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;
};
classNum
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();
}
setProblem
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();
}
setGrade
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;
}
main
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
时间： 2024-11-09 07:34:51