1 #include <iostream>
2 #include <string>
3 #include <cstring>
4 #include <cstdio>
5 #include <cctype>
6 #include <sstream>
7 using namespace std;
8
9 template<typename T>
10 class Stack
11 {
12 private:
13 T *base; //栈底指针
14 int top; //栈顶
15 int stackSize; //栈容量
16 public:
17 Stack(int m = 16); //构造函数
18 ~Stack() {
19 delete[]base; top = 0; stackSize = 0;
20 }
21 void Push(T x); //入栈
22 T Pop(); //出栈
23 T Top(); //获取栈顶元素
24 bool StackEmpty(); //测栈空
25 void ClearStack(); //清空栈
26 void StackTop(); //返回栈顶指针
27 void Capacity(); //返回栈容量
28 void StackTranverse(); //显示栈中元素(遍历)
29 };
30
31 template<typename T>
32 void Stack<T>::Capacity()
33 {
34 return stackSize;
35 }
36
37 template<typename T>
38 Stack<T>::Stack(int m)
39 {
40 base = new T[m];
41 if (!base) {
42 cout << "创建栈失败，退出!\n"; exit(1);
43 }
44 stackSize = m; top = -1; //栈顶(top = -1)为最底单元地址的下一处
45 }
46
47 template<typename T>
48 void Stack<T>::Push(T x)
49 {
50 if (top == stackSize - 1) throw "栈满，无法入栈";
51 base[++top] = x;
52 //cout << "top: " << top << endl;
53 }
54
55 template<typename T>
56 T Stack<T>::Pop()
57 {
58 T x;
59 if (top == -1) throw "栈空，不能出栈";
60 x = base[top--];
61 //cout << "top: " << top << endl;
62 return x;
63 }
64
65 template<typename T>
66 T Stack<T>::Top()
67 {
68 if (top == -1) throw "栈空，栈顶无元素";
69 //cout << "top: " << top << endl;
70 return base[top];
71 }
72
73 template<typename T>
74 bool Stack<T>::StackEmpty()
75 {
76 if (top == -1) return true;
77 return false;
78 }
79
80 template<typename T>
81 void Stack<T>::ClearStack()
82 {
83 top = -1;
84 }
85
86 //返回栈顶指针
87 template<typename T>
88 void Stack<T>::StackTop()
89 {
90 cout << "栈顶 top = " << top;
91 }
92
93 template<typename T>
94 void Stack<T>::StackTranverse()
95 {
96 int i = top;
97 while (i >= 0) {
98 cout << base[i--] << ‘\t‘;
99 }
100 cout << endl;
101 }
102
103
104 const int EXP_MAX = 50 + 10;
105 double Pow(double x, int n);
106 long long facI(int b);
107
108 //运算符优先级比较---栈顶优先级大,要出栈进行运算，栈顶小，当前运算符入栈
109 char Precede(char t1, char t2) //t1--栈顶, t2--当前运算符
110 {
111 switch (t2)
112 {
113 case ‘+‘:
114 case ‘-‘: if (t1 == ‘(‘ || t1 == ‘=‘) return ‘<‘; //栈顶运算符小，当前运算符直接入栈
115 else return ‘>‘;
116 case ‘*‘:
117 case ‘/‘:
118 case ‘%‘: if (t1 == ‘*‘ || t1 == ‘/‘ || t1 == ‘%‘ || t1 == ‘^‘ || t1 == ‘!‘ || t1 == ‘)‘) return ‘>‘;
119 else return ‘<‘; //如果t1是以上运算符，就 > , 否则就小
120 case ‘^‘: if (t1 == ‘)‘ || t1 == ‘!‘) return ‘>‘;
121 else return ‘<‘;
122 case ‘!‘: if (t1 == ‘)‘ || t1 == ‘!‘) return ‘>‘; //大于除了 , = 之外的常规运算符
123 else return ‘<‘;
124 case ‘(‘: if (t1 == ‘)‘) {
125 cout << "ERROR !\n"; exit(0);
126 }
127 else return ‘<‘;
128 case ‘)‘: switch (t1) {
129 case ‘(‘: return ‘=‘;
130 case ‘=‘: cout << "ERROR2" << endl; exit(0);
131 default: return ‘>‘;
132 }
133
134 case ‘=‘: switch (t1) {
135 case ‘=‘: return ‘=‘;
136 case ‘(‘: cout << "ERROR2" << endl; exit(0);
137 default: return ‘>‘;
138 }
139
140
141 default: cout << "Opera error !\n"; break;
142 }
143 }
144
145 //判断c是否是运算符
