Cod sursa(job #3244504)

Utilizator gabrielvGabriel Vanca gabrielv Data 25 septembrie 2024 02:57:31
Problema Algoritmul lui Euclid extins Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 9.76 kb
#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;
}