#include <array>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <iostream>
#include <unordered_map>
#ifdef PROFILING
#include <chrono>
#endif
constexpr char INPUT_FILE_NAME[] = "euclid3.in";
constexpr char OUTPUT_FILE_NAME[] = "euclid3.out";
class IO_Base
{
protected:
IO_Base() = default;
virtual ~IO_Base() = default;
// https://cplusplus.com/reference/system_error/errc/
const std::unordered_map<int, std::string> FILE_OPEN_ERROR = {
{ENOENT, "File does not exist."},
{EACCES, "Permission denied."},
{EEXIST, "File already exists."},
{EISDIR, "File is a directory."},
{ENOSPC, "No space left on device."},
{EROFS, "Read-only file system."},
{ETXTBSY, "Text file busy."},
{-1, "Unlisted error type."},
{0, "No error."}
};
virtual void Close_IN() = 0;
virtual void Close_OUT() = 0;
virtual void PrintError(const char* const _file_name,
const int _error_num,
const std::string& _error_source) = 0;
};
class IO final : IO_Base
{
// C++ I/O functions: https://en.cppreference.com/w/cpp/io
protected:
// The Singleton has a private constructor to prevent direct instantiation.
IO(const char input_file_name[], const char output_file_name[])
{
GetInputStream(input_file_name);
GetOutputStream(output_file_name);
}
// The Singleton has a private destructor to prevent deletion.
~IO() override
{
is_instance_destroyed() = true;
Close_IN();
Close_OUT();
}
public:
// Don't make these nullptr. They are not pointers.
std::ifstream IN;
std::ofstream OUT;
// Delete copy constructor. Singletons should not be cloneable.
IO(const IO&) = delete;
// Delete move constructor. Singletons should not be movable.
IO(const IO&&) = delete;
// Delete assignment operator. Singletons should not be assignable.
IO& operator=(const IO&) = delete;
/* Singleton pattern. Only one instance of the class can exist.
* Thread safe: Initialization is guaranteed to happen only once.
* A static member object instance is declared. This object is only created
* the first time the function is called. Static local variables are
* guaranteed to be initialized only once, even in multithreaded environments.
* Subsequent calls to GetInstance() simply return the existing instance object.
* Returning reference instead of pointer further discourages attempts to delete.
*/
static IO& GetInstance(const char input_file_name[], const char output_file_name[])
{
static IO io_Instance(input_file_name, output_file_name);
if (is_instance_destroyed())
{
// We check for The Dead Reference Problem.
// Our singleton is designed to only be destroyed at program termination.
std::cerr << "ERROR: Attempt to access destroyed singleton instance." << std::endl;
assert(false);
}
return io_Instance;
}
private:
static bool& is_instance_destroyed()
{
/* This variable is used to check for The Dead Reference Problem
* by enabling the class to check if its singleton has been destroyed.
