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题目1：完成一个命令行的四则运算程序
前言
刚刚看到这个题目的时候，我在想，不就是一个加减乘除的程序么？分分钟就写完了。等我看到需求的时候，我头都大了一圈……。我将需求分成了几个需要解决的问题：
1：支持分数运算。
2：表达式生成与计算。
3：判断正误。
正文
首先，是如何支持分数运算。既然要支持分数运算，那么肯定要表示分数，所以就要创建一个分数类。而分数和整数是要混合运算的，那么显然，整数其实也是可以表现成分数。于是有了下面的类。在类中对操作符进行重载，便于计算表达式。在运算时自动执行transFrac()成员函数以保证计算后得到分数分子分母都不可再约分，以便输出时判断是按整数输出还是按分数输出。
class Num{public: Num(int numerator=0, int denominator = 1){ a = numerator; b = denominator; int p; p = (a + b - abs(a - b)) / 2; for (int i = 2; i <= p; ++i){ if (a%i == 0 && b%i == 0){ a /= i; b /= i; i = 2; } } } int getNume(){ return a; } int getDeno(){ return b; } void transFrac(Num &fra){ int p; p = (fra.a + fra.b - abs(fra.a - fra.b)) / 2; for (int i = 2; i <= p; ++i){ if (fra.a%i == 0 && fra.b%i == 0){ fra.a /= i; fra.b /= i; i = 2; } } } Num operator+(const Num rhs){ Num result; result.b = b*rhs.b; result.a = a*rhs.b + rhs.a*b; transFrac(result); return result; } Num operator-(const Num rhs){ Num result; result.b = b*rhs.b; result.a = a*rhs.b - rhs.a*b; transFrac(result); return result; } Num operator*(const Num rhs){ Num result; result.a = a*rhs.a; result.b = b*rhs.b; transFrac(result); return result; } Num operator/(const Num rhs){ Num result; result.a = a*rhs.b; result.b = b*rhs.a; transFrac(result); return result; } bool operator==(const Num rhs){ if (a == rhs.a&&b == rhs.b) return true; else return false; } Num operator=(const int rhs){ a = rhs; b = 1; return *this; } Num operator=(const Num rhs){ a = rhs.a; b = rhs.b; return *this; }private: int a; int b;};
其次，是表达式生成与计算。如果是任意生成的表达式，那么在计算表达式的值的时候，就需要在表达式求值上做大量的工作，如判断优先级，通过栈等转化表达式，最后才是计算得到结果。时间有限，我就使用了比较低端的方法，那就是固定表达式的格式，然后通过分配各个位置上的值和运算符来完成简易的表达式生成，并通过检查结果来判断两个表达式是否重复。将生成的表达式存储在题库中等待完成。
void setProbAndAns(int proNum, int proLevel){ ofstream ofsQues; ofstream ofsAnsw; ofsQues.open("Questions.txt", ofstream::out); ofsAnsw.open("Answer.txt", ofstream::out); char Expression[100]; char Answer[10]; srand((unsigned)time(NULL)); int a, b, c, d, e1, e2, e3; Num lhs, rhs, res; for (int i = 0; i < proNum; ++i){ vector<Num>A(proNum); vector<Num>B(proNum); vector<Num>C(proNum); vector<Num>D(proNum); //4 position of number vector<Num>R(proNum); //result a = rand() % proLevel; b = rand() % proLevel+1; c = rand() % proLevel; d = rand() % proLevel+1; A[i] = a; B[i] = b; C[i] = c; D[i] = d; vector<char>E1(proNum); vector<char>E2(proNum); vector<char>E3(proNum); e1 = rand() % 4; e2 = rand() % 2; e3 = rand() % 4; switch (e1){ case 0: E1[i] = ‘+‘; lhs = A[i] + B[i]; break; case 1: E1[i] = ‘-‘; lhs = A[i] - B[i]; break; case 2: E1[i] = ‘*‘; lhs = A[i] * B[i]; break; case 3: E1[i] = ‘/‘; lhs = A[i] / B[i]; break; } switch (e3){ case 0: E3[i] = ‘+‘; rhs = C[i] + D[i]; if (e2 == ‘-‘) rhs = C[i] - D[i]; break; case 1: E3[i] = ‘-‘; rhs = C[i] - D[i]; if (e2 == ‘-‘) rhs = C[i] + D[i]; break; case 2: E3[i] = ‘*‘; rhs = C[i] * D[i]; break; case 3: E3[i] = ‘/‘; rhs = C[i] / D[i]; break; } switch (e2){ case 0: E2[i] = ‘+‘; res = lhs + rhs; break; case 1: