【C++】C++大数的运算

比眉伴天荒 2023-10-17 15:12 3阅读 0赞

#### 一、实验项目内容 ####

##### (HugeInteger Class) Create a class HugeInteger that uses a 40-element array of digits to store integers as large as 40 digits each. #####

1.Provide member functions input, output, add and subtract.
      2.For comparing HugeInteger objects, provide functions isEqualTo, isNotEqualTo, isGreaterThan, isLessThan, isGreaterThanOrEqualTo and isLessThanOrEqualTo — each of these is a “predicate” function that simply returns true if the relationship holds between the two HugeIntegers and returns false if the relationship does not hold.
      3.Also, provide a predicate function isZero.
      4.If you feel ambitious, provide member functions multiply, divide and modulus.

#### 二、实验过程或算法 ####

**HugeInteger.h:**

#ifndef CIRCLE_H
    #define CIRCLE_H
    #include <algorithm>
    #include <string.h>
    using namespace std;
    
    class HugeInteger{
        private:
        char* HugeInteger1;                                  //声明私有成员HugeInteger1
        char* HugeInteger2;                                  //声明私有成员HugeInteger2
    //    char* AddNumber;
    //    char* SubNumber;
        int compareFlag;                                     //判断标志
        int isEqual=0;                                       //HugeInteger1=HugeInteger2
        int isGreater=1;                                     //HugeInteger1>HugeInteger2
        int isLess=-1;                                       //HugeInteger1<HugeInteger2
    
    public:
        HugeInteger();                                       //构造函数1
        HugeInteger( char* HugeInteger1, char* HugeInteger2);//构造函数2
    
        char* getAddNumber();                                //加法运算
        char* getSubNumber();                                //减法运算
    
        char* getHugeInteger1();                             //getter and setter
        void setHugeInteger1(char* hugeInteger1);
        char* getHugeInteger2();
        void setHugeInteger2(char* hugeInteger2);
    
        bool isEqualTo();                                     //compare
        int isNotEqualTo();                                  //return true or false
        int isGreaterThan();
        int isLessThan();
        int isGreaterThanOrEqualTo();
        int isLessThanOrEqualTo();
    
        void compare();                                      //比较两数大小的函数
    
    };
    
    #endif

**HugeInteger.cpp:**

#include "HugeInteger.h"
    
    HugeInteger::HugeInteger(){
        this->HugeInteger1="88888888888888888888888888888888888888888888888888888888888888888888888888";
        this->HugeInteger2="66666666666666666666666666666666666666666666666666666666666666666666666666";
    
        compare();
    }
    
    HugeInteger:: HugeInteger( char* HugeInteger1, char* HugeInteger2){
        this->HugeInteger1=HugeInteger1;
        this->HugeInteger2=HugeInteger2;
    
        compare();
    }
    
    char* HugeInteger::getHugeInteger1(){
        return HugeInteger1;
    }
    char* HugeInteger::getHugeInteger2(){
        return HugeInteger2;
    }
    
    void HugeInteger::setHugeInteger1(char* hugeInteger1){
        this->HugeInteger1=HugeInteger1;
    }
    void HugeInteger::setHugeInteger2(char* hugeInteger2){
        this->HugeInteger1=HugeInteger2;
    }
    
    void HugeInteger::compare(){
        int lHugeInteger1=strlen(HugeInteger1), lHugeInteger2=strlen(HugeInteger2);
        if(lHugeInteger1>lHugeInteger2){                       //HugeInteger1的位数大于HugeInteger2，则HugeInteger1大
            compareFlag=isGreater;
        }
        else if(lHugeInteger1<lHugeInteger2){                  //HugeInteger1的位数小于HugeInteger2,则HugeInteger1小
            compareFlag=isLess;
        }
        else{                                                  //位数相等
            char* pHugeInteger1 = HugeInteger1;
            char* pHugeInteger2 = HugeInteger2;
    
