【C++】C++大数之运算符重载

Bertha 。 2023-10-17 15:11 120阅读 0赞

#### 一、实验项目内容 ####

##### Modify the “HugeInteger” Class. The new class should also provide the following overloaded operator capabilities: #####

. Overload the addition operator (+), the subtraction operator (-), the multiplication operator (*) and the division operator (/).
    . Overload output operator (<<).
    . Overload all the relational and equality operators.

You can use the following code to test your class design.

// HugeInt test program.
    #include <iostream>
    #include "Hugeint.h"
    using namespace std;
    
    int main()
    {
       HugeInt n1( 7654321 );
       HugeInt n2( 7891234 );
       HugeInt n3( "99999999999999999999999999999" );
       HugeInt n4( "1" );
       HugeInt n5;
    
       cout << "n1 is " << n1 << "\nn2 is " << n2
          << "\nn3 is " << n3 << "\nn4 is " << n4
          << "\nn5 is " << n5 << "\n\n";
    
       n5 = n1 + n2;
       cout << n1 << " + " << n2 << " = " << n5 << "\n\n";
    
       cout << n3 << " + " << n4 << "\n= " << ( n3 + n4 ) << "\n\n";
    
       n5 = n1 + 9;
       cout << n1 << " + " << 9 << " = " << n5 << "\n\n";
    
       n5 = n2 + "10000";
       cout << n2 << " + " << "10000" << " = " << n5 << endl;
    }

#### 二、实验过程或算法 ####

**HugeInteger.h：**

#ifndef HUGEINTER_H
    #define HUGEINTER_H
    #include <iostream>
    #include <algorithm>
    #include <string.h>
    using namespace std;
    
    class HugeInteger{
    
    private:
        string hugeInteger;                                  //声明私有成员hugeInteger
    
    public:
    
        HugeInteger();                                       //default构造函数
        HugeInteger( string HugeInteger1);                    //构造函数1
        HugeInteger( int HugeInteger1);                       //构造函数2
        string getHugeInteger();                              //getting
        void setHugeInteger(const string& hugeInteger);       //setting
    
        //重载<<
        friend ostream& operator<<(ostream& output, const HugeInteger& aHugeInter) ;
    
        //重载+
        friend HugeInteger operator +(const HugeInteger& aHugeInteger, const HugeInteger& bHugeInteger);
        friend HugeInteger operator +(const HugeInteger& aHugeInteger, const string s);
        friend HugeInteger operator +(const HugeInteger& aHugeInteger, const int i);
        //重载-
        friend HugeInteger operator -(const HugeInteger& aHugeInteger, const HugeInteger& bHugeInteger);
        friend HugeInteger operator -(const HugeInteger& aHugeInteger, const string s);
        friend HugeInteger operator -(const HugeInteger& aHugeInteger, const int i);
    
        //重载*
        friend HugeInteger operator *(const HugeInteger& aHugeInteger,const HugeInteger& bHugeInteger);
        friend HugeInteger operator *(const HugeInteger& aHugeInteger,const string s);
        friend HugeInteger operator *(const HugeInteger& aHugeInteger, const int i);
    
        //重载/
        friend HugeInteger operator /(const HugeInteger& aHugeInteger,
                const HugeInteger& bHugeInteger);
        friend HugeInteger operator /(const HugeInteger& aHugeInteger,
                const string s);
        friend HugeInteger operator /(const HugeInteger& aHugeInteger, const int i);
    
    };
    #endif

**HugeInteger.cpp:**

#include "HugeInteger.h"
    #include <iostream>
    #include <stdio.h>
    #include <algorithm>
    #include <string.h>
    using namespace std;
    
    HugeInteger::HugeInteger(){
        this->hugeInteger="null";
    }
    
    HugeInteger:: HugeInteger( string HugeInteger1){
        this->hugeInteger=HugeInteger1;
    }
    HugeInteger:: HugeInteger( int HugeInteger1){
    
        char t[256];
        sprintf(t, "%d", HugeInteger1);
        this->hugeInteger=t;
    }
    
    string HugeInteger::getHugeInteger() {
            return hugeInteger;
        }
    
    void HugeInteger:: setHugeInteger(const string& hugeInteger) {
            this->hugeInteger = hugeInteger;
        }
    //加法运算
    char* getAddNumber(char* HugeInteger1,char* HugeInteger2) {
        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;
    }
    
    //减法运算
    char* getSubNumber(char* HugeInteger1,char* HugeInteger2){
    
        int isNegative=0;                   //定义结果是否为负数的标志，初始为0,不是负数
    
        int lHugeInteger1 = strlen(HugeInteger1), lHugeInteger2 = strlen(
                HugeInteger2);
        if (lHugeInteger1 > lHugeInteger2) { //HugeInteger1的位数大于HugeInteger2，则HugeInteger1大
            isNegative=0;
        } else if (lHugeInteger1 < lHugeInteger2) { //HugeInteger1的位数小于HugeInteger2,则HugeInteger1小
            char* temp = HugeInteger1;
            HugeInteger1 = HugeInteger2;
            HugeInteger2 = temp;
    
            isNegative=1;
        } 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+c)) > (*(pHugeInteger2+c))) {         //不等，则比较大小
                    isNegative=0;
                    break;
                } else if ((*(pHugeInteger1+c)) <(*(pHugeInteger2+c))) {
                    char* temp = HugeInteger1;
                    HugeInteger1 = HugeInteger2;
                    HugeInteger2 = temp;
                    isNegative = 1;
                    break;
                } else {                                          //相等继续
                    continue;
                }
            }
        }
    
