (int k = prev; k <= num; k++){
// next element of array is k
numbersArray[index] = k;
// call recursively with reduced number
findCombinationGivenSize(numbersArray, index + 1, num,reducedNum - k, maxNum);
}
}
void findCombinations(int number, int maxSubset){
int arrayNumbers[number];
findCombinationGivenSize(arrayNumbers, 0, number, number, maxSubset);
}
int main(){
int number = 7;
int maxPartitions = 3;
findCombinations(number, maxPartitions);
return 0;
}