            for(int c=0;c<lHugeInteger1;c++){                  //依次比较每一位数的大小
                if((*pHugeInteger1)>(*pHugeInteger2)){         //不等，则比较大小
                    compareFlag=isGreater;
                    break;
                }
                else if((*pHugeInteger1)<(*pHugeInteger2)){
                    compareFlag=isLess;
                    break;
                }
                else{                                          //相等继续
                    continue;
                }
            }
        }
    }
    
    char* HugeInteger::getAddNumber() {
        int maxlen = max(strlen(HugeInteger1), strlen(HugeInteger2));
        //多两个字符，一个是结束符'/0'，另一个保存当两个数最高位相加后有进位的情况
        char* p = new char[maxlen + 2];
        //结束符
        *(p + maxlen + 1) = '\0';
        //声明两个指针分别指向HugeInteger1和HugeInteger2的末尾，不含结束符
        char* pHugeInteger1 = HugeInteger1 + strlen(HugeInteger1) - 1;
        char* pHugeInteger2 = HugeInteger2 + strlen(HugeInteger2) - 1;
        int m = 0;
        int n = 0;
        //进位
        int c = 0;
        for (int i = maxlen; i > 0; i--) {
            m = n = 0;
            //因为当pHugeInteger1到达第一个字符时，即pHugeInteger1=a时，也要进行计算，所以这里用(pHugeInteger1-1)来判断
            //'0'的Asic是48，减去48转成数字
            if ((pHugeInteger1 + 1) != HugeInteger1) {
                m = *pHugeInteger1 - 48;
                pHugeInteger1--;
            }
            if ((pHugeInteger2 + 1) != HugeInteger2) {
                n = *pHugeInteger2 - 48;
                pHugeInteger2--;
            }
            //为p指针的第i个字符赋值
            *(p + i) = (m + n + c) % 10 + 48;
            //取得进位
            c = (m + n + c) / 10;
        }
        *p = 48 + c;
    
        if(*p=='0'){                        //如果结果的第一位是‘0’，表示没有进位
            return p+1;                     //返回第二位的指针，以去除第一位多余的0
        }
        return p;
    }
    char* HugeInteger::getSubNumber(){
    
        int isNegative=0;                   //定义结果是否为负数的标志，初始为0,不是负数
    
        if(compareFlag==isLess){            //如果HugeInteger1小于HugeInteger2,置换两数
            char* temp=HugeInteger1;
            HugeInteger1=HugeInteger2;
            HugeInteger2=temp;
    
            isNegative=1;                   //结果为负
        }
    
        int maxlen = max(strlen(HugeInteger1), strlen(HugeInteger2));
        //应为HugeInteger1始终大于HugeInteger2,不考虑被减数最高位不够减的情况
        char* p = new char[maxlen + 1];
        //最后一位是结束符
        *(p + maxlen) = '\0';
        //声明两个指针分别指向HugeInteger1和HugeInteger2的末尾，不包含结束符
        char* pHugeInteger1 = HugeInteger1 + strlen(HugeInteger1) - 1;
        char* pHugeInteger2 = HugeInteger2 + strlen(HugeInteger2) - 1;
        int m = 0;
        int n = 0;
        //借位位
        int c = 0;
        for (int i = maxlen - 1; i >=0; i--) {
            m = n = 0;
            //'0'的Asic是48，减去48转成数字
            if ((pHugeInteger1 + 1) != HugeInteger1) {
                m = *pHugeInteger1 - 48;
                pHugeInteger1--;
            }
            if ((pHugeInteger2 + 1) != HugeInteger2) {
                n = *pHugeInteger2 - 48;
                pHugeInteger2--;
            }
            //不够减，要借位
            if (m < n) {
                //为p指针的第i个字符赋值
                *(p + i) = 10 + m - n - c + 48;
                c = 1;
            } else {
                //虽然够减，但是如果再算是借走的一位，那么就小于0了
                if (m - n - c < 0)
                    *(p + i) = 10 + m - n - c + 48;
                else {
                    *(p + i) = m - n - c + 48;
                    c = 0;
                }
            }
        }
        if (isNegative == 1) {
            if (*p == '0') {                        //如果结果的第一位是‘0’，表示没有进位
                char* temp = new char[maxlen];
                temp = p + 1;                            //返回第二位的指针，以去除第一位多余的0
                char* newp = new char[maxlen + 1];
                *newp = '-';                             //首地址带符号‘-’
                for (int i = 0; i < maxlen; i++) {
                    *(newp + 1 + i) = *(temp+i);
                }
                return newp;                          //返回带符号的新字符串
            }
            else {
                char* temp2 = new char[maxlen+1];
                temp2 = p ;
                char* newp2 = new char[maxlen +2];
                *newp2 = '-';                             //首地址带符号‘-’
                for (int i = 0; i < maxlen+1; i++) {
                    *(newp2 + 1 + i) = *(temp2+i);
                }
                return newp2;                          //返回带符号的新字符串
            }
        }
        else {
            if (*p == '0') {                        //如果结果的第一位是‘0’，表示没有进位
                return p+1;                     //返回第二位的指针，以去除第一位多余的0
            }
            return p;
        }
    }
    