        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;
        }
    }
    
    //乘法运算
    char* getMultNumber(char* a, char* b) {
        int sizea = strlen(a);
        int sizeb = strlen(b);
        char* p = new char[sizea + sizeb + 1];
    //两数相乘所得的积的位数最大为两个数位数只和，多申请一位放'\0'
        char* pA = a + sizea - 1;
        char* pB = b + sizeb - 1;
        int m = 0;
        int n = 0;
        //进位
        int c = 0;
    //存放该位置原有的数
        int s = 0;
    //记数
        int i = 0;
        int j = 0;
    //具体实现过程详见说明文件
        for (i = 0; i < sizea; i++) {
            m = *(pA - i) - 48;
            c = 0;
            for (j = 0; j < sizeb; j++) {
                n = *(pB - j) - 48;
    //判断该位置原来是否为0
                if ((*(p + i + j) >= '0') && (*(p + i + j) <= '9'))
                    s = *(p + i + j) - 48;
                else
                    s = 0;
                *(p + i + j) = (m * n + c + s) % 10 + 48;
                c = (m * n + c + s) / 10;
            }
            *(p + i + j) = 48 + c;
        }
        if (c > 0)
            *(p + i + j) = '\0';
        else
            *(p + i + j - 1) = '\0';
    
        int size1 = strlen(p) - 1;
        int size2 = (size1 + 1) / 2;
        char temp;
        for (int i = 0; i < size2; i++) {
            temp = p[i];
            p[i] = p[size1 - i];
            p[size1 - i] = temp;
        }
        return p;
    }
    
    //除法运算（保留个位）
    string getDivNumber(const string &str1,const string &str2)  //  str1/str2
    {
        int i;
        int length,len1,len2,len,index;
        bool flag;
    
        len1=str1.length();
        len2=str2.length();
        length=len1-len2;
        if(length<0) return "0";
    
        int *num1=new int[len1+1];
        int *num2=new int[len2+1];
        int *quotient=new int[length+2];
    
        memset(num1,0,sizeof(int)*(len1+1));
        memset(num2,0,sizeof(int)*(len2+1));
        memset(quotient,0,sizeof(int)*(length+2));
    
        for(i=len1-1,index=0;i>=0;i--)
        {
            num1[index++]=str1[i]-'0';
        }
        for(i=len2-1,index=0;i>=0;i--)
        {
            num2[index++]=str2[i]-'0';
        }
    
        while(true)
        {
            for(i=len1-1;i>=0;i--)
            {
                if(num1[i])
                {
                    len1=i+1;
                    break;
                }
                if(i==0) len1=0;
            }
    
            len=len1-len2;
            if(len<0) break;
    
            flag=false;
            index=0;
    
            for(i=len1-1;i>=len;i--)
            {
                if(num1[i]==num2[i-len]) continue;
                else if(num1[i]<num2[i-len])
                {
                    flag=true;
                    break;
                }
                else
                {
                    break;
                }
            }
    
            if(flag) --len;
            if(len<0) break;
    
            while(++index)
            {
                flag=false;
                for(i=len1-1;i>=len;i--)
                {
                    if(num1[i]==num2[i-len]) continue;
                    else if(num1[i]<num2[i-len])
                    {
                        flag=true;
                        break;
                    }
                    else
                    {
                        break;
                    }
                }
                if(flag)
                {
                    --index;
                    break;
                }
    
                for(i=len;i<len1;i++)
                {
                    num1[i]-=num2[i-len];
                    if(num1[i]<0)
                    {
                        num1[i]+=10;
                        --num1[i+1];
                    }
                }
            }
            if(index==0) break;
            else quotient[len]=index;
        }
    
        string ans;
        flag=false;
        for(i=length;i>=0;i--)
        {
            if(flag||quotient[i])
            {
                flag=true;
                ans+='0'+quotient[i];
            }
        }
        if(!flag) ans="0";
    
        delete [] num1;
        delete [] num2;
        delete [] quotient;
    
        return ans;
    }
    
    //重载<<
    ostream& operator<<(ostream& output, const HugeInteger& aHugeInter) {
    
        output << aHugeInter.hugeInteger;
        return output;
    }
    
    //重载+
    HugeInteger operator +(const HugeInteger& aHugeInteger,
            const HugeInteger& bHugeInteger) {
    
        const char* a = aHugeInteger.hugeInteger.c_str();    //sting转换成char*
        const char* b = bHugeInteger.hugeInteger.c_str();
    
        return HugeInteger(getAddNumber((char*)a,(char*)b));
    
