zmodn-1.cpp (1261B)
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 class Zmod { 13 public: 14 int value; 15 16 Zmod(int z) : value{(z%N + N) % N} {} 17 18 Zmod operator+(const Zmod& z) const { return value + z.value; } 19 Zmod operator-(const Zmod& z) const { return value - z.value; } 20 Zmod operator*(const Zmod& z) const { return value * z.value; } 21 22 std::optional<Zmod> inverse() const { 23 auto [g, a, _] = extended_gcd(value, N); 24 return g == 1 ? Zmod(a) : std::optional<Zmod>{}; 25 } 26 27 std::optional<Zmod> operator/(const Zmod& d) const { 28 auto i = d.inverse(); 29 return i ? (*this) * i.value() : i; 30 } 31 32 std::optional<Zmod> operator/=(const Zmod& d) { 33 auto q = *this / d; 34 return q ? (*this = q.value()) : q; 35 } 36 }; 37 38 int main() { 39 Zmod<57> x(34); 40 Zmod<57> y(11); 41 42 std::cout << "34 * 11 = " << (x * y).value << " (mod 57)" << std::endl; 43 44 if (auto inv = y.inverse(); inv) 45 std::cout << "11 * " << inv.value().value << " = 1 (mod 57)" << std::endl; 46 else 47 std::cout << "11 is not invertible in Z/57Z" << std::endl; 48 49 50 // The following line gives a run-time exception 51 // Zmod<0> z(157); 52 53 return 0; 54 }