模板--大位数加减乘除

喜欢ヅ旅行 2022-06-11 04:22 93阅读 0赞

/*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();
        }
    }