四则运算3

二柱子马不停蹄地把02版本做完，岂料老师棋高一招，又提出了版本03的要求

二柱子只好硬着头皮继续战斗下去， 男人，不能说不行 ！！！

废话少说，要求如下：

1. 能够判断用户输入的答案是否正确。
2. 能够处理四种运算的混合运算。

P.S.连续的减法和除法，应遵守左结合的规定；连续除法要打括号，否则引起歧义。

勤劳善良的二柱子编啊编，调啊调，总算在不懈努力下完成了老师的要求

代码如下：

#include <iostream>
#include <iomanip>
#include <fstream>
#include <ctime>
#include <cstdlib>
#include <sstream>
#include <string>
#include <vector>
#include <algorithm>
#include <stack>
#include <cctype>
#include <cmath>
using namespace std;
bool checkResult(string exp,string result);
string pri[7][7]={
    {">",">","<","<","<",">",">"},
    {">",">","<","<","<",">",">"},
    {">",">",">",">","<",">",">"},
    {">",">",">",">","<",">",">"},
    {"<","<","<","<","<","=",""},
    {">",">",">",">","",">",">"},
    {"<","<","<","<","<","","="}
};

bool isTrueFraction(int numerator, int denominator)    //判断产生的分数是否是真分数
{
    if(numerator >= denominator)
        return false;

    for(int i = 2 ; i <= numerator ; i++)      //判断分数是否能够约分
    {
        if(numerator % i ==0 && denominator % i == 0)
            return false;
    }

    return true;
}

string getNum(int start = 0, int end = 100, bool isParentheses = false, int depth = 0)
{
    int n = rand();
    if(isParentheses)      // 若带括号 则为 a op ( b op c ) 的形式 op为运算符
    {
        int num1 = rand() % (end - start + 1) + start;
        stringstream ss;
        ss << num1;

        if(depth  < 9)     //控制递归层数，带括号的式子少于10个
        {
            string num2 = "( " + getNum(start, end, n % 2 == 0,depth + 1) + " )";
            return ss.str() +" , "+ num2;
        }
        else
        {
            string num2 = "( " + getNum(start, end, false) + " )";
            return ss.str() +" , "+ num2;
        }
    }else
    {
        if(n % 7 == 0)       //若随机数n是7的倍数，产生一个真分数和一个整数，否则为两个整数
        {
            int num1 = rand() % (end - start + 1) + start;
            int num2 = rand() % (end - start + 1) + start;
            int num3 = rand() % (end - start + 1) + start;

            if(isTrueFraction(num1,num2))
            {
                stringstream s1,s2,s3;   //将int转为string
                s1<<num1;
                s2<<num2;
                s3<<num3;
                return s1.str()+"/"+s2.str()+" , "+s3.str();
            }else
            {
                return getNum(start,end);
            }
        }else
        {
            int num1 = rand() % (end - start + 1) + start;
            int num2 = rand() % (end - start + 1) + start;
            stringstream s1,s2;
            //string ss1,ss2;
            s1<<num1;
            s2<<num2;
            return s1.str()+" , "+s2.str();
        }
    }


}

char getOperator(string num2 = "1", bool isMulandDiv = true)   // 默认第二个参数不为0，默认包括乘除法
{
    char op[] = {'+','-','*','/'};

    if(isMulandDiv)
    {
        if(num2 == "0") //避免除数为0
            return op[rand() % 3];
        else
            return op[rand() % 4];
    }else
    {
        return op[rand() % 2];     //只包含加减
    }
}

bool isDup(vector<string> &items, string item)    //若重复返回true,否则返回false
{
    if(find(items.begin(),items.end(),item) == items.end())
        return false;
    else
        return true;
}

bool isNegative(string num1, string num2, char op)      //判断两数加减的正负
{
    stringstream ss1,ss2;
    int n1,n2;
    ss1 << num1;
    ss1 >> n1;
    ss2 << num2;
    ss2 >> n2;
    if(op == '-')
    {
        if(n1 < n2)
        {
            return true;
        }else
        {
            return false;
        }
    }else
    {
        if(n1 + n2 < 0)
            return true;
        else
            return false;
    }

}

bool isRemainder(string num1, string num2)   //判断两数相除有无余数
{
    stringstream ss1,ss2;
    int n1,n2;
    ss1 << num1;
    ss1 >> n1;
    ss2 << num2;
    ss2 >> n2;

    if(n1 % n2 == 0)
        return false;
    else
        return true;
}

void printAndCheck(vector<string> &items, bool isCmd)
{
    vector<string>::iterator it = items.begin();
    string answer;
    if(isCmd)  //答案是分数或整数
    {

        for(;it != items.end(); it++)
        {
            cout << (*it) <<endl;
            cout << "answer:";
            cin >> answer;
            if(checkResult((*it),answer))
            {
                cout << "Bingo!!!" <<endl;
            }else
            {
                cout << "Oh ,stupid guy!!" <<endl;
            }
        }

        cout << "Problems finished!" << endl;
    }else
    {
        ofstream of("problems.txt");
        if(!of)
            exit(1);

        for(;it != items.end() ; it++)
            of<<*it <<endl;

