numero decomposto em todas as somas

#include <iostream>
#include <string>
#include <vector>

std::vector < std::vector< int >> vec_vec;

void somarec( int max, int iter, int pos, std::vector<int> vec )
{
    if( vec.size() == 0 )
    {
        std::vector <int> novo_vec;

        if( max <= 0 )
        {
            novo_vec.push_back( 0 );
            vec_vec.push_back( novo_vec );
        }
        else
        {
            for( int i = 0; i < max; i++ )
                novo_vec.push_back( 1 );

            vec_vec.push_back( novo_vec );
            somarec( max, max, pos, novo_vec );
        }
    }
    else if( pos < vec.size() )

        for( int i = 2; i <= iter; i++ )
        {
            vec[ pos ] = i;

            int soma_parc = 0;
            for( int j = 0; j <= pos; j++ )
                soma_parc += vec[ j ];

            if( soma_parc <= max )
            {
                soma_parc = max - soma_parc;
                for( int j = 1; j <= soma_parc; j++ )
                    vec[ j + pos ] = 1;
                vec.resize( soma_parc + pos + 1 );

                vec_vec.push_back( vec );
            }

            somarec( max, i, pos + 1, vec );

        }

}

void debug_vec()
{
    for( int i = 0; i < vec_vec.size(); i++ )
        for( int j = 0, ult = vec_vec[ i ].size(); j < ult; j++ )
            std::cout << vec_vec[i][ j ] << (j == ult - 1 ? "\x0d\x0a" : "+");
}

int main()
{
    std::vector<int> vec( 0 );

    somarec( 7, 0, 0, vec );

    debug_vec();
}