Generarea partitiilor

#include <iostream>

using namespace std;
int n , mat[101][101],cnt;
// mat[i][0] - dimensiunea submultimii.
void gen(int nr, int cateSubmultimi)
{
    if(nr == n + 1)
    {
        cnt++;
        cout <<"\t";
        for(int i = 1;i<=cateSubmultimi;i++)
        {
            cout << "{ ";
            for(int j = 1;mat[i][j]!=0;j++)
                cout << mat[i][j] << ' ';
            cout << "}";
            cout << "  ";
        }
        cout << '\n';
        return;
    }
    /// Adaugam elementul la una dintre submultimile existente.
    for(int i = 1;i<= cateSubmultimi;i++)
    {
        mat[i][0]++;
        mat[i][mat[i][0]] = nr;
        gen(nr+1,cateSubmultimi);
        mat[i][mat[i][0]] = 0;
        mat[i][0]--;
    }
    /// Adaugam elementul intr-o noua submultime
    if(mat[cateSubmultimi][0]!=0)
    {
        cateSubmultimi++;
        mat[cateSubmultimi][0] = 1;
        mat[cateSubmultimi][1] = nr;
        gen(nr + 1, cateSubmultimi);
        mat[cateSubmultimi][1] = 0;
        mat[cateSubmultimi][0] = 0;
        cateSubmultimi--;
    }

}
int main() {
    cout<<"\n\n\tPartiile multimii {1,2,3.....,n}\n" << "\n\tDati valoarea lui n: ";
    cin >> n;
    cout << '\n';
    gen(1,1);
    cout <<"\n\tNumar solutii: " << cnt << '\n';
    return 0;
}