*/
static bool is_instance_destroyed = false;
return is_instance_destroyed;
}
void GetInputStream(const char _input_file_name[])
{
IN.open(_input_file_name);
if (!IN.is_open()) // Check if the open operation failed
{
if (IN.fail())
{
PrintError(_input_file_name, errno, "Failed to open input");
assert(IN);
}
if (IN.bad())
{
PrintError(_input_file_name, errno, "Fatal I/O error: bad-bit is set in input");
assert(IN);
}
}
}
void GetOutputStream(const char _output_file_name[])
{
OUT.open(_output_file_name);
if (!OUT.is_open()) // Check if the open operation failed
{
if (OUT.fail())
{
PrintError(_output_file_name, errno, "Failed to open output");
assert(OUT);
}
if (OUT.bad())
{
PrintError(_output_file_name, errno, "Fatal I/O error: bad-bit is set in output");
assert(OUT);
}
}
}
void Close_IN() override final
{
IN.close();
}
void Close_OUT() override final
{
OUT.close();
}
void PrintError(const char* const _file_name,
const int _error_num,
const std::string& _error_source) final override
{
int error_code = -1;
if (FILE_OPEN_ERROR.find(_error_num) != FILE_OPEN_ERROR.end())
{
error_code = _error_num;
}
std::cerr << _error_source << " file: " << _file_name << "\n"
<< "ERROR: " << strerror(errno) << "\n"
<< " " << FILE_OPEN_ERROR.at(error_code) << std::endl;
}
};
#ifdef PROFILING
class Profiling
{
private:
std::chrono::time_point<std::chrono::system_clock> time_begin, time_end;
std::chrono::duration<double, std::nano> duration_nano = std::chrono::nanoseconds(0);
const char* functionName;
const char* comment;
public:
explicit Profiling(const char* _functionName, const char* _comment)
: functionName(_functionName), comment(_comment)
{
Begin_Profiling();
}
void Begin_Profiling()
{
time_begin = std::chrono::high_resolution_clock::now();
}
void End_Profiling()
{
time_end = std::chrono::high_resolution_clock::now();
/* Getting number of nanoseconds as a double. */
duration_nano = std::chrono::duration_cast<std::chrono::nanoseconds>(time_end - time_begin);
Show_Profiling_Results();
}
void Show_Profiling_Results() const
{
std::cout << functionName << " : "
<< duration_nano.count() / 1000000 << "ms | "
<< duration_nano.count() / 1000 << "\xE6s | "
<< duration_nano.count() << "ns\n"
<< " " << comment << "\n";
}
};
#endif
struct euclid_solution
{
int gcd;
int Bezout_x;
int Bezout_y;
};
/* Using Euclid's extender algorithm to find the greatest common divisor (gcd).
* https://zerobone.net/blog/math/extended-euklidean-algorithm/
* https://www.infoarena.ro/algoritmul-lui-euclid
* https://crypto.stanford.edu/pbc/notes/numbertheory/euclid.html
*/
euclid_solution euclid_extended(int a, int b)
{
bool swapped = false;
if (std::abs(b) > std::abs(a))
{
std::swap(a, b);
swapped = true;
}
std::array<int, 3> a_coef = {1, 0}; // the coefficients of a (in order: previous, current, next)
std::array<int, 3> b_coef = {0, 1}; // the coefficients of b (in order: previous, current, next)
constexpr int prev = 0;
constexpr int curr = 1;
constexpr int next = 2;
int quotient;
int remainder;
while (b)
{
// Calculate GCD (simple Euclid)
quotient = a / b;
remainder = a - quotient * b;
a = b;
b = remainder;
// Calculate the new coefficients (extended Euclid)
a_coef[next] = a_coef[prev] - quotient * a_coef[curr];
b_coef[next] = b_coef[prev] - quotient * b_coef[curr];
// Update the coefficients.
a_coef[prev] = a_coef[curr];
b_coef[prev] = b_coef[curr];
a_coef[curr] = a_coef[next];
b_coef[curr] = b_coef[next];
}
if (swapped)
{
std::swap(a_coef[prev], b_coef[prev]);
}
// Returns the gcd and the Bézout coefficients.
return {a, a_coef[prev], b_coef[prev]};
}
int main()
{
#ifdef PROFILING
Profiling profiling = Profiling(__PRETTY_FUNCTION__, "Add two numbers from a file.");
#endif
IO& io = IO::GetInstance(INPUT_FILE_NAME, OUTPUT_FILE_NAME);
unsigned int T_counter; // 1 ≤ T ≤ 100
int a, b; // -1 000 000 000 ≤ a ≤ b ≤ 1 000 000 000
int c; // -2 000 000 000 ≤ c ≤ 2 000 000 000 (not zero)
io.IN >> T_counter;
while (T_counter--)
{
io.IN >> a >> b >> c;
const auto solution = euclid_extended(a, b);
const int multiplier = c / solution.gcd;
const int unsolvable = c - multiplier * solution.gcd;
if (unsolvable)
{
io.OUT << "0 0\n";
}
else
{
io.OUT << solution.Bezout_x * multiplier << " "
<< solution.Bezout_y * multiplier << "\n";
}
}
#ifdef PROFILING
profiling.End_Profiling();
#endif
return 0;
}