zmodn-2.cpp (1297B)
1 #include <iostream> 2 #include <optional> 3 #include <tuple> 4 5 std::tuple<int, int, int> extended_gcd(int a, int b) { 6 if (b == 0) return {a, 1, 0}; 7 auto [g, x, y] = extended_gcd(b, a%b); 8 return {g, y, x - y*(a/b)}; 9 } 10 11 template<int N> 12 requires (N > 1) 13 class Zmod { 14 public: 15 int value; 16 17 Zmod(int z) : value{(z%N + N) % N} {} 18 19 Zmod operator+(const Zmod& z) const { return value + z.value; } 20 Zmod operator-(const Zmod& z) const { return value - z.value; } 21 Zmod operator*(const Zmod& z) const { return value * z.value; } 22 23 std::optional<Zmod> inverse() const { 24 auto [g, a, _] = extended_gcd(value, N); 25 return g == 1 ? Zmod(a) : std::optional<Zmod>{}; 26 } 27 28 std::optional<Zmod> operator/(const Zmod& d) const { 29 auto i = d.inverse(); 30 return i ? (*this) * i.value() : i; 31 } 32 33 std::optional<Zmod> operator/=(const Zmod& d) { 34 auto q = *this / d; 35 return q ? (*this = q.value()) : q; 36 } 37 }; 38 39 int main() { 40 Zmod<57> x(34); 41 Zmod<57> y(11); 42 43 std::cout << "34 * 11 = " << (x * y).value << " (mod 57)" << std::endl; 44 45 if (auto inv = y.inverse(); inv) 46 std::cout << "11 * " << inv.value().value << " = 1 (mod 57)" << std::endl; 47 else 48 std::cout << "11 is not invertible in Z/57Z" << std::endl; 49 50 51 // Contrary to zmodn-1.cpp, the following line does not compile at all 52 Zmod<0> z(157); 53 54 return 0; 55 }