    int HugeInteger::isGreaterThan(){
        if(compareFlag==isGreater){
            return true;
        }
        else{
            return false;
        }
    }
    int HugeInteger::isLessThan(){
        if(compareFlag==isLess){
            return true;
        }
        else{
            return false;
        }
    }
    bool HugeInteger::isEqualTo(){
        if(compareFlag==isEqual){
            return true;
        }
        else{
            return false;
        }
    }
    int HugeInteger::isNotEqualTo(){
        if(compareFlag==isEqual){
            return false;
        }
        else{
            return true;
        }
    }
    int HugeInteger::isGreaterThanOrEqualTo(){
        if(compareFlag==isLess){
            return false;
        }
        return true;
    }
    int HugeInteger::isLessThanOrEqualTo(){
        if(compareFlag==isGreater){
            return false;
        }
        return true;
    }

**测试类：**

#include <iostream>
    #include "HugeInteger.h"
    #include <string>
    
    using namespace std;
    
    int main() {
        string hugeInt1,hugeInt2;                      //声明两个string来存储HugeIntegers
    
        cout<<"please enter the first hugeInteger :";   //输入HugeIntegers
        cin>>hugeInt1;
        cout<<"please enter the second hugeInteger:";
        cin>>hugeInt2;
    
        const char* a =hugeInt1.c_str();                //sting转换成char*
        const char* b =hugeInt2.c_str();
    /*
        HugeInteger hugeInteger1;                       //HugeInteger默认构造函数
        cout << hugeInteger1.getAddNumber() << endl;    //
        cout << hugeInteger1.getSubNumber() << endl;
    */
    
        HugeInteger hugeInteger((char*)a,(char*)b);    //声明一个hugeInteger的object
                                                       //输出原始数据
        cout <<"The first hugeInteger is :"<<hugeInteger.getHugeInteger1() << endl;
        cout <<"The second hugeInteger is:"<<hugeInteger.getHugeInteger2() << endl;
    
        cout <<"\n";                                    //输出相加相减结果
        cout <<"The AddNumber is:"<<hugeInteger.getAddNumber() << endl;
        cout <<"The SubNumber is:"<<hugeInteger.getSubNumber() << endl;
    
        cout <<"\n";
        cout << "isEqualTo:"<<hugeInteger.isEqualTo()<< endl;      //输出比较大小的结果
        cout << "isGreaterThan:"<<hugeInteger.isGreaterThan()<< endl;
        cout << "isGreaterThanOrEqualTo:"<<hugeInteger.isGreaterThanOrEqualTo()<< endl;
        cout <<"isLessThan:"<< hugeInteger.isLessThan()<< endl;
        cout << "isLessThanOrEqualTo:"<<hugeInteger.isLessThanOrEqualTo()<< endl;
        cout << "isNotEqualTo:"<<hugeInteger.isNotEqualTo()<< endl;
    
        return 0;
    }

三、实验结果和截图