427 lines
14 KiB
C++
427 lines
14 KiB
C++
#include <iostream>
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#include <cstring>
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#include <iomanip>
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#include <vector>
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#include <algorithm>
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/*
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Класс Number -- класс положительных больших чисел
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Большое число будет храниться в динамическом массиве data
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Каждый элемент этого массива содержит разряд числа в 100-ричной системе счисления
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(так как base = 100)
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По сути, каждый элемент data хранит две цифры числа в десятичной записи
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Значение 100 для системы счисления выбрано как компромис между
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эффективностью и удобством написания программы.
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Если выбрать значения базы 10 - то программа будет не так эффективна по памяти
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Если выбрать значения базы 256 (максимально эффективное использование памяти для типа char),
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то алгоритм печати на экран сильно усложнится
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В качестве альтернативы, можно было выбрать базу 1e9,
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изменив при этом тип элементов c char на int
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capacity - размер массива data
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size - сколько ячеек занимет число в массиве data
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size <= capacity
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Для удобства разряды числа хранятся в обратном порядке
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Например, число 12345678 соответствует массиву
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data = {78, 56, 34, 12}
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(это упрощает многие алгоритмы с такими числами)
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*/
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class Number
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{
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private:
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static const int base = 100;
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std::size_t size;
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std::size_t capacity;
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char* data;
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public:
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Number(int a)
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{
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#ifdef _DEBUG_CONSTRUCTOR
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std::cout << "(Number constructor " << a << " -> ";
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#endif
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// Находим размер необходимой памяти под это число
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int temp = a;
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capacity = 0;
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while (temp != 0)
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{
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temp /= base;
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capacity += 1;
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}
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// Отдельно обрабатываем случай, когда число равно 0
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if (capacity == 0)
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capacity = 1;
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// Выделяем память и записывем число a в массив data
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// Например, число 12345678 представится в виде массива [78, 56, 34, 12]
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data = new char[capacity];
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for (int i = 0; i < capacity; ++i)
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{
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data[i] = a % base;
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a /= base;
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}
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// В данном случае размер будет равен вместимости
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size = capacity;
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#ifdef _DEBUG_CONSTRUCTOR
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std::cout << *this << ")" << std::endl;
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#endif
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}
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// Конструктор по умолчанию
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Number() : Number(0) {}
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// Конструктор копирования
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Number(const Number& n) {
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size = n.size;
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capacity = n.capacity;
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data = new char[capacity];
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for (int i = 0; i < size; i++) {
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data[i] = n.data[i];
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}
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}
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Number(const char* str) {
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int len = std::strlen(str);
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size = (len + len % 2) / 2;
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capacity = size;
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data = new char[capacity];
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char buf[2];
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for (int i = 0; i < size; i++) {
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buf[1] = str[len - 2 * i - 1];
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if (len - 2 * i - 1 > 0) {
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buf[0] = str[len - 2 * i - 2];
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}
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else {
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buf[0] = '0';
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}
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data[i] = std::stoi(buf);
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}
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}
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~Number()
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{
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delete [] data;
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}
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Number& operator=(const Number& right) {
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capacity = right.capacity;
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size = right.size;
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data = new char[capacity];
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for (int i = 0; i < size; i++) {
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data[i] = right.data[i];
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}
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return *this;
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}
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Number operator+(Number a) {
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#ifdef _DEBUG_ADD
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std::cout << "arg1=" << a << "capacity=" << a.capacity << ",size="<< a.size<< std::endl;
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std::cout << "arg2=" << *this << "capacity=" << this->capacity << ",size="<< this->size<< std::endl;
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#endif
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Number result;
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Number temp;
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int i;
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int carry = 0;
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if (size < a.size) {
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temp = *this;
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*this = a;
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a = temp;
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}
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result.capacity = size + 1;
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//result.data = new char[capacity];
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result.data = (char*)calloc(result.capacity, sizeof(char));
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for (i = 0; i < a.size; ++i) {
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result.data[i] = (data[i] + a.data[i] + carry) % base;
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carry = (data[i] + a.data[i] + carry) / base;
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}
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for (; i < size; ++i) {
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result.data[i] = (data[i] + carry) % base;
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carry = (data[i] + carry) / base;
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}
