大整数类设计（C++）
2024-06-03 17:27:02
简介
在平时的功能需求中，C/C++语言内置的整形变量表示范围已经足够大了，但是在一些特定的场合，例如解决数学问题的时候，可能需要表示极大的整数。这时候C/C++语言提供的类型就不能满足需求了，需要自己来实现超大整数的实现，当然仅仅是能够存储超大整数还不行，还要能够进行运算。
设计功能
- 能够表达正数与负数
- 能够由整形或字符串转化得到
- 能够使用 + - * / 等符号进行运算
- 可以与int 类型进行混合运算
- 可以使用输入输出流
- 当发生除数为零等错误时会抛出异常
源码分享
头文件：big_int.h
#ifndef BIGINT_H
#define BIGINT_H#include <iostream>
#include <vector>
using std::istream;
using std::ostream;
using std::string;
using std::vector;
class BigInt {public:BigInt(long long num = 0);explicit BigInt(string str);virtual ~BigInt();int digit_at(size_t index) const;BigInt& operator=(const BigInt& number2);BigInt& operator+=(const BigInt& number2);BigInt& operator*=(const BigInt& number2);BigInt& operator-=(const BigInt& number2);BigInt& operator/=(const BigInt& number2);BigInt& operator%=(const BigInt& number2);BigInt& operator++();BigInt& operator--();BigInt operator++(int);BigInt operator--(int);friend bool operator==(const BigInt& number1, const BigInt& number2);friend bool operator!=(const BigInt& number1, const BigInt& number2);friend bool operator<(const BigInt& number1, const BigInt& number2);friend bool operator>(const BigInt& number1, const BigInt& number2);friend bool operator<=(const BigInt& number1, const BigInt& number2);friend bool operator>=(const BigInt& number1, const BigInt& number2);friend BigInt operator+(const BigInt& number1, const BigInt& number2);friend BigInt operator*(const BigInt& number1, const BigInt& number2);friend BigInt operator-(const BigInt& number1, const BigInt& number2);friend BigInt operator/(const BigInt& number1, const BigInt& number2);friend BigInt operator%(const BigInt& number1, const BigInt& number2);friend ostream& operator<<(ostream& output, const BigInt& num);friend istream& operator>>(istream& intput, BigInt& num);private:vector<char> number;bool negtive;static void simple_calc(vector<char>& number1, const vector<char>& number2,bool plus);static void add_at(vector<char>& num, int i, unsigned char x);static bool greater(const vector<char>& number1, const vector<char>& number2);
};
#endif
源文件：big_int.cpp
#include "big_int.h"
using std::cin;
using std::cout;
using std::endl;BigInt::BigInt(long long num) {negtive = false;if (num < 0) {num *= -1;negtive = true;}while (num) {number.emplace_back(num % 10);num /= 10;}if (number.empty()) {number.emplace_back(0);}
}BigInt::BigInt(string str) {negtive = false;for (int i = str.length() - 1; i >= 0; i--) {if (str[i] >= '0' && str[i] <= '9') {number.emplace_back(str[i] - '0');} else if (i == 0 && str[0] == '-') {negtive = true;} else {break;}}while (number.back() == 0) {number.pop_back();}if (number.empty()) {number.emplace_back(0);negtive = false;}
}
BigInt::~BigInt() {}int BigInt::digit_at(size_t index) const {if (index >= number.size()) {throw "Out of range";}return number[index];
}
void BigInt::add_at(vector<char>& number, int index, unsigned char x) {if (x == 0) {return;}int size = number.size();if (index >= size) {number.insert(number.end(), index - size + 1, 0);size = index + 1;}number[index] += x;while (index < size && number[index] >= 10) {if (index + 1 == size) {number.emplace_back(number[index] / 10);size++;} else {number[index + 1] += number[index] / 10;}number[index] %= 10;index++;}
}BigInt& BigInt::operator=(const BigInt& number2) {number = number2.number;negtive = number2.negtive;return *this;
}
BigInt& BigInt::operator+=(const BigInt& number2) {if (negtive != number2.negtive && BigInt::greater(number2.number, number)) {BigInt ans = number2;BigInt::simple_calc(ans.number, number, false);*this = ans;return *this;}BigInt::simple_calc(number, number2.number, negtive == number2.negtive);if (number.size() == 1 && number[0] == 0) {negtive = false;}return *this;
}
BigInt& BigInt::operator*=(const BigInt& number2) {*this = (*this) * number2;return *this;
}
BigInt& BigInt::operator-=(const BigInt& number2) {*this = (*this) - number2;return *this;
}
BigInt& BigInt::operator/=(const BigInt& number2) {*this = (*this) / number2;return *this;
}
BigInt& BigInt::operator%=(const BigInt& number2) {if (number2 == 0){throw "Divide by zero";}if (BigInt::greater(number2.number, number)) {return *this;}int index = number.size() - number2.number.size();while (index >= 0) {vector<char> temp(index, 0);temp.insert(temp.end(), number2.number.begin(), number2.number.end());while (!BigInt::greater(temp, number)) {BigInt::simple_calc(number, temp, false);}index--;}if (number.size() == 1 && number[0] == 0){negtive = false;}return *this;
}BigInt& BigInt::operator++() {(*this) += 1;return *this;
}
BigInt& BigInt::operator--() {(*this) -= 1;return *this;
}
BigInt BigInt::operator++(int) {BigInt temp = (*this);(*this) += 1;return temp;
}
BigInt BigInt::operator--(int) {BigInt temp = (*this);(*this) -= 1;return temp;