        of.close();
    }


}
int getOpersNum(string op)    //返回运算符编号，用于比较优先级 +-*/()# 对应 0123456
{
    if(op == "+")
    {
        return 0;
    }else if(op == "-")
    {
        return 1;
    }else if(op == "*")
    {
        return 2;
    }else if(op == "/")
    {
        return 3;
    }else if(op == "(")
    {
        return 4;
    }else if(op == ")")
    {
        return 5;
    }else if(op == "#")
    {
        return 6;
    }else
    {
        cout << "Error!" << endl;
        exit(1);
    }
}

double calculate(double n1, double n2, string op)
{
    if(op == "+")
    {
        return n1 + n2;
    }else if(op == "-")
    {
        return n1 - n2;
    }else if(op == "*")
    {
        return n1 * n2;
    }else if(op == "/")
    {
        return n1 / n2;
    }else
    {
        cout << "Error" <<endl;
        exit(1);
    }
}

bool checkResult(string exp,string result)
{
    stack<string> ops;
    stack<double> nums;
    ops.push("#");
    exp = exp + " #";    //加起始结束标识
    int flag = -1;  //字符串扫描标识 标识" "的位置
    while (!( exp[flag + 1] == '#' && ops.top() == "#"))  //当符号栈栈顶元素和扫描出的下一个元素不同时为#时
    {
        string str = exp.substr(flag + 1, exp.find(" ",flag + 1) - flag -1);
        if(str != "+" && str != "-" && str != "*" && str != "/" && str != ")" && str != "(" && str != "#")    //不是运算符
        {
            if(str.find("/") == string::npos)   //str为整数的情况
            {
                stringstream ss;
                double n;
                ss << str;
                ss >> n;
                nums.push(n);
                flag = exp.find(" ",flag + 1);
            }else    //分数的情况
            {
                stringstream ssNum,ssDen;
                double numerator,denominator;     //分子 分母
                ssNum << str.substr(0,str.find("/"));
                ssDen << str.substr(str.find("/") + 1);
                ssNum >> numerator;
                ssDen >> denominator;
                nums.push(numerator/denominator);  //以double型压栈
                flag = exp.find(" ",flag + 1);
            }
        }else   //str是运算符
        {
            if(pri[getOpersNum(ops.top())][getOpersNum(str)] == "<")
            {
                ops.push(str);
                flag = exp.find(" ",flag + 1);
            }else if(pri[getOpersNum(ops.top())][getOpersNum(str)] == ">")
            {
                string op = ops.top();
                ops.pop();
                double num2 = nums.top();
                nums.pop();
                double num1 = nums.top();
                nums.pop();
                nums.push(calculate(num1,num2,op));
            }else if (pri[getOpersNum(ops.top())][getOpersNum(str)] == "=")
            {
                ops.pop();
                flag = exp.find(" ",flag + 1);
            }else
            {
                cout << "Error!!!";
                exit(1);
            }
        }
    }
    double res;
    if(result.find("/") == string::npos)  //结果是整数
    {
        stringstream ss;
        ss << result;
        ss >>res;
    }else  //结果是分数
    {
        stringstream ssNum,ssDen;
        double numerator,denominator;     //分子 分母
        ssNum << result.substr(0,result.find("/"));
        ssDen << result.substr(result.find("/") + 1);
        ssNum >> numerator;
        ssDen >> denominator;
        res = numerator/denominator;
    }

    if(fabs(nums.top() - res) < 1e-4)    //int,double,string多次转换可能结果有偏差，设置10的-4次方为阈值检验结果正确性
    {
        return true;
    }else{
        return false;
    }
}

int main(int argc, char *argv[])
{
    srand((int)time(0));    //设定时间种子
    vector<string> items;   //将题目存在items中，用于判断是否重复和输出
    int itemNum,tmp;  //题目数量
    char ttmp;
    bool isCmd;    //打印方式
    bool isMulandDiv;     //是否有乘除法
    bool isParentheses;  //是否带括号
    int start,end;  //数值范围
    bool isNeg;    //有无负数
    bool isRem;    //有无余数
    bool addFlag = false;  //添加标识

    cout << "Please input the problem number:" << endl;       //定制题目数量、打印方式等
    cin >> itemNum;
    if(itemNum < 0 )
    {
        cout << "Error input!" <<endl;
        exit(1);
    }

    cout << "Please input the display mode(0. screen 1.file)" <<endl;
    cin >> tmp;
    if(tmp == 0)
    {
        isCmd = true;
    }else if(tmp == 1)
    {
        isCmd = false;
    }else
    {
        cout << "Error input!" <<endl;
        exit(1);
    }

    cout << "Include multiplication or division? (Y/N)" <<endl;
    cin >>ttmp;
    if(ttmp == 'y' || ttmp == 'Y')
    {
        isMulandDiv = true;
    }else if (ttmp == 'N' || ttmp == 'n')
    {
        isMulandDiv = false;
    }else
    {
        cout << "Error!"<<endl;
        exit(1);
    }