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if (carry) {
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#ifdef _DEBUG_ADD
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std::cout << "applied carry" << std::endl;
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#endif
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result.data[i] = carry;
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result.size = size + 1;
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}
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else {
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result.size = size;
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}
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#ifdef _DEBUG_ADD
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std::cout << result << " capacity=" << result.capacity << ",size="<<result.size<< std::endl;
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#endif
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return result;
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}
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void operator+=(const Number& a) {
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*this = *this + a;
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}
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bool isEven() const {
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if (data[0] % 2) {
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return false;
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}
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return true;
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}
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Number operator*(const Number& right) const {
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#ifdef _DEBUG_MUL
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std::cout << "arg1=" << *this << "(capacity=" << capacity << ",size=" << size << ")" << " " << "arg2=" << right << "(capacity=" << right.capacity << ",size=" << right.size << ")"<< std::endl;
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#endif
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int i, j;
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int temp;
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Number result;
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result.capacity = capacity + right.capacity;
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int *carry = (int*)std::calloc(result.capacity, sizeof(int));
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result.data = (char*)calloc(result.capacity, sizeof(char));
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#ifdef _DEBUG_MUL
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std::cout << "carry:[" << carry[0];
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for (int k = 1; k < result.capacity; ++k) {
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std::cout << "," << carry[k];
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}
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std::cout << "]" << std::endl;
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#endif
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for (i = 0; i < size; ++i) {
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for (j = 0; j < right.size; ++j) {
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#ifdef _DEBUG_MUL
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std::cout << i + j << ":" << static_cast<int>(result.data[i + j]) << " + " << static_cast<int>(data[i]) << " * " << static_cast<int>(right.data[j]) << " + " << carry[i+j] << std::endl;
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#endif
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temp = (result.data[i + j] + data[i] * right.data[j] + carry[i + j]);
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result.data[i + j] = temp % base;
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carry[i + j + 1] += temp / base;
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carry[i + j] = 0;
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}
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}
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#ifdef _DEBUG_MUL
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std::cout << "result before applying carry:" << result << std::endl;
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std::cout << "carry:[" << carry[0];
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for (int k = 1; k < result.capacity; ++k) {
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std::cout << "," << carry[k];
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}
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std::cout << "]" << std::endl;
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#endif
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if (carry[i + j - 1]) {
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result.data[i + j - 1] = carry[i + j - 1];
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result.size = i + j;
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}
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else {
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result.size = i + j - 1;
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}
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#ifdef _DEBUG_MUL
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std::cout << "before correcting capacity, result=" << result << std::endl;
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#endif
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// correcting capacity
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/*char* temp_data = (char *)calloc(result.size, sizeof(char));
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for (i = 0; i < result.size; ++i) {
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temp_data[i] = result.data[i];
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}
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free(result.data);
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result.capacity = result.size;
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result.data = (char*)calloc(result.size,sizeof(char));
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for (i = 0; i < result.size; ++i) {
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result.data[i] = temp_data[i];
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}
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free(temp_data);*/
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free(carry);
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#ifdef _DEBUG_MUL
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std::cout << "return value=" << result << "(capacity=" << result.capacity << ",size=" << result.size << ")" << std::endl << "======" << std::endl;
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#endif
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return result;
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}
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void operator*=(const Number& a) {
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*this = *this * a;
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}
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bool operator==(const Number& a) const {
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if (size != a.size) {
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return false;
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}
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for (int i = 0; i < size; ++i) {
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if (data[i] != a.data[i]) {
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return false;
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}
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}
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return true;
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}
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bool operator!=(const Number& a) const {
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return not (*this == a);
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}
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bool operator>(const Number& a) const {
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#ifdef _DEBUG_COMP
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std::cout << "comp " << *this << "(size=" << size << ") and " << a << "(size=" << a.size << ")" << std::endl;
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#endif
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if (size > a.size) {
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#ifdef _DEBUG_COMP
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std::cout << "size > a.size => true" << std::endl;
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#endif
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return true;
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}
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if (size < a.size) {
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#ifdef _DEBUG_COMP
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std::cout << "size < a.size => false" << std::endl;
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#endif
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return false;
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}
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for (int i = size - 1; i >= 0; --i) {
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if (data[i] > a.data[i]) {
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return true;
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#ifdef _DEBUG_COMP
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std::cout << static_cast<int>(data[i]) << ">" << static_cast<int>(a.data[i]) << std::endl;
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#endif
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}