146 bool isOper(char c)
147 {
148 switch (c) {
149 case ‘+‘: case ‘-‘: case ‘*‘: case ‘/‘:
150 case ‘%‘: case ‘^‘: case ‘!‘:
151 case ‘(‘: case ‘)‘: case ‘=‘: return true;
152 default: return false;
153 }
154 }
155
156 //实施一次运算 --- 二元运算符
157 double Operate(double a, char op, double b)
158 {
159 switch (op) {
160 case ‘+‘: return a + b;
161 case ‘-‘: return a - b;
162 case ‘*‘: return a * b;
163 case ‘/‘: return a / b;
164 case ‘%‘: return (int)a % (int)b;
165 case ‘^‘: return Pow(a, b);
166 default:
167 cerr << "Opera wrong !\n"; exit(1);
168 }
169 }
170 //重载实施一次一元运算符运算
171 double Operate(double a, char op)
172 {
173 switch (op) {
174 case ‘!‘: return facI(a);
175 default:
176 cout << "Opera wrong !\n"; exit(1);
177 }
178 }
179
180 //将起始于p的子串解析为数值,并存入操作数栈
181 void readNumber(char *&p, Stack<double> &stk)
182 {
183 stk.Push((double)(*p - ‘0‘)); //当前数位对应的数位进栈
184 while (isdigit(*(++p))) {
185 stk.Push(stk.Pop() * 10 + (*p - ‘0‘));
186 }
187 if (‘.‘ != *p) return;
188 float fraction = 1; //否则,意味着还有小数部分,操作数解析完成
189 while (isdigit(*(++p))) {
190 stk.Push(stk.Pop() + (*p - ‘0‘)*(fraction /= 10));
191 }
192 }
193
194 //计算阶乘
195 long long facI(int b) { //计算阶乘
196 long long result = 1;
197 for (int i = 1; i <= b; i++)
198 result *= i;
199 return result;
200 }
201
202 double Pow(double x, int n) //计算乘方
203 {
204 if (n == 0) return 1;
205 if (n == 1) return x;
206 if (n % 2 == 0) return Pow(x * x, n / 2);
207 else
208 return Pow(x * x, n / 2) * x;
209 }
210
211 //中缀表达式求值
212 double evaluate(char *exp)
213 {
214 Stack<char> optr(EXP_MAX); //运算符栈
215 Stack<double> opnd(EXP_MAX); //运算数栈
216 char op;
217
218 double pnd1, pnd2;
219 // char opstack; //用于opcur--当前运算符, opstack--栈顶运算符
220 // char conv[EXP_MAX]; //存放浮点数字符串
221
222 optr.Push(‘=‘); //将结束标志=推入栈中
223
224 // opcur = *exp++; //当前元素
225 // opstack = optr.Top(); //栈顶元素
226
227 while (*exp != ‘=‘ || optr.Top() != ‘=‘) //当前元素遇到 =, 或者到栈顶结束符 =
228 {
229 if (isdigit(*exp)) {
230 readNumber(exp, opnd);
231 }
232 else {
233 switch (Precede(optr.Top(), *exp))
234 {
235 case ‘<‘:
236 optr.Push(*exp); exp++;
237 break;
238 case ‘=‘: //遇到 ‘)‘,将栈顶的‘(‘弹出，并*exp++
239 optr.Pop(); exp++; break;
240 case ‘>‘:
241 op = optr.Pop();
242 if (op == ‘!‘) {
243 pnd1 = opnd.Pop(); //若属于一元运算符
244 opnd.Push(Operate(pnd1, op)); //实施一元运算
245 }
246 else { //对其他二元运算符
247 pnd2 = opnd.Pop(), pnd1 = opnd.Pop(); //后出栈的在运算符前:pnd1 op pnd2
248 opnd.Push(Operate(pnd1, op, pnd2));
249 }
250 break;
251 }
252 }
253 }
254 return opnd.Pop(); //返回最后计算出的数
255 }
256
257 //转换成后缀表达式
258 void CreatePostExp(const char *exp, char *&postexp)
259 {
260 Stack<char> op(EXP_MAX); //定义一个操作数栈
261 op.Push(‘=‘); //=是结束标志
262 // cout << "Exp : " << exp << endl;
263
264 // unsigned int j;
265 // unsigned int len = strlen(exp);
266 // //只有一个数的情况
267 // for (unsigned j = 0; j < len && (isdigit(exp[j]) || exp[j] == ‘.‘); j++) {
268 // postexp[j] = exp[j];
269 // }
270 // if (j == len) {
271 // postexp[j] = ‘ ‘;
272 // return;
273 // }