    cout << "Include parenthesses? (Y/N)" <<endl;
    cin >>ttmp;
    if(ttmp == 'y' || ttmp == 'Y')
    {
        isParentheses = true;
    }else if (ttmp == 'N' || ttmp == 'n')
    {
        isParentheses = false;
    }else
    {
        cout << "Error input!"<<endl;
        exit(1);
    }

    cout << "Please input the number range:(devide by a blank)" << endl;
    cin >> start >> end ;
    if(start > end)
    {
        swap(start, end);
    }

    cout << "Is additions and subtractions have negative result?(Y/N)" <<endl;
    cin >> ttmp;
    if(ttmp == 'y' || ttmp == 'Y')
    {
        isNeg = true;
    }else if (ttmp == 'N' || ttmp == 'n')
    {
        isNeg = false;
    }else
    {
        cout << "Error input!"<<endl;
        exit(1);
    }

    cout << "Is divisions have remainder?(Y/N)" <<endl;
    cin >> ttmp;
    if(ttmp == 'y' || ttmp == 'Y')
    {
        isRem = true;
    }else if (ttmp == 'N' || ttmp == 'n')
    {
        isRem = false;
    }else
    {
        cout << "Error input!"<<endl;
        exit(1);
    }

    for(;items.size() != itemNum ;)    //根据条件生成问题
    {
        string num = getNum(start,end,isParentheses);
        while (num.find(",") != string::npos)
        {
            addFlag = true;
            if( num[num.find(",") + 2] == '(')     //运算符后紧跟括号,运算符选取只和isMulandDiv有关
            {
                char op = getOperator("1",isMulandDiv);
                stringstream ss;
                ss << op;
                num = num.replace(num.find(","),1,ss.str());
            }else                             //运算符后是数字，运算符选取和num2和isMulandDiv有关，此时是不带括号或最右边的算式
            {
                string num2 = num.substr(num.find_last_of(",") + 2, num.find_first_of(")") - num.find_last_of(",") - 3);   //error at num.find(")",num.find(",") + 2) - 1
                char op = getOperator(num2,isMulandDiv);
                stringstream ss;
                ss << op;
                num = num.replace(num.find(","),1,ss.str());
                int begin = 0;    //找到形如 a op b 的式子
                if(num.find("(") != string::npos)   //如果式子里有()的话
                    begin = num.find_last_of("(") + 2;
                string num1 = num.substr(begin,num.find(ss.str()) - 1);
                //num2 = num.substr(num.find_last_of(ss.str()) + 2,num.find_first_of(")") - 1);
                if(op == '-' || op == '+')
                {

                    if(!isNeg && isNegative(num1,num2,op))
                    {
                        addFlag = false;
                        break;
                    }

                }else if(op == '/')
                {
                    if(!isRem && isRemainder(num1,num2))
                    {
                        addFlag = false;
                        break;
                    }
                }
            }

        }
        if(!addFlag)    //满足要求，可以添加
        {
            continue;
        }

        if(!isDup(items,num))    //判断是否重复,不重复则添加
        {
            items.push_back(num);
        }
    }
    printAndCheck(items,isCmd);

    return 0;
}

该版本在02版本的基础上有所改动，生成的数字和运算符之间都由空格分隔，以便于计算结果。
03版本主要添加的是bool checkResult(string exp,string result) 函数，
改函数的核心就是数据结构课本上栈的应用---表达式计算。
运算符的优先级关系表如下：

	+	-	*	/	(	)	#
+	>	>	<	<	<	>	>
-	>	>	<	<	<	>	>
*	>	>	>	>	<	>	>
/	>	>	>	>	<	>	>
(	<	<	<	<	<	=
)	>	>	>	>		>	>
#	<	<	<	<	<		=

checkResult(string exp,string result) 中表达式是以string传入
通过一个扫描标识位flag记录游标移动到的位置，

1. 建立并初始化符号栈ops和数值栈nums，将表达式起始符 # 压入符号栈ops。
2. 由扫描标识位flag扫描获取表达式中的数值或运算符，循环执行3~5直至求出整个表达式的值。
3. 取出ops的栈顶元素，当ops的栈顶元素和当前扫描到的符号均为 # 时，整个表达式求值完成，这时nums的栈顶元素为表达式的值。
4. 若取出的字符串不是运算符，则压入nums，并继续扫描。
5. 若取出的字符串是运算符，则根据ops栈顶元素和运算符优先级比较结果，做不同处理。

　　　　①若 <，则运算符压入ops栈，并继续扫描。

　　　　②若 >,则弹出ops的栈顶运算符，从nums弹出两个数(此处弹出顺序注意)，进行相应计算，结果压入nums栈。

　　　　③若 =，则ops的站定元素是"("且运算符是")"，这时弹出ops的栈顶元素"("，相当于去掉括号，然后继续扫描。

在02版本print()函数改为void printAndCheck(vector<string> &items, bool isCmd)，当cmd输出时执行检查结果功能，(鉴于是小学题目，结果只接受整数和分数)。

结果的判断是用两个double类型变量进行比较。如果两者的差的绝对值小于10^-4 ，则认为两数相等。

附上运行结果截图两张：

03版本完成，欢迎老师同学提出批评意见。。。。

我的结对开发队友 信1301-1 刘伟