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@ -1,347 +1,8 @@
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#include <iostream>
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#include <iostream>
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#include <cstring>
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#include <cstring>
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#include <iomanip>
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#include <vector>
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#include <vector>
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#include <algorithm>
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#include <algorithm>
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#include "number.h"
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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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|
}
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|
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|
free(temp_data);*/
|
|
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|
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|
free(carry);
|
|
|
|
|
|
|
|
#ifdef _DEBUG_MUL
|
|
|
|
|
|
|
|
std::cout << "return value=" << result << "(capacity=" << result.capacity << ",size=" << result.size << ")" << std::endl << "======" << std::endl;
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
return result;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
void operator*=(const Number& a) {
|
|
|
|
|
|
|
|
*this = *this * a;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
bool operator==(const Number& a) const {
|
|
|
|
|
|
|
|
if (size != a.size) {
|
|
|
|
|
|
|
|
return false;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
for (int i = 0; i < size; ++i) {
|
|
|
|
|
|
|
|
if (data[i] != a.data[i]) {
|
|
|
|
|
|
|
|
return false;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
return true;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
bool operator!=(const Number& a) const {
|
|
|
|
|
|
|
|
return not (*this == a);
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
bool operator>(const Number& a) const {
|
|
|
|
|
|
|
|
#ifdef _DEBUG_COMP
|
|
|
|
|
|
|
|
std::cout << "comp " << *this << "(size=" << size << ") and " << a << "(size=" << a.size << ")" << std::endl;
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
if (size > a.size) {
|
|
|
|
|
|
|
|
#ifdef _DEBUG_COMP
|
|
|
|
|
|
|
|
std::cout << "size > a.size => true" << std::endl;
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
return true;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
if (size < a.size) {
|
|
|
|
|
|
|
|
#ifdef _DEBUG_COMP
|
|
|
|
|
|
|
|
std::cout << "size < a.size => false" << std::endl;
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
return false;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
for (int i = size - 1; i >= 0; --i) {
|
|
|
|
|
|
|
|
if (data[i] > a.data[i]) {
|
|
|
|
|
|
|
|
return true;
|
|
|
|
|
|
|
|
#ifdef _DEBUG_COMP
|
|
|
|
|
|
|
|
std::cout << static_cast<int>(data[i]) << ">" << static_cast<int>(a.data[i]) << std::endl;
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
if (data[i] < a.data[i]) {
|
|
|
|
|
|
|
|
#ifdef _DEBUG_COMP
|
|
|
|
|
|
|
|
std::cout << static_cast<int>(data[i]) << "<" << static_cast<int>(a.data[i]) <<std::endl;
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
return false;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
#ifdef _DEBUG_COMP
|
|
|
|
|
|
|
|
std::cout << "using final false" << std::endl;
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
return false;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
bool operator<(const Number& a) const {
|
|
|
|
|
|
|
|
return not (*this > a) and (*this != a);
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
void div2() {
|
|
|
|
|
|
|
|
#ifdef _DEBUG_DIV2
|
|
|
|
|
|
|
|
std::cout << "n = " << *this << std::endl;
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
int carry = 0;
|
|
|
|
|
|
|
|
int temp;
|
|
|
|
|
|
|
|
for (int i = size - 1; i >= 0; --i) {
|
|
|
|
|
|
|
|
temp = data[i] + carry * base;
|
|
|
|
|
|
|
|
data[i] = temp / 2;
|
|
|
|
|
|
|
|
carry = temp % 2;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
if (data[size-1] == 0) {
|
|
|
|
|
|
|
|
--size;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
#ifdef _DEBUG_DIV2
|
|
|
|
|
