中缀表达式求值
通过把“中缀转后缀”和“后缀求值”两个算法功能集成在一起(非简单的顺序调用),
实现对中缀表达式直接求值,新算法还是从左到右扫描中缀表达式,
但同时使用两个栈,一个暂存操作符,一个暂存操作数,来进行求值。
(支持 + - * / ^ 五种运算)
输入格式:
共1行,为1个字符串,即一个中缀表达式,
其中每个数字或符号间由一个空格隔开。
输出格式:
共1行,为一个整数,即求值的结果。
输入样例:
( 2 + 3 ) * 6 + 4 / 2
输出样例:
32
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <malloc.h>
#include <math.h>
#define maximum 100000
typedef struct
{
float data[maximum];
int top;
}number;
typedef struct
{
char data[maximum];
int top;
}sign;
void InitNumber(number *stack);
void GetTopNumber(number stack, float *e);
void PushNumber(number *stack, float e);
void PopNumber(number *stack, float *e);
void InitSign(sign *stack);
void GetTopSign(sign stack, char *e);
void PushSign(sign *stack, char e);
void PopSign(sign *stack, char *e);
void Calculate(number *stack, char e);
number Num;
sign sig;
char expression[maximum];
int main()
{
gets(expression);
int length;
length=strlen(expression);
int i;
float en,n;
char es;
InitNumber(&Num);
InitSign(&sig);
for (i=0;i<length;i++)
{
if(expression[i]>='0'&&expression[i]<='9')
{
n=expression[i]-'0';
while (expression[i+1]!='\0')
{
if (expression[i+1]>='0'&&expression[i+1]<='9')
{
n=n*10+expression[i+1]-'0';
++i;
}
else break;
}
PushNumber(&Num,n);
}
else if (expression[i]=='+'||expression[i]=='-'||expression[i]=='*'||expression[i]=='/'||expression[i]=='^'||expression[i]=='('||expression[i]==')')
{
switch (expression[i])
{
case '+':
if(sig.data[sig.top-1]!='+'&&sig.data[sig.top-1]!='-'&&sig.data[sig.top-1]!='*'&&sig.data[sig.top-1]!='/'&&sig.data[sig.top-1]!='^')
PushSign(&sig,'+');
else
{
while (sig.top>0&&sig.data[sig.top-1]!='(')
{
PopSign(&sig,&es);
Calculate(&Num,es);
}
PushSign(&sig,'+');
}
break;
case '-':
if(sig.data[sig.top-1]!='+'&&sig.data[sig.top-1]!='-'&&sig.data[sig.top-1]!='*'&&sig.data[sig.top-1]!='/'&&sig.data[sig.top-1]!='^')
PushSign(&sig,'-');
else
{
while (sig.top>0&&sig.data[sig.top-1]!='(')
{
PopSign(&sig,&es);
Calculate(&Num,es);
}
PushSign(&sig,'-');
}
break;
case '*':
if(sig.data[sig.top-1]!='*'&&sig.data[sig.top-1]!='/'&&sig.data[sig.top-1]!='^')
PushSign(&sig,'*');
else
{
while (sig.top>0&&sig.data[sig.top-1]!='(')
{
PopSign(&sig,&es);
Calculate(&Num,es);
}
PushSign(&sig,'*');
}
break;
case '/':
if(sig.data[sig.top-1]!='*'&&sig.data[sig.top-1]!='/'&&sig.data[sig.top-1]!='^')
PushSign(&sig,'/');
else
{
while (sig.top>0&&sig.data[sig.top-1]!='(')
{
PopSign(&sig,&es);
Calculate(&Num,es);
}
PushSign(&sig,'/');
}
break;
case '^':
if(sig.data[sig.top-1]!='^')
PushSign(&sig,'^');
else
{
while (sig.top>0&&sig.data[sig.top-1]!='(')
{
PopSign(&sig,&es);
Calculate(&Num,es);
}
PushSign(&sig,'^');
}
case '(':
PushSign(&sig,'(');
break;
case ')':
while (sig.data[sig.top-1]!='(')
{
PopSign(&sig,&es);
Calculate(&Num,es);
}
PopSign(&sig,&es);
}
}
}
while (sig.top>0)
{
PopSign(&sig,&es);
Calculate(&Num,es);
}
GetTopNumber(Num,&en);
printf("%.0f\n",en);
return 0;
}
void InitNumber(number *stack)
{
stack->top=0;
}
void GetTopNumber(number stack, float *e)
{
if(stack.top==0) return;
else *e=stack.data[stack.top-1];
}
void PushNumber(number *stack, float e)
{
if(stack->top>=maximum) return;
else stack->data[stack->top++]=e;
}
void PopNumber(number *stack, float *e)
{
if(stack->top==0) return;
else *e=stack->data[--stack->top];
}
void InitSign(sign *stack)
{
stack->top=0;
}
void GetTopSign(sign stack, char *e)
{
if(stack.top==0) return;
else *e=stack.data[stack.top-1];
}
void PushSign(sign *stack, char e)
{
if(stack->top>=maximum) return;
else
{
stack->data[stack->top]=e;
stack->top++;
}
}
void PopSign(sign *stack, char *e)
{
if(stack->top==0) return;
else *e=stack->data[--stack->top];
}
void Calculate(number *stack, char e)
{
float num1,num2,result;
PopNumber(stack, &num2);
PopNumber(stack, &num1);
switch (e)
{
case '+':
result=num1+num2;
PushNumber(stack,result);
break;
case '-':
result=num1-num2;
PushNumber(stack,result);
break;
case '*':
result=num1*num2;
PushNumber(stack,result);
break;
case '/':
if (num2==0) printf("表达式错误!");
else
{
result=num1/num2;
PushNumber(stack,result);
break;
}
case '^':
result=pow(num1,num2);
PushNumber(stack,result);
break;
}
}