数据结构——栈的应用（表达式求值）（C语言）

char Precede(char t1, char t2)函数用于输出t1,t2两个运算符的优先级（t1为先出现的运算符（已经压入栈OPTR中），t2为后出现的运算符）

char Precede(char t1, char t2){  
    int i,j;  
    char pre[][7]={           
    //运算符之间的优先级制作成一张表格  
        {'>','>','<','<','<','>','>'},  
        {'>','>','<','<','<','>','>'},  
        {'>','>','>','>','<','>','>'},  
        {'>','>','>','>','<','>','>'},  
        {'<','<','<','<','<','=','0'},  
        {'>','>','>','>','0','>','>'},  
        {'<','<','<','<','<','0','='}};  
    switch(t1){  
        case '+': i=0; break;  
        case '-': i=1; break;  
        case '*': i=2; break;  
        case '/': i=3; break;  
        case '(': i=4; break;  
        case ')': i=5; break;  
        case '=': i=6; break;  
    }  
    switch(t2){  
        case '+': j=0; break;  
        case '-': j=1; break;  
        case '*': j=2; break;  
        case '/': j=3; break;  
        case '(': j=4; break;  
        case ')': j=5; break;  
        case '=': j=6; break;  
    }  
    return pre[i][j];  
}  

调试代码：（栈的相关操作实现也在其中）

#include 
#include 

#define TRUE 1
#define FALSE 0
#define OK 1
#define ERROR 0
#define INFEASIBLE -1  
#define OVERFLOW -2
#define STACK_INIT_SIZE 100   //存储空间初始分配量
#define STACKINCREMENT 10   //存储空间分配增量

typedef char SElemType;
typedef char OperandType;   //表达式求值的运算类型
typedef int Status;

typedef struct
{
	SElemType *base;
	SElemType *top;
	int stacksize;
}SqStack;

//构造一个空栈
Status InitStack(SqStack *S)
{
	S->base = (SElemType *)malloc(STACK_INIT_SIZE * sizeof(SElemType));
	if(!S->base)
	{
		printf("内存分配失败!\n");
		exit(OVERFLOW);
	}

	S->top = S->base;
	S->stacksize = STACKINCREMENT;
	return OK;
}

//若栈不为空，则用e返回S的栈顶元素，并返回OK；否则返回ERROR
Status GetTop(SqStack *S, SElemType *e)
{
	if(S->top == S->base)
		return ERROR;

	*e = *(S->top - 1);
	return OK;
}

//插入元素e为新的栈顶元素
Status Push(SqStack *S, SElemType e)
{
	if(S->top - S->base >= STACK_INIT_SIZE)   //栈满， 追加存储空间
	{
		S->base = (SElemType *)realloc(S->base, (S->stacksize + STACKINCREMENT) * sizeof(SElemType));
		if(!S->base)
		{
			printf("内存分配失败!\n");
			exit(OVERFLOW);
		}

		S->top = S->base + S->stacksize;
		S->stacksize += STACKINCREMENT;
	}

	*S->top++ = e;
	
	return OK;
}

//若栈不为空，则删除S的栈顶元素，用e返回其值，并返回Ok；否则返回ERROR
Status Pop(SqStack *S, SElemType *e)
{
	if(S->top == S->base)
		return ERROR;

	*e =  *--S->top;

	return OK;
}
//销毁栈S，使其不复存在
Status StackDestroy(SqStack *S)
{
	free(S->base);
	S->base = NULL;
	S->top = NULL;
	S->stacksize = 0;
	return OK;
}

//清空栈S，保留栈底指针
void ClearStack(SqStack *S)
{
	S->top = S->base;
}

//根据教科书表3.1，判断两符号的优先关系
char Precede(char t1, char t2){  
    int i,j;  
    char pre[][7]={           
    //运算符之间的优先级制作成一张表格  
        {'>','>','<','<','<','>','>'},  
        {'>','>','<','<','<','>','>'},  
        {'>','>','>','>','<','>','>'},  
        {'>','>','>','>','<','>','>'},  
        {'<','<','<','<','<','=','0'},  
        {'>','>','>','>','0','>','>'},  
        {'<','<','<','<','<','0','='}};  
    switch(t1){  
        case '+': i=0; break;  
        case '-': i=1; break;  
        case '*': i=2; break;  
        case '/': i=3; break;  
        case '(': i=4; break;  
        case ')': i=5; break;  
        case '=': i=6; break;  
    }  
    switch(t2){  
        case '+': j=0; break;  
        case '-': j=1; break;  
        case '*': j=2; break;  
        case '/': j=3; break;  
        case '(': j=4; break;  
        case ')': j=5; break;  
        case '=': j=6; break;  
    }  
    return pre[i][j];  
}  
//判断c是否为运算符
Status In(OperandType c)
{
	switch(c)
	{
	case '+':
	case '-':
	case '*':
	case '/':
	case '(':
	case ')':
	case '=':
		return TRUE;
	default:
		return FALSE;
	}

}

//二元运算(a theta b)
OperandType Operate(OperandType a, OperandType theta, OperandType b)
{
	OperandType c;
	switch(theta)
	{
	case '+':
		c = a + b;
		break;
	case '-':
		c = a - b;
		break;
	case '*':
		c = a * b;
		break;
	case '/':
		c = a / b;
		break;
	}
	return c;
}

//算术表达式求值的算符优先算法，设OPTR和OPND分别为运算符栈和运算数栈，OP为运算符集合
OperandType EvaluateExpression()
{
	SqStack OPTR, OPND;
	OperandType a, b, d, x, theta;
	char c;   //存放有键盘输入的字符串
	char z[6];   //存放整数字符串
	int i;
	InitStack(&OPTR);   //初始化运算符栈
	Push(&OPTR, '=');   //=是表达式结束符
	InitStack(&OPND);   //初始化运算数栈

	c = getchar();
	GetTop(&OPTR, &x);
	while(c != '=' || x != '=')
	{
		if(In(c))   //是7种运算符之一
		{
			switch(Precede(x, c))
			{
			case '<':   //当前已经压栈一个运算符（x）比后一个运算符（c）低时，就将c压栈
				Push(&OPTR, c);
				c = getchar();
				break;
			case '=':
				Pop(&OPTR, &x);   //脱括号并接收下一字符
				c = getchar();
				break;
			case '>':
				Pop(&OPTR, &theta);   //退栈并将运算结果压入OPND中
				Pop(&OPND, &b);
				Pop(&OPND, &a);
				Push(&OPND, Operate(a, theta, b));
				break;
			}
		}
			else if(c >= '0' && c <= '9')   //c是操作数
			{
				i = 0;
				do
				{
					z[i] = c;
					i ++;
					c = getchar();
				}while(c >= '0' && c <= '9');
				z[i] = 0;
				d = atoi(z);   //将字符数组转为整型存于d
				Push(&OPND, d);
			}
			else   //c为非法字符
			{
				printf("ERROR3\n");
				exit(1);
			}
			GetTop(&OPTR, &x);
		}
	GetTop(&OPND, &x);
	StackDestroy(&OPTR);
	StackDestroy(&OPND);
	return x;
}

int main()
{
	printf("请输入算术表达式，负数要用（0-正数:\n");
	printf("%d\n", EvaluateExpression());
	return 0;