问题描述：给定一个算术表达式，通过程序求出最后的结果。
基本要求：
1． 从键盘输入要求解的算术表达式；
2． 采用栈结构进行算术表达式的求解过程；
3． 能够判断算术表达式正确与否；
4． 对于错误表达式给出提示；
5． 对于正确的表达式给出最后的结果；
附程序和图加主要思想
#include<stdio.h>
#include<stdlib.h>
#define STACK_SIZE 10 //存储空间初始分配量
#define STACK_INCREASE 5 //存储空间分配增量
typedef struct { //寄存运算符
char* base; //栈底指针
char* top; //栈顶指针
int stacksize; //当前可使用最大容量
}OPTR;
typedef struct { //寄存操作数
double* base;
double* top;
int stacksize;
}OPND;
int InitStack(OPTR* s);
int InitStack(OPND* s);
int Push(OPTR* s, char e);
int Push(OPND* s, double e);
int Pop(OPTR* s, char* e);
int Pop(OPND* s, double* e);
char Gettop(OPTR* s);
double Gettop(OPND* s);
int In(char e);
char Precede(char a, char b);
double Operate(double a, double b, char t);
//主函数
int main()
{
OPTR optr;
OPND opnd;
OPND temp; //临时存储数字，构造多位数
char c; //接收表达式
char y; //接收脱掉的括号和井号
char theta; //接收脱出进行运算的运算符
double a, b; //接收脱出进行运算的操作数
int g = 1;
while(g)
{
system("cls");
double x = 0, z = 0; //多位数转换
int n = 1; //幂
int error = 0; //输入格式错误则报错
InitStack(&optr);
InitStack(&opnd);
InitStack(&temp);
printf("请输入整数表达式（以#结束）：\n");
Push(&optr, '#');
c = getchar();
while (c != '#' || Gettop(&optr) != '#')
{
if (c == '0') {
Push(&opnd, (double)z);
c = getchar();
}
else
{
while (!In(c))
{ //将多位数存入临时栈
Push(&temp, c - '0'); //字符转数字
c = getchar();
}
while (temp.base != temp.top)
{ //将临时栈中的数重组为多位数
Pop(&temp, &x);
z = z + x * n;
n *= 10;
}
n = 1;
if (z)Push(&opnd, (double)z);//重组后的多位数入栈
z = 0;
}
if (In(c))
{
switch (Precede(Gettop(&optr), c))
{
case '<':
Push(&optr, c);
c = getchar();
break;
case '=':
Pop(&optr, &y);
c = getchar();
break;
case '>':
Pop(&optr, &theta);
Pop(&opnd, &b);
Pop(&opnd, &a);
Push(&opnd, Operate(a, b, theta));
break;
case '!':
printf("输入错误！");
error = 1;
break;
}
}
if (error)break;
}
if (!error)
printf("结果为：%.2f\n", Gettop(&opnd));
system("pause");
}
return 0;
}
//构造空栈s
int InitStack(OPTR* s) {
s->base = (char*)malloc(STACK_SIZE * sizeof(char));
if (!s->base)
exit(0);//存储分配失败
s->top = s->base;
s->stacksize = STACK_SIZE;
return 1;
}
int InitStack(OPND* s) {
s->base = (double*)malloc(STACK_SIZE * sizeof(double));
if (!s->base)
exit(0);
s->top = s->base;
s->stacksize = STACK_SIZE;
return 1;
}
//插入元素e为新的栈顶
int Push(OPTR* s, char e) {
if (s->top - s->base >= s->stacksize) {//栈满，追加存储空间
s->base = (char*)realloc(s->base,
(s->stacksize + STACK_INCREASE) * sizeof(char));
if (!s->base)
exit(0);
s->top = s->base + s->stacksize;
s->stacksize += STACK_INCREASE;
}
*(s->top) = e;
s->top++;
}
int Push(OPND* s, double e) {
if (s->top - s->base >= s->stacksize) {
s->base = (double*)realloc(s->base,
(s->stacksize + STACK_INCREASE) * sizeof(double));
if (!s->base)
exit(0);
s->top = s->base + s->stacksize;
s->stacksize += STACK_INCREASE;
}
*(s->top) = e;
s->top++;
}
//删除栈顶元素,返回其值
int Pop(OPTR* s, char* e) {
if (s->top == s->base)return 0;
s->top--;
*e = *(s->top);
return 1;
}
int Pop(OPND* s, double* e) {
if (s->top == s->base)return 0;
s->top--;
*e = *(s->top);
return 1;
}
//判断栈是否为空，不为空则返回栈顶元素e
char Gettop(OPTR* s) {
if (s->top == s->base)
return 0;
char* e = s->top;
e--;
return *e;
}
double Gettop(OPND* s) {
if (s->top == s->base)
return 0;
double* e = s->top;
e--;
return *e;
}
//判断是否为运算符
int In(char e) {
if (e == '+' || e == '-' || e == '*' || e == '/' || e == '(' || e == ')' || e == '#')
return 1;
else return 0;
}
//判断优先级
char Precede(char a, char b) {
if (a == '+')
{
if (b == '*' || b == '/' || b == '(') return '<';
else return '>';
}
else if (a == '-')
{
if (b == '*' || b == '/' || b == '(') return '<';
else return '>';
}
else if (a == '*')
{
if (b == '(')return '<';
else return '>';
}
else if (a == '/')
{
if (b == '(')return '<';
else return '>';
}
else if (a == '(')
{
if (b == ')')return '=';
else if (b == '#') return '!';
else return '<';
}
else if (a == ')')
{
if (b == '(')return '!';
else return '>';
}
else if (a == '#')
{
if (b == ')')return '!';
if (b == '#')return '=';
else return '<';
}
}
//计算
double Operate(double a, double b, char theta) {
switch (theta)
{
case '+':
return a + b;
case '-':
return 1.0 * a - b;
case '*':
return a * b;
case '/':if (b != 0)
return 1.0 * a / b;
else
printf("输入错误！");
exit(0);
}
}