|
|
|
std::cout << "unstripped result "<< *this << std::endl;
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
friend std::ostream& operator<<(std::ostream& stream, const Number& right);
|
|
|
|
|
|
|
|
friend int main();
|
|
|
|
|
|
|
|
friend Number factorial(int n);
|
|
|
|
|
|
|
|
};
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
std::ostream& operator<<(std::ostream& stream, const Number& right)
|
|
|
|
|
|
|
|
{
|
|
|
|
|
|
|
|
#ifdef _DEBUG_COUT
|
|
|
|
|
|
|
|
stream << "[";
|
|
|
|
|
|
|
|
for (std::size_t i = 0; i < right.size; ++i) {
|
|
|
|
|
|
|
|
stream << static_cast<int>(right.data[right.size - 2 - i]) << ",";
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
stream << "]";
|
|
|
|
|
|
|
|
#else
|
|
|
|
|
|
|
|
// Печатаем самый большой разряд
|
|
|
|
|
|
|
|
stream << (int)right.data[right.size - 1];
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// Печатаем остальные разряды с заполнением нулями до 2-х цифр
|
|
|
|
|
|
|
|
// setfill и setw это то же самое, что и в языке C спецификатор %02d
|
|
|
|
|
|
|
|
for (std::size_t i = 0; i < right.size - 1; ++i)
|
|
|
|
|
|
|
|
stream << std::setfill('0') << std::setw(2) << (int)right.data[right.size - 2 - i];
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
return stream;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Number fib(int n) {
|
|
|
|
Number fib(int n) {
|
|
|
|
Number a = 0; // F0
|
|
|
|
Number a = 0; // F0
|
|
|
@ -374,7 +35,6 @@ void grad(Number n) {
|
|
|
|
Number max = n;
|
|
|
|
Number max = n;
|
|
|
|
unsigned long long int steps = 0;
|
|
|
|
unsigned long long int steps = 0;
|
|
|
|
while (n != Number(1)) {
|
|
|
|
while (n != Number(1)) {
|
|
|
|
//std::cout << steps << ":" << n << std::endl;
|
|
|
|
|
|
|
|
if (n > max) {
|
|
|
|
if (n > max) {
|
|
|
|
#ifdef _DEBUG_COMP
|
|
|
|
#ifdef _DEBUG_COMP
|
|
|
|
std::cout << n << " is greater than " << max << std::endl;
|
|
|
|
std::cout << n << " is greater than " << max << std::endl;
|
|
|
@ -387,10 +47,12 @@ void grad(Number n) {
|
|
|
|
else {
|
|
|
|
else {
|
|
|
|
n = Number(3) * n + Number(1);
|
|
|
|
n = Number(3) * n + Number(1);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
//if(steps > 100) {
|
|
|
|
#ifdef _DEBUG_GRAD
|
|
|
|
// std::cout << "break" << std::endl;
|
|
|
|
if(steps > 100) {
|
|
|
|
// break;
|
|
|
|
std::cout << "break" << std::endl;
|
|
|
|
//}
|
|
|
|
break;
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
#endif
|
|
|
|
++steps;
|
|
|
|
++steps;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
std::cout << " steps = " << steps << " max = " << max << std::endl;
|
|
|
|
std::cout << " steps = " << steps << " max = " << max << std::endl;
|
|
|
@ -398,19 +60,7 @@ void grad(Number n) {
|
|
|
|
|
|
|
|
|
|
|
|
int main()
|
|
|
|
int main()
|
|
|
|
{
|
|
|
|
{
|
|
|
|
Number x = Number("12");
|
|
|
|
std::cout << fib(1000) << std::endl;
|
|
|
|
Number y = Number("122");
|
|
|
|
|
|
|
|
//y.div2();
|
|
|
|
|
|
|
|
//char s[3];
|
|
|
|
|
|
|
|
//Number result = "1";
|
|
|
|
|
|
|
|
//for (int i = 1; i < 26; ++i) {
|
|
|
|
|
|
|
|
//s = std::to_string(i);
|
|
|
|
|
|
|
|
//sprintf(s, "%d", i);
|
|
|
|
|
|
|
|
// result = (Number{i} * result);
|
|
|
|
|
|
|
|
//}
|
|
|
|
|
|
|
|
//x += y;
|
|
|
|
|
|
|
|
//Number z = x + y;
|
|
|
|
|
|
|
|
//std::cout << fib(1000) << std::endl;
|
|
|
|
|
|
|
|
//x = x * Number(24)*Number{25};
|
|
|
|
//x = x * Number(24)*Number{25};
|
|
|
|
//y = factorial(5);
|
|
|
|
//y = factorial(5);
|
|
|
|
//std::cout << x << " " << x.capacity << " " << x.size << std::endl;
|
|
|
|
//std::cout << x << " " << x.capacity << " " << x.size << std::endl;
|
|
|
@ -420,7 +70,7 @@ int main()
|
|
|
|
//std::cout << factorial(1000) << std::endl;
|
|
|
|
//std::cout << factorial(1000) << std::endl;
|
|
|
|
//std::cout << Number("620448401733239439360000") * Number(25) << std::endl;
|
|
|
|
//std::cout << Number("620448401733239439360000") * Number(25) << std::endl;
|
|
|
|
//std::cout << (y < x) << std::endl;
|
|
|
|
//std::cout << (y < x) << std::endl;
|
|
|
|
grad(Number("4761963248413673697"));
|
|
|
|
//grad(Number("4761963248413673697"));
|
|
|
|
//grad(Number("256"));
|
|
|
|
//grad(Number("256"));
|
|
|
|
//std::cout << Number(128) * Number(3) + Number(1) + Number(2) + Number(3) + Number(4) << std::endl;
|
|
|
|
//std::cout << Number(128) * Number(3) + Number(1) + Number(2) + Number(3) + Number(4) << std::endl;
|
|
|
|
}
|
|
|
|
}
|
|
|
|