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if (data[i] < a.data[i]) {
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#ifdef _DEBUG_COMP
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std::cout << static_cast<int>(data[i]) << "<" << static_cast<int>(a.data[i]) <<std::endl;
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#endif
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return false;
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}
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}
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#ifdef _DEBUG_COMP
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std::cout << "using final false" << std::endl;
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#endif
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return false;
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}
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bool operator<(const Number& a) const {
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return not (*this > a) and (*this != a);
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}
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void div2() {
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#ifdef _DEBUG_DIV2
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std::cout << "n = " << *this << std::endl;
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#endif
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int carry = 0;
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int temp;
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for (int i = size - 1; i >= 0; --i) {
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temp = data[i] + carry * base;
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data[i] = temp / 2;
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carry = temp % 2;
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}
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if (data[size-1] == 0) {
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--size;
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}
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#ifdef _DEBUG_DIV2
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std::cout << "unstripped result "<< *this << std::endl;
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#endif
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}
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friend std::ostream& operator<<(std::ostream& stream, const Number& right);
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friend int main();
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friend Number factorial(int n);
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};
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std::ostream& operator<<(std::ostream& stream, const Number& right)
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{
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#ifdef _DEBUG_COUT
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stream << "[";
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for (std::size_t i = 0; i < right.size; ++i) {
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stream << static_cast<int>(right.data[right.size - 2 - i]) << ",";
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}
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stream << "]";
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#else
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// Печатаем самый большой разряд
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stream << (int)right.data[right.size - 1];
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// Печатаем остальные разряды с заполнением нулями до 2-х цифр
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// setfill и setw это то же самое, что и в языке C спецификатор %02d
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for (std::size_t i = 0; i < right.size - 1; ++i)
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stream << std::setfill('0') << std::setw(2) << (int)right.data[right.size - 2 - i];
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#endif
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return stream;
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}
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Number fib(int n) {
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Number a = 0; // F0
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Number b = 1; // F1
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for (int i = 1; i <=n; ++i) {
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if (i % 2) {
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a += b;
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}
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else {
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b += a;
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}
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}
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if (n % 2) {
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return b;
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}
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return a;
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}
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Number factorial(int n) {
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Number result{1};
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for (int i = 2; i < n + 1; ++i) {
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result = Number(i) * result;
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}
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return result;
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}
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void grad(Number n) {
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std::cout << "n = " << n;
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Number max = n;
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unsigned long long int steps = 0;
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while (n != Number(1)) {
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//std::cout << steps << ":" << n << std::endl;
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if (n > max) {
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#ifdef _DEBUG_COMP
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std::cout << n << " is greater than " << max << std::endl;
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#endif
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max = n;
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}
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if (n.isEven()) {
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n.div2();
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}
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else {
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n = Number(3) * n + Number(1);
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}
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//if(steps > 100) {
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// std::cout << "break" << std::endl;
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// break;
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//}
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++steps;
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}
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std::cout << " steps = " << steps << " max = " << max << std::endl;
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}
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int main()
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{
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Number x = Number("12");
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Number y = Number("122");
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//y.div2();
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//char s[3];
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//Number result = "1";
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//for (int i = 1; i < 26; ++i) {
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//s = std::to_string(i);
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//sprintf(s, "%d", i);
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// result = (Number{i} * result);
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//}
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//x += y;
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//Number z = x + y;
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//std::cout << fib(1000) << std::endl;
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//x = x * Number(24)*Number{25};
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//y = factorial(5);
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//std::cout << x << " " << x.capacity << " " << x.size << std::endl;
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//std::cout << y << " "<< y.capacity << " " << y.size << std::endl;
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//std::cout << "===" << std::endl << Number(2) * Number(3) << " "<< Number(3) * Number(2) << std::endl;
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//std::cout << "5! = " << Number(2) * Number(3) * Number(4) * Number(5) << std::endl;
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//std::cout << factorial(1000) << std::endl;
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//std::cout << Number("620448401733239439360000") * Number(25) << std::endl;
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//std::cout << (y < x) << std::endl;
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grad(Number("4761963248413673697"));
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//grad(Number("256"));
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//std::cout << Number(128) * Number(3) + Number(1) + Number(2) + Number(3) + Number(4) << std::endl;
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}
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