#include <iostream>
#include <list>

using namespace std;

static int offsets[2303];

static int merge(int position, int mask) {
    return position << 8 | mask;
}

static bool is_bit_set(int mask, int position) {
    return ((mask >> position) & 1) == 1;
}

static int count_bits_left(int mask, int position) {
    int result = 0;
    for (int pos = 7; pos > position; pos--) {
        if (is_bit_set(mask, pos)) {
            result++;
        }
    }
    return result;
}

static void fill_offsets() {
    for (int position = 0; position < 8; position++) {
        for (int mask = 0; mask < 256; mask++) {
            int index = merge(position, mask);
            int value = count_bits_left(mask, position);
            offsets[index] = value;
        }
    }
}

class Polynom {

    private:
        int mask = 0;
        double* koeffs;

    public:
        Polynom (double , double , double , double , double , double , double , double );
        double get_koeff(int);
        void print(void);

};

Polynom::Polynom (double k7, double k6, double k5, double k4, double k3, double k2, double k1, double k0) {
    std::list<double> ks;
    int size = 0;
    if (k7 != 0) {
        mask |= (1 << 7);
        ks.push_back(k7);
    }
    if (k6 != 0) {
        mask |= (1 << 6);
        ks.push_back(k6);
    }
    if (k5 != 0) {
        mask |= (1 << 5);
        ks.push_back(k5);
    }
    if (k4 != 0) {
        mask |= (1 << 4);
        ks.push_back(k4);
    }
    if (k3 != 0) {
        mask |= (1 << 3);
        ks.push_back(k3);
    }
    if (k2 != 0) {
        mask |= (1 << 2);
        ks.push_back(k2);
    }
    if (k1 != 0) {
        mask |= (1 << 1);
        ks.push_back(k1);
    }
    if (k0 != 0) {
        mask |= (1 << 0);
        ks.push_back(k0);
    }
    koeffs = new double[ks.size()];
    int i = 0;
    for (double const &k: ks) {
        koeffs[i++] = k;
    }
}

double Polynom::get_koeff(int position) {
    if (!is_bit_set(mask, position)) {
        return 0.0;
    } else {
        int idx = merge(position, mask);
        int leftBits = offsets[idx];
        return koeffs[leftBits];
    }
}

void Polynom::print(){
    for (int i = 7; i >= 0; i--){
        cout << get_koeff(i) << "*x^" << i;
        if (i > 0){
            cout << " + ";
        }
    }
    cout << "\n";
}

int main()
{
    fill_offsets();

    Polynom* p = new Polynom(1, 2, 3, 4, 5, 6, 7, 8);
    p->print();
    //1*x^7 + 2*x^6 + 3*x^5 + 4*x^4 + 5*x^3 + 6*x^2 + 7*x^1 + 8*x^0

    Polynom* p1 = new Polynom(1, 0, 0, 0, 0, 6, 0, 8);
    p1->print();
    //1*x^7 + 0*x^6 + 0*x^5 + 0*x^4 + 0*x^3 + 6*x^2 + 0*x^1 + 8*x^0

    return 0;
}