}bool operator==(const BigInt& number1, const BigInt& number2) {if (number1.negtive != number2.negtive) {return false;}return number1.number == number2.number;
}
bool operator!=(const BigInt& number1, const BigInt& number2) {return !(number1 == number2);
}
bool operator<(const BigInt& number1, const BigInt& number2) {return number2 > number1;
}
bool operator>(const BigInt& number1, const BigInt& number2) {if (number1.negtive == false) {if (number2.negtive == true) {return true;} else {return BigInt::greater(number1.number, number2.number); //全为正数}} else {if (number2.negtive == false) {return false;} else {return BigInt::greater(number2.number, number1.number); //全为负数}}
}
bool operator<=(const BigInt& number1, const BigInt& number2) {return !(number1 > number2);
}
bool operator>=(const BigInt& number1, const BigInt& number2) {return !(number1 < number2);
}BigInt operator+(const BigInt& number1, const BigInt& number2) {BigInt ans = number1;ans += number2;return ans;
}
BigInt operator*(const BigInt& number1, const BigInt& number2) {BigInt ans = 0;if (number1 == 0 || number2 == 0) {return ans;}ans.negtive = (number1.negtive != number2.negtive); //同号得正，异号得负for (size_t i = 0; i < number1.number.size(); i++) {for (size_t j = 0; j < number2.number.size(); j++) {BigInt::add_at(ans.number, i + j,number1.number[i] * number2.number[j]);}}return ans;
}BigInt operator-(const BigInt& number1, const BigInt& number2) {BigInt temp = number2;temp.negtive = !number2.negtive; // temp 是number2的相反数return operator+(number1, temp); // n1 - n2 = n1 + (-1 * n2)
}
BigInt operator/(const BigInt& number1, const BigInt& number2) {BigInt ans = 0;if (number2 == 0){throw "Divide by zero";}if (BigInt::greater(number2.number, number1.number)) {return ans;}ans.negtive = (number1.negtive != number2.negtive);vector<char> left = number1.number;int index = left.size() - number2.number.size();while (index >= 0) {vector<char> temp(index, 0);temp.insert(temp.end(), number2.number.begin(), number2.number.end());while (!BigInt::greater(temp, left)) {BigInt::simple_calc(left, temp, false);BigInt::add_at(ans.number, index, 1);}index--;}return ans;
}
BigInt operator%(const BigInt& number1, const BigInt& number2) {BigInt ans = number1;ans %= number2;return ans;
}
istream& operator>>(istream& in, BigInt& num) {string str;in >> str;num = BigInt(str);return in;
}
ostream& operator<<(ostream& out, const BigInt& num) {if (num.negtive) {out << '-';}for (int i = num.number.size() - 1; i >= 0; --i) {out << (char)(num.number[i] + '0');}return out;
}void BigInt::simple_calc(vector<char>& num1, const vector<char>& num2,bool plus) {int size1 = num1.size();int size2 = num2.size();if (plus) {for (int i = 0; i < size2; i++) {add_at(num1, i, num2[i]);}return;} else {for (int i = 0; i < size2; i++) {num1[i] -= num2[i];}for (int i = 0; i < size1; i++) {if (num1[i] >= 0) {continue;}char temp = (9 - num1[i]) / 10;num1[i + 1] -= temp;num1[i] += temp * 10;}while (size1 > 1 && num1.back() == 0) {num1.pop_back();size1--;}return;}
}bool BigInt::greater(const vector<char>& number1, const vector<char>& number2) {if (number1.size() != number2.size()) {return number1.size() > number2.size();}for (int i = number1.size() - 1; i >= 0; i--) {if (number1[i] != number2[i]) {return number1[i] > number2[i];}}return false;
}int main() {BigInt num1, num2;while (1) {cout << "please enter two long number:" << endl;cin >> num1 >> num2;cout << "num1 = " << num1 << endl;cout << "num2 = " << num2 << endl;if (num1 == num2) {cout << "num1 == num2" << endl;} else if (num1 < num2) {cout << "num1 < num2" << endl;} else {cout << "num1 > num2" << endl;}cout << "num1 + num2 = " << num1 + num2 << endl;cout << "num1 - num2 = " << num1 - num2 << endl;cout << "num1 * num2 = " << num1 * num2 << endl;cout << "num1 / num2 = " << num1 / num2 << endl;cout << "num1 % num2 = " << num1 % num2 << endl;}return 0;
}
试验结果
please enter two long number:
666666
233
num1 = 666666
num2 = 233
num1 > num2
num1 + num2 = 666899
num1 - num2 = 666433
num1 * num2 = 155333178
num1 / num2 = 2861
num1 % num2 = 53
please enter two long number:
999999999
-111111111
num1 = 999999999
num2 = -111111111
num1 > num2
num1 + num2 = 888888888
num1 - num2 = 1111111110
num1 * num2 = -111111110888888889
num1 / num2 = -9
num1 % num2 = 0
please enter two long number:
0
-5
num1 = 0
num2 = -5
num1 > num2
num1 + num2 = -5
num1 - num2 = 5
num1 * num2 = 0
num1 / num2 = 0
num1 % num2 = 0
please enter two long number:
-4545454545454545
154423
num1 = -4545454545454545
num2 = 154423
num1 < num2
num1 + num2 = -4545454545300122
num1 - num2 = -4545454545608968
num1 * num2 = -701922727272727202535
num1 / num2 = -29435087684
num1 % num2 = -28213
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