    }
    HugeInteger operator +(const HugeInteger& aHugeInteger, const string s){
        const char* a = aHugeInteger.hugeInteger.c_str();    //sting转换成char*
        const char* b = s.c_str();
    
        return HugeInteger(getAddNumber((char*)a,(char*)b));
    }
    HugeInteger operator +(const HugeInteger& aHugeInteger, const int i){
        char t[256];
        sprintf(t, "%d", i);
        string temp=t;
        const char* a = aHugeInteger.hugeInteger.c_str();    //sting转换成char*
        const char* b =temp.c_str();
    
        return HugeInteger(getAddNumber((char*)a,(char*)b));
    }
    
    //重载-
    HugeInteger operator -(const HugeInteger& aHugeInteger,
            const HugeInteger& bHugeInteger) {
    
        const char* a = aHugeInteger.hugeInteger.c_str();    //sting转换成char*
        const char* b = bHugeInteger.hugeInteger.c_str();
    
        return HugeInteger(getSubNumber((char*)a,(char*)b));
    
    }
    HugeInteger operator -(const HugeInteger& aHugeInteger, const string s){
        const char* a = aHugeInteger.hugeInteger.c_str();    //sting转换成char*
        const char* b = s.c_str();
    
        return HugeInteger(getSubNumber((char*)a,(char*)b));
    }
    
    HugeInteger operator -(const HugeInteger& aHugeInteger, const int i){
        char t[256];
        sprintf(t, "%d", i);
        string temp=t;
        const char* a = aHugeInteger.hugeInteger.c_str();    //sting转换成char*
        const char* b =temp.c_str();
    
        return HugeInteger(getSubNumber((char*)a,(char*)b));
    }
    //重载*
    HugeInteger operator *(const HugeInteger& aHugeInteger,
            const HugeInteger& bHugeInteger) {
    
        const char* a = aHugeInteger.hugeInteger.c_str();    //sting转换成char*
        const char* b = bHugeInteger.hugeInteger.c_str();
    
        return HugeInteger(getMultNumber((char*)a,(char*)b));
    
    }
    HugeInteger operator *(const HugeInteger& aHugeInteger, const string s){
        const char* a = aHugeInteger.hugeInteger.c_str();    //sting转换成char*
        const char* b = s.c_str();
    
        return HugeInteger(getMultNumber((char*)a,(char*)b));
    }
    
    HugeInteger operator *(const HugeInteger& aHugeInteger, const int i){
    
        char t[256];
        sprintf(t, "%d", i);
        string temp=t;
        const char* a = aHugeInteger.hugeInteger.c_str();    //sting转换成char*
        const char* b =temp.c_str();
    
        return HugeInteger(getMultNumber((char*)a,(char*)b));
    }
    
    //重载/
    HugeInteger operator /(const HugeInteger& aHugeInteger,
            const HugeInteger& bHugeInteger) {
    
        return HugeInteger(getDivNumber(aHugeInteger.hugeInteger,bHugeInteger.hugeInteger));
    
    }
    HugeInteger operator /(const HugeInteger& aHugeInteger, const string s){
    
        return HugeInteger(getDivNumber(aHugeInteger.hugeInteger,s));
    }
    
    HugeInteger operator /(const HugeInteger& aHugeInteger, const int i){
    
        char t[256];
        sprintf(t, "%d", i);
        string temp=t;
    
        return HugeInteger(getDivNumber(aHugeInteger.hugeInteger,temp));
    }

**测试类：**

#include <iostream>
    #include "HugeInteger.h"
    using namespace std;
    
    int main() {
    
        HugeInteger n1(7654321);
        HugeInteger n2(7891234);
        HugeInteger n3("99999999999999999999999999999");
        HugeInteger n4("1");
        HugeInteger n5;
    
        cout << "n1 is " << n1 << "\nn2 is " << n2 << "\nn3 is " << n3 << "\nn4 is "
                << n4 << "\nn5 is " << n5 << "\n\n";
    
        n5 = n1 + n2;
        cout << n1 << " + " << n2 << " = " << n5 << "\n\n";
    
        n5 = n1 - n2;              //小减大
        cout << n1 << " - " << n2 << " = " << n5 << "\n\n";
        n5 = n2- n1;               //大减小
        cout << n2<< " - " << n1<< " = " << n5 << "\n\n";
    
        n5 = n2 * n1;               //乘法
        cout << n2 << " * " << n1 << " = " << n5 << "\n\n";
    
        n5 = n2 / n1;               //除法  保留到整数
        cout << n2 << " / " << n1 << " = " << n5 << "\n\n";
    
        cout << n3 << " + " << n4 << "\n= " << (n3 + n4) << "\n\n";
    
        n5 = n1 + 9;               //与int类型运算
        cout << n1 << " + " << 9 << " = " << n5 << "\n\n";
    
        n5 = n2 + "10000";         //与string类型运算
        cout << n2 << " + " << "10000" << " = " << n5 << endl;
    
        n5 = n2 * "10000";         //乘法运算
        cout << n2 << " * " << "10000" << " = " << n5 << endl;
    
        n2= n5 /"10000";         //除法运算
        cout << n5<< " / " << "10000" << " = " << n2<< endl;
    
        return 0;
    }

#### 三、实验结果和截图 ####