大整数的加减乘除C++实现

大整数的乘法由于用分治法理解起来有点困难，就采用人的计算方法实现，大整数为string 类型，结果也为string类型。

大整数的除法采用先乘后减的方法，例如：

　　665/20

　　首先20*10=200；然后665去减200，通过循环计入减了3次，则结果记入3*10=30；然后20*1=20，上次减了之后还剩65，65-20，又减了3次，所以结果记入30+3*1=33；最后还剩5，比20小，则余数为5。

大整数的加法减法和人工打草稿过程类似，不做详细分析。实现代码仅供参考：

#include<iostream>
#include<string>
using namespace std;

const int MAX = 256;
int a_pos , b_pos ;
int a_len, b_len; 
string remain="0"; //保存除法的余数

string def_multiply(string a, string b) //默认的乘法（正正）
{
    char result[MAX] = { 0 };
    int length;
    a_len = a.length(), b_len = b.length();
    string result_str = "";
    int flag = 0,sum=0;
    int top;
    for (int i1 = 0, a_pos = a_len - 1; i1 < a_len; i1++, a_pos--)
    {
        for (int i2 = 0, b_pos = b_len - 1; i2 < b_len; i2++, b_pos--)
        {
            top = i1 + i2;
            sum = result[top] + (a[a_pos] - 48)*(b[b_pos] - 48) + flag;
            result[top] = sum % 10;
            flag = sum / 10;
        }
        if (flag>0)
        {
            top++;
            result[top] = result[top]+flag % 10;
            flag = flag / 10;
        }
        length = top;
    }
    for (; length >= 0; length--)
    {
        result_str+= result[length]+48;
    }
    return result_str;
}

string def_add(string a, string b)//默认加法（正正）
{
    string result_str = "";
    char result[MAX] = { 0 };
    int flag = 0, sum = 0;
    int length;
    a_len = a.length(), b_len = b.length();
    int  len = (a_len > b_len ? a_len : b_len);
    length = len-1;
    for (int i = 0, b_pos = b_len - 1, a_pos = a_len - 1; i < len; i++, a_pos--,b_pos--)
    {
        if (b_pos < 0)
        {
            sum = a[a_pos] - 48 + flag;
            result[i] = sum%10;
            flag = sum / 10;
        }
        else if (a_pos < 0)
        {
            sum = b[b_pos] - 48 + flag;
            result[i] = sum % 10;
            flag = sum / 10;
        }
        else
        {
            sum = a[a_pos] + b[b_pos] - 96+flag;
            result[i] = sum % 10;
            flag = sum / 10;
        }
    }
    if (flag > 0)
    {
        length++;
        result[len]=flag;
    }
    for (; length >= 0; length--)
    {
        result_str += result[length] + 48;
    }
    return result_str;
}


string def_subtract(string a, string b) //默认减法（大的正减小的正数）
{
    char result[MAX] = { 0 };
    a_len = a.length(), b_len = b.length();
    int flag = 0;
    int i = 0;
    string str = "";
    for (b_pos = b_len - 1, a_pos = a_len - 1; i < b_len; i++, a_pos--, b_pos--)
    {
        if (a[a_pos] < b[b_pos])
        {
            result[i] = a[a_pos] + 10 - b[b_pos];
            a[a_pos - 1]-=1;
        }
        else
        {
            result[i] = a[a_pos]  - b[b_pos];
        }

    }
    for (i = a_len - b_len - 1; i >= 0; i--)
    {
        if (a[i] < '0')
        {
            a[i - 1]--;
            result[a_len - i - 1] = a[i] - 38;
        }
        else{ result[a_len - i - 1] = a[i] - 48; }
    }
    
    for (i=a_len-1; i >= 0; i--)
    {
        str += result[i] + 48; 
    }
    int j = 0;
    while (str[j] == '0'&&j!=str.length())
    {
        j++;
    }
    if (j != 0)str.erase(0, j);
    if (str.length()==0)str = "0";
    return str;
}

