模板--大位数加减乘除

/*这里专门就算法中的大数问题进行一个统一归纳
*/#include<iostream>#include<string>#include<
using namespace std;

//结果支持的最大位数
//这个可以依据具体需求调整
const static int M = 2000;


int numA[M];
int numB[M];


//使用string重置numA
void resetNumA(string numAStr)
{
    memset(numA,0,M*sizeof(int));

    //将字符串的每一位都转换成数字传入数组
    for (int i = 0; i < numAStr.length(); i++)
    {
        numA[i] = numAStr[numAStr.length()-i-1] - '0';
    }
}

//使用string重置numB
void resetNumB(string numBStr)
{
    memset(numB,0,M*sizeof(int));

    //将字符串的每一位都转换成数字传入数组
    for (int i = 0; i < numBStr.length(); i++)
    {
        numB[i] = numBStr[numBStr.length()-i-1] - '0';
    }
}


//将数组转换为字符串，用于输出
string getNumString(int* num)
{
    string numString;
    bool isBegin = false;
    for (int i = M-1; i >= 0 ; i--)
    {
        if(num[i] != 0)
        {
            isBegin = true;
        }

        if (isBegin)
        {
            numString += num[i] +'0';
        }
    }
    return numString;
}

//判断两个数字哪个大
int compare(string numAStr,string numBStr)
{
    if (numAStr.length() > numBStr.length())
    {
        return 1;
    }
    else if (numAStr.length() < numBStr.length())
    {
        return -1;
    }
    else
    {
        for (int i = 0; i < numAStr.length(); i++)
        {
            if (numAStr[i]>numBStr[i])
            {
                return 1;
            }

            if (numAStr[i]<numBStr[i])
            {
                return -1;
            }
        }
        return 0;
    }
}

//加法
string plus(string numAStr, string numBStr)
{
    resetNumA(numAStr);
    resetNumB(numBStr);

    for (int i = 0; i < M; i++)
    {
        //结果保存在numA中
        numA[i] += numB[i];

        //数字大于9则进位
        if(numA[i]>9)
        {
            numA[i] -= 10;
            numA[i+1]++;
        }
    }

    return getNumString(numA);
}

//减法
string minus(string numAStr, string numBStr)
{
    bool isNegative = false;

    //如果numA比numB小
    //则结果为负数
    //调换位置进行计算
    if (compare(numAStr,numBStr)==-1)
    {
        isNegative = true;
        string temp = numAStr;
        numAStr = numBStr;
        numBStr = temp;
    }
    else if (compare(numAStr,numBStr)==0)
    {
        return "0";
    }

    resetNumA(numAStr);
    resetNumB(numBStr);



    for (int i = 0; i < M; i++)
    {
        //减数小于被减数就借位
        if (numA[i]<numB[i])
        {
            numA[i] = numA[i]+10-numB[i]; 
            numA[i+1]--;
        }
        else
        {
            numA[i] -= numB[i];
        }
    }
    if (isNegative)
    {
        return "-"+  getNumString(numA);
    }
    else
    {
        return getNumString(numA);
    }

}

//乘法

string mul(string numAStr, string numBStr)
{
    resetNumA(numAStr);
    resetNumB(numBStr);

    vector<string> nums;
    for (int i = 0; i < numBStr.length(); i++)
    {
        //初始化一个临时数据来保存被乘数与乘数的某一位相乘的结果
        int temp[M];
        memset(temp,0,M*sizeof(int));


        for (int j = i; j < numAStr.length()+i; j++)
        {
            temp[j] += numA[j-i]*numB[i]%10;

            temp[j+1] = numA[j-i]*numB[i]/10;

            //如果大于9，那么就做进位处理
            if (temp[j]>9)
            {
                temp[j]-=10;
                temp[j+1]++;
            }
        }
        nums.push_back(getNumString(temp));
    }

    //每位相乘的结果再用加法加起来
    string result = nums[0];
    for (int i = 1; i < nums.size(); i++)
    {
        result = plus(result,nums[i]);
    }

    return result;
}



//除,结果精确到个位
string div(string numAStr, string numBStr)
{
    resetNumA(numAStr);
    resetNumB(numBStr);

    string result;
    string left;

    if (compare(numAStr,numBStr)==-1)
    {
        return "0";
    }

    //标记第一个不为0的位数的出现
    bool flag = false;
    for (int i = 0; i < numAStr.length(); i++)
    {
        left +=numAStr[i];

        //余数比除数大
        if (compare(left,numBStr)==1)
        {
            flag = true;

            int count = 1;
            string temp = numBStr;

            while (true)
            {
                //每循环一次加上一个余数
                temp = plus(temp,numBStr);

                //余数仍然大于除数，继续累加
                if (compare(left,temp)==1)
                {
                    count++;
                }
                //余数小于除数
                //可以计算结果
                else if (compare(left,temp)==-1)
                {
                    result += count + '0';
                    left = minus(left, minus(temp,numBStr));
                    break;
                }
                //此时余数刚好是除数的倍数
                else if (compare(left,temp) == 0)
                {
                    count ++;
                    result += count + '0';
                    left = "";
                    break;
                }
            }
        }
        //刚好除尽
        else if(compare(left,numBStr)==0)
        {
            flag = true;
            result +="1";
            left = "";
        }
        //余数比除数小，跳到下一位
        else if(flag)
        {
            result +="0";
        }


    }

    return result;
}

void printTitle()
{
    cout << endl;
    cout << "输入1：加法" << endl;
    cout << "输入2：减法" << endl;
    cout << "输入3：乘法" << endl;
    cout << "输入4：除法" << endl;
    cout << "选择 : ";
}

int main()
{

    string numAStr,numBStr;
    string operation;
    string result;

    printTitle();

    while (cin >> operation)
    {
        cout << "输入两个数字： ";
        cin >> numAStr >> numBStr;

        if(operation == "1")
        {
            result = plus(numAStr,numBStr);
        }
        else if(operation == "2")
        {
            result = minus(numAStr,numBStr);
        }
        else if(operation == "3")
        {
            result = mul(numAStr,numBStr);
        }
        else 
        {
            result = div(numAStr,numBStr);
        }

        cout << "结果为：" << result << endl;

        printTitle();
    }
}