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prg8.cpp
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prg8.cpp
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#include <iostream>
#include <gmpxx.h>
#include <vector>
mpz_class find_greatest_common_divisor(mpz_class a, mpz_class b) {
if (a == 0) {
return b;
}
return find_greatest_common_divisor(b % a, a);
}
mpz_class modular_inverse(mpz_class a, mpz_class m) {
mpz_class initial_mod = m, temp, quotient;
mpz_class x0 = 0, x1 = 1;
if (m == 1) {
return 0;
}
while (a > 1) {
quotient = a / m;
temp = m;
m = a % m;
a = temp;
temp = x0;
x0 = x1 - quotient * x0;
x1 = temp;
}
if (x1 < 0) {
x1 += initial_mod;
}
return x1;
}
int main(int argc, char *argv[]) {
int equation_count = std::stoi(argv[1]);
std::vector<mpz_class> coefficients(equation_count);
std::vector<mpz_class> remainders(equation_count);
std::vector<mpz_class> moduli(equation_count);
mpz_class product = 1;
mpz_class solution = 0;
for (int i = 0; i < equation_count; ++i) {
coefficients[i] = argv[3 * i + 2];
remainders[i] = argv[3 * i + 3];
moduli[i] = argv[3 * i + 4];
}
for (int i = 0; i < equation_count; ++i) {
mpz_class gcd = find_greatest_common_divisor(coefficients[i], moduli[i]);
coefficients[i] = coefficients[i] / gcd;
remainders[i] = remainders[i] / gcd;
moduli[i] = moduli[i] / gcd;
mpz_class inv = modular_inverse(coefficients[i], moduli[i]);
remainders[i] = remainders[i] * inv;
}
for (int i = 0; i < equation_count; i++) {
product = product * moduli[i];
}
for (int i = 0; i < equation_count; i++) {
mpz_class val = product / moduli[i];
solution += remainders[i] * modular_inverse(val, moduli[i]) * val;
}
if (solution != 0) {
std::cout << "Y " << solution % product;
} else {
std::cout << "N";
}
return 0;
}