E2[i] = ‘-‘; res = lhs - rhs; break; } if (res.getNume() < 0){ i -= 1; continue; } else{ R[i] = res; } //ganrantee no repeat int flag = 0; for (int j = 0; j < i; ++j){ if (R[i] == R[j]){ flag = 1; break; } } if (flag == 1){ i -= 1; continue; } sprintf_s(Expression, "%d %c %d %c %d %c %d = ", A[i].getNume(), E1[i], B[i].getNume(), E2[i], C[i].getNume(), E3[i], D[i].getNume()); if (R[i].getDeno() == 1||R[i].getNume() == 0) sprintf_s(Answer, "%d:%d", i + 1, R[i].getNume()); else sprintf_s(Answer, "%d:%d/%d", i + 1, R[i].getNume(), R[i].getDeno()); ofsQues << Expression << endl;; ofsAnsw << Answer << endl; } ofsQues.close(); ofsAnsw.close();}
最后，是判断正误。在题库生成的同时，答案也同时生成。此时程序会等待用户在题库中填写答案。填写完毕后输入1得到结果。由于有分数的存在，所以我通过比较题库中=后面略过所有空白符后的字符串与答案:后面的字符串来对比是否正确，正确的题号会被记录，最终格式化输出置Grade文件里保存起来以供用户查看。
void setGrade(int proNum){ ifstream ifsQus; ifstream ifsAns; ofstream ofsGra; ifsQus.open("Questions.txt",ifstream::in); ifsAns.open("Answer.txt",ifstream::in); ofsGra.open("Grade.txt",ofstream::app); char ques[100]; char answ[10]; char grade[500]; int gra; vector<int>right(proNum); int i,j; int a, b; for (i = 0; i < proNum; ++i) right[i] = 0; for (i = 0,j=0; i < proNum;++i){ ifsQus.getline(ques, 100); ifsAns.getline(answ, 10); for (a = 0; ques[a] != ‘=‘; ++a) ; for (b = a; ques[b] != ‘ ‘; ++b) ; for (a = 0; answ[a] != ‘:‘; ++a) ; if (isCorrect(b+1,a+1,ques,answ)){ j++; right[i] = 1; } } vector<int>rightPos(j); for (i = 0,j=0; i < proNum; ++i){ if (right[i] == 1){ rightPos[j] = i; ++j; } } char num[10]; sprintf_s(grade,"Correct:%d( ",j); for (i = 0; i < j; ++i){ sprintf_s(num,"%d ",rightPos[i]+1); strcat_s(grade,num); } strcat_s(grade, ")"); ofsGra << grade << endl; ifsQus.close(); ifsAns.close(); ofsGra.close();}
在主函数中提供了选项让用户选择生成什么样规模和数量的问题，由于我觉得不会有人一下子做几百道这种题，所以我并没有写出那些离谱的选项，当然程序本身其实是支持生成上千上万道题的（笑）。
int main(void){ int option; int proNum; int proLevel; cout << "Please choose the number of the problem:" << endl; cout << "1.10 2.100" << endl; cout << "3.200 4.500" << endl; cin >> option; switch (option){ case 1: proNum = 10; break; case 2: proNum = 100; break; case 3: proNum = 200; break; case 4: proNum = 500; break; default: proNum = 50; break; } cout << "Please choose the level of the problem:" << endl; cout << "1.10 2.50" << endl; cout << "3.100 " << endl; cin >> option; switch (option){ case 1: proLevel = 10; break; case 2: proLevel = 50; break; case 3: proLevel = 100; break; default: proLevel = 30; break; } setProbAndAns(proNum, proLevel); cout << "Please write the answers in the Questions.txt and save." << endl; cout << "Enter 1 to get the Grade" << endl; cin >> option; while (option != 1){ cout << "Please enter again:" << endl; cin >> option; } setGrade(proNum); cout << "Open the Grade.txt to check your grade!" << endl; Sleep(10000); return 0;}
这个程序还有很多很多不完善的地方，尤其是生成表达式和计算表达式那一块，完全可以更好更完善，这就有待以后有时间在github上慢慢改进了（笑）。
完整程序地址：https://github.com/MorriganMesser/ArithmeticBank
博客编辑：尉智辉
题目1：完成一个命令行的四则运算程序
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