274
275 // for (unsigned int i = 0; i < len; i++) postexp[i] = ‘0‘;
276
277 int k = 0;
278 while (*exp)
279 {
280 if (isdigit(*exp) || *exp == ‘.‘) {
281 postexp[k++] = *exp++;
282 }
283 if (isOper(*exp)) {
284 postexp[k++] = ‘ ‘; //计算表达式时，‘ ‘可以作为一组数字结束的标志
285 switch (Precede(op.Top(), *exp)) {
286 case ‘<‘: //栈顶小，当前运算符进操作符栈
287 op.Push(*exp); exp++; break;
288 case ‘=‘: //遇到右括号，弹出左括号，*exp++
289 op.Pop(); exp++; break;
290 case ‘>‘: //遇到栈顶运算符优先级高的，则出栈，添加到后缀表达式的后面
291 postexp[k++] = op.Pop(); break;
292 }
293 }
294 postexp[k] = ‘\0‘; //填上结束标志
295 }
296 cout << "后缀表示为: " << postexp << endl;
297 }
298
299 //计算后缀表达试
300 double evaluateRPN(const char *postexp)
301 {
302 Stack<double> ans(EXP_MAX); //操作数栈
303
304 string tmp; //用来转换数字
305
306 // int len = strlen(postexp)
307 // for (int i = 0; i < len; i++)
308 while (*postexp != ‘\0‘) //末尾有结束标志
309 {
310 if (isdigit(*postexp) || *postexp == ‘.‘) {
311 tmp.push_back(*postexp); postexp++;
312 }
313 else if (*postexp == ‘ ‘) {
314 if (!tmp.empty()) {
315 double dtmp; istringstream ss(tmp); ss >> dtmp; //将tmp转换为double型数据
316 ans.Push(dtmp); tmp.clear(); //将数push到栈顶
317 }
318 postexp++;
319 }
320 else if (isOper(*postexp)) {
321 double opnd1 = 0, opnd2 = 0;
322 switch (*postexp)
323 {
324 case ‘!‘: //对于一元运算符
325 opnd1 = ans.Pop();
326 ans.Push(Operate(opnd1, *postexp)); //实施一元运算
327 postexp++; break;
328 default: //其他二元运算符
329 opnd2 = ans.Pop(), opnd1 = ans.Pop();
330 ans.Push(Operate(opnd1, *postexp, opnd2));
331 postexp++; break;
332 }
333 }
334 }
335 return ans.Pop();
336
337 }
338
339 int main()
340 {
341 //int i;
342 char exp[EXP_MAX] = "(2.2+5)+4*(5-3.1)=";
343
344 char *postexp;
345 postexp = new char[20];
346 *postexp = ‘\0‘;
347 //char c;
348 double v1;
349 int choice;
350 char pause;
351
352 do
353 {//显示主菜单
354 cout << "1-创建表达式\n";
355 cout << "2-表达式求值\n";
356 cout << "3-求后缀表达式\n";
357 cout << "4-后缀表达式求值\n";
358 cout << "5-显示表达式\n";
359 cout << "6-退出\n";
360 cout << "Enter choice:";
361 cin >> choice;
362 switch (choice)
363 {
364 case 1://创建表达式
365 cout << "请输入表达式，以=结束" << endl;
366 cin >> exp;
367 cin.get(pause);
368 system("pause");
369 break;
370 case 2://表达式求值
371 v1 = evaluate(exp);
372 cout << exp;
373 cout << v1 << endl;
374 cin.get(pause);
375 system("pause");
376 break;
377 case 3://求后缀表达式
378 CreatePostExp(exp, postexp);
379 cin.get(pause);
380 system("pause");
381 break;
382 case 4://后缀表达式求值
383 v1 = evaluateRPN(postexp);
384 cout << postexp << "=" << v1 << endl;
385 cin.get(pause);
386 system("pause");
387 break;
388 case 5:// 显示表达式
389 cout << endl;
390 cout << "已创建的表达式为：";
391 cout << exp << endl;
392 if (strlen(postexp))
393 {
394 cout << "后缀表达式为：";
395 cout << postexp << endl;
396 }
397 cin.get(pause);
398 system("pause");
399 break;
400 case 6://退出
401 cout << "结束运行，Bye-Bye!" << endl;
402 break;
403 default://
404 cout << "Invalid choice\n";
405 break;
406 }
407 } while (choice != 6);
408
409 return 0;
410 }//end main
测试:
时间： 2024-10-16 01:35:02