string multiply(string a, string b)  //整数的乘法
{
    string str;
    if (a[0] == '-'&&b[0] != '-')
    {
        a = a.substr(1);
        str ="-"+ def_multiply(a, b);
        return str;
    }
    else if (b[0] == '-'&&a[0] != '-')
    {
        b = b.substr(1);
        str = "-" + def_multiply(a, b);
        return str;
    }
    else if (b[0] == '-'&&a[0] == '-')
    {
        a = a.substr(1);
        b = b.substr(1);        
        return def_multiply(a, b);
    }
    else
    {
        return def_multiply(a, b);
    }
}

string subtract(string a, string b) //整数的减法
{
    string str;
    if (a[0] == '-'&&b[0] != '-')
    {
        a = a.substr(1);
        str = "-" + def_add(a, b);
        return str;
    }
    else if (b[0] == '-'&&a[0] != '-')
    {
        b = b.substr(1);
        str = def_add(a, b);
        return str;
    }
    else if (b[0] == '-'&&a[0] == '-')
    {
        a = a.substr(1);
        b = b.substr(1);
        return subtract(b, a);
    }
    else
    {
        if (a.length() > b.length() || (a.length() == b.length() && a >= b))
        {
            str=def_subtract(a, b);
            return str;
        }
        else
        {
            str = "-" + def_subtract(b, a);
            return str;
        }
    }
}

string add(string a, string b)//整数的加法
{
    string str;
    if (a[0] == '-'&&b[0] != '-')
    {
        a = a.substr(1);        
        return subtract(b, a);
    }
    else if (b[0] == '-'&&a[0] != '-')
    {
        b = b.substr(1);
        return subtract(a, b);
    }
    else if (b[0] == '-'&&a[0] == '-')
    {
        a = a.substr(1);
        b = b.substr(1);
        str="-" + def_add(a, b);
        return str;
    }
    else
    {
        return def_add(a, b);
    }
}

string def_divide(string a, string b) //默认的除法（正的除正的）
{
    int length,j=0;
    string s, b2,sum="0", temp="";
    a_len = a.length(), b_len = b.length();
    if (a == b)
        return "1";
    if (a_len > b_len)
    {    
        s = a;
        length = a_len - b_len;
        for (; length >= 0; length--)
        {
            b2 = b;
            for (int i = 0; i < length; i++)
                b2 = b2 + '0';
            
            while (s[0] != '-')
            {        
                s = subtract(s, b2);
                j++ ;
            }
            s = add(s, b2);
            char ch = j + 48-1;
            temp += ch;
            for (int i = 0; i < length; i++)
                temp = temp + "0";
            sum = def_add(sum,temp);
            temp = "",j=0;
        }
        remain = s;
        return sum;
    }
    else if (a_len == b_len  && a > b)
    {
        s = a;
        sum = (a[0] - 48) / (b[0] - 48)+48;    
        for (int i = 0; i < (a[0] - 48) / (b[0] - 48); i++)
        {
            s = def_subtract(s, b);
        }
        return sum;
    }
    else
    {
        return "0";
    }
}

string divide(string a, string b) //整数的除法
{
    string str;
    if (a[0] == '-'&&b[0] != '-')
    {
        a = a.substr(1);
        str="-"+def_divide(a, b);
        remain = "-" + remain;
        return str;
    }
    else if (b[0] == '-'&&a[0] != '-')
    {
        b = b.substr(1);
        return "-" + def_divide(a, b);
    }
    else if (b[0] == '-'&&a[0] == '-')
    {
        a = a.substr(1);
        b = b.substr(1);
        str = def_divide(a, b);
        remain = "-" + remain;
        return str;
    }
    else
    {
        return def_divide(a, b);
    }
}

写一个main函数测试:

#include<iostream>
#include"BigNum.h"
using namespace std;
int main()
{
    string a;
    string b;
    cin >> a >> b;
    cout << a << "+" << b << "=" << add(a, b) << endl;
    cin >> a >> b;
    cout << a << "-" << b << "=" << subtract(a, b) << endl;
    cin >> a >> b;
    cout << a << "*" << b << "=" << multiply(a, b) << endl;
    cin >> a >> b;
    cout << a<<"/"<<b<<"="<<divide(a, b) <<" remainder is " << remain<< endl;
    system("pause");
    return 0;
}