A3

#include <iostream>
#include <map>
#include <utility>
#include <array>
#include <math.h>

template <typename T, int N>
class MultivariatePolynomial {
private:
    std::map<std::array<int, N>, T> Monom;
public:
    MultivariatePolynomial(std::map<std::array<int, N>, T> monom) {
        for (auto x : monom)
            if (x.second != 0)
                Monom.insert(x);
    }
    MultivariatePolynomial(T koeff) {
        std::array<int, N> null;
        null.fill(0);
        Monom[null] = koeff;
    }
    MultivariatePolynomial() {
        std::map<std::array<int, N>, T> emptypoly;
        Monom = emptypoly;
    }
    int operator () (std::array<T, N> point) {
        int result = 0;
        for (auto x : Monom) {
            int mininom = 1;
            for (size_t i = 0; i < N; i++)
                mininom = mininom * pow(point[i], x.first[i]);
            result = result + x.second * mininom;
        }
        return result;
    }
    friend bool operator == (MultivariatePolynomial<T, N>& poly, MultivariatePolynomial<T, N>& poly1) {
        if (poly.Monom == poly1.Monom) {
            return true;
        } return false;
    }
    friend bool operator == (MultivariatePolynomial<T, N> poly, T value) {
        if (((poly.Monom.size() == 1) && ((((poly.Monom).begin())->second) == value)) || (poly.Monom.size() == 0)) { return true; }
        else { return false; }
    }
    friend bool operator != (MultivariatePolynomial<T, N>& poly, MultivariatePolynomial<T, N>& poly1) {
        if (poly.Monom != poly1.Monom) {
            return true;
        } return false;
    }
    friend bool operator != (MultivariatePolynomial<T, N>& poly, T value) {
        if ((poly.Monom.size() != 1) || ((((poly.Monom).begin())->second) != value)) { return true; }
        else { return false; }
    }
    friend MultivariatePolynomial<T, N> operator + (MultivariatePolynomial<T, N>& poly, MultivariatePolynomial<T, N>& poly1) {
        MultivariatePolynomial<T, N> result = poly;
        for (auto x2 : poly1.Monom) {
            if ((result.Monom).find(x2.first) == (result.Monom).end()) { (result.Monom).insert(x2); }
            else {
                (result.Monom)[x2.first] += x2.second;
                if ((result.Monom)[x2.first] == 0) { (result.Monom).erase(x2.first); }
            }
        } return result;
    }
    friend MultivariatePolynomial<T, N> operator - (MultivariatePolynomial<T, N>& poly, MultivariatePolynomial<T, N>& poly1) {
        MultivariatePolynomial<T, N> result = poly;
        for (auto x2 : poly1.Monom) {
            if ((result.Monom).find(x2.first) == (result.Monom).end()) {
                x2.second *= -1;
                (result.Monom).insert(x2);
            }
            else {
                (result.Monom)[x2.first] -= x2.second;
                if ((result.Monom)[x2.first] == 0) { (result.Monom).erase(x2.first); }
            }
        } return result;
    }
    friend void operator += (MultivariatePolynomial<T, N>& poly, MultivariatePolynomial<T, N>& poly1) {
        poly = poly + poly1;
    }
    friend void operator -= (MultivariatePolynomial<T, N>& poly, MultivariatePolynomial<T, N>& poly1) {
        poly = poly - poly1;
    }
    typename std::map<std::array<int, N>, T>::const_iterator begin() const {
        return Monom.begin();
    }
    typename std::map<std::array<int, N>, T>::const_iterator end() const {
        return Monom.end();
    }
    friend MultivariatePolynomial<T, N> operator * (MultivariatePolynomial<T, N>& poly, MultivariatePolynomial<T, N>& poly1) {
        MultivariatePolynomial<T, N> result;
        std::pair<std::array<int, N>, T> buff;
        for (auto x : poly.Monom) {
            for (auto x2 : poly1.Monom) {
                for (auto i = 0; i < N; i++) {
                    buff.first[i] = x.first[i] + x2.first[i];
                } buff.second = x.second * x2.second;
                if ((result.Monom).find(buff.first) == (result.Monom).end()) { (result.Monom).insert(buff); }
                else { (result.Monom)[buff.first] += buff.second; }
            }
        } return result;
    }
    friend void operator *= (MultivariatePolynomial<T, N>& poly, MultivariatePolynomial<T, N>& poly1) {
        poly = poly * poly1;
    }
    friend void operator *= (MultivariatePolynomial<T, N>& poly, T value) {
        MultivariatePolynomial<T, N> result;
        for (auto x : poly.Monom) {
            (result.Monom)[x.first] = x.second * value;
        } poly = result;
    }
    int Degree() {
        if (Monom.size() == 0) return 0;
        int max = 0;
        for (auto x : Monom) {
            int summ = 0;
            for (auto i = 0; i < N; i++) {
                summ += x.first[i];
            } if (summ > max) { max = summ; }
        } if (max == 0) { return -1; }
        else { return max; }
    }
    friend std::ostream& operator << (std::ostream& out, MultivariatePolynomial<T, N> poly) {
        if (poly.Monom.size() == 0) { out << "0"; return out; }
        typename std::map<std::array<int, N>, T>::reverse_iterator x = (poly.Monom.rend());
        for (; x != (poly.Monom.rbegin()); x--) {
            int numb = -1;
            bool sum = false;
            for (auto xx : x->first)
                if (xx != 0) {
                    numb = numb + 1;
                    sum = true;
                }
            if (sum == false) {
                if ((x->second < 0) || (x == (poly.Monom.rend()))) { out << x->second; }
                else { out << "+" << x->second; }
            }
            else {
                if ((x->second < -1) || ((x->second > 1) && (x == (poly.Monom.rend())))) { out << x->second << "*"; }
                else if (x->second == -1) { out << "-"; }
                else if ((x->second > 1) && (x != (poly.Monom.rend()))) { out << "+" << x->second << "*"; }
                else if ((x->second == 1) && (x != (poly.Monom.rend()))) { out << "+"; }
                for (auto xx = 0; xx != (x->first).size(); xx++) {
                    if (((x->first)[xx] > 1) || ((x->first)[xx] <= -1)) { out << "x" << xx << "^" << (x->first)[xx]; }
                    if ((x->first)[xx] == 1) { out << "x" << xx; }
                    if ((numb != 0) && ((x->first)[xx])) {
                        out << "*";
                        numb -= 1;
                    }
                }
            }
        }
        return out;
    }
};