栈应用---计算表达式

为实现运算符优先级，可以使用两个工作栈，一个用来存操作数(opnd)，另一个存操作符(optr)

基本思想是：1.首先置两个栈为空栈.依次读入表达式中的每个字符，若是操作数，则进opnd,若是运算符，则和optr栈顶元素比较，这时分三种情况

1.栈顶元素优先级低

直接进栈

2.相等('栈顶为'(',与之想比较的操作符为')'')

出栈,(脱去左括号)

3.栈顶元素优先级大

1.optr出栈op，得到操作符

2opnd,出栈,s1,出栈s2,

3.s1,s2,op,进行运算，并将结果放入opnd中

上述操作完成后，基本工作已经完成，之后，再一一取栈中元素，运算

+ - * / ( ) #

+ > > < < < > >

- > > < < < > >

* > > > > < > >

/ > > > > < > >

( < < < < < =

) > > > > > >

# < < < < < =

#include <stdio.h>
#include <malloc.h>
#include <string.h>

#define NULL 0
#define TRUE 1
#define FALSE 0

#define RIGHT 1
#define DOWN  2
#define LEFT  3
#define UP    4

const int width = 10;
const int height = 10;
int maze[height][width]={
//0,1,2,3,4,5,6,7,8,9
{1,1,1,1,1,1,1,1,1,1},//0
{1,0,0,1,0,0,0,1,0,1},//1
{1,0,0,1,0,0,0,1,0,1},//2
{1,0,0,0,0,1,1,0,0,1},//3
{1,0,1,1,1,0,0,0,0,1},//4
{1,0,0,0,1,0,0,0,0,1},//5
{1,0,1,0,0,0,1,0,0,1},//6
{1,0,1,1,1,0,1,1,0,1},//7
{1,1,0,0,0,0,0,0,0,1},//8
{1,1,1,1,1,1,1,1,1,1},//9
};

int foot[height][width]={0};

typedef struct PosType
{
int x;
int y;
}PosType;

/*typedef struct {
PosType pos;
int di;
}ElemType;
*/

typedef char ElemType;

typedef struct
{
int **path;
int width;
int height;
}MazePath;
//地图
MazePath mazepath = {(int **)maze,width,height};

typedef struct _stack
{
ElemType data;
struct _stack* next;
}Stack , *PStack;

const int nLEN = sizeof(Stack);

void InitStack(PStack* head)
{
(*head) = (PStack)malloc(nLEN);
//	(*head)->data = NULL;
(*head)->next = 0;
}

void DestroyStack(PStack *head)
{
PStack p = *head;
PStack p1 = p;
while(p)
{
p = p->next;
free(p1);
p1 = p;
}
}

void CleadStack(PStack *head)
{

PStack p = (*head)->next;
PStack p1 = p;
while(p)
{
p = p->next;
free(p1);
p1 = p;
}
}

int StackEmpty(PStack s)
{
s = s->next;
if(s!=NULL)
return FALSE;
else return TRUE;
}

int StackLength(PStack s)
{
s = s->next;
int nSize = 0;
while(s!=NULL)
{
nSize++;
s = s->next;
}
return nSize;
}

int GetTop(PStack s,ElemType *data)
{
if(!StackEmpty(s))
{
s = s->next;
*data = s->data;
return TRUE;
}
return FALSE;
}

int Push(PStack s,ElemType data)
{
PStack temp = (PStack)malloc(nLEN);
temp->data = data;
temp->next = NULL;

//
temp->next = s->next;
s->next = temp;

return TRUE;
}

int Pop(PStack s,ElemType *data)
{
if(StackEmpty(s))
return FALSE;

PStack temp = s->next;
*data = temp->data;
s->next = s->next->next;

free(temp);

return TRUE;
}

//能否通过
int Canpass(PosType pos)
{
int x = pos.x;
int y = pos.y;
//已经走过
if(foot[y][x]==1)
{
return FALSE;
}
//有障碍
int (*p)[width] = (int(*)[width])(mazepath.path);
if(p[y][x]==1)
{
return FALSE;
}
return 1;
}

//留下足迹
void MarkFoot(PosType pos)
{
int x = pos.x;
int y = pos.y;
foot[y][x] = 1;
}

PosType NextPos(PosType pos,int di)
{
PosType p;
if(di==RIGHT)
{
p.x = pos.x +1;
p.y = pos.y;
}
else if(di == LEFT)
{
p.x = pos.x-1;
p.y = pos.y;
}
else if(di==DOWN)
{
p.x = pos.x;
p.y = pos.y+1;
}
else if(di == UP)
{
p.x = pos.x;
p.y = pos.y-1;
}

return p;
}
char Precede(char ch1,char ch2)
{
//	if(ch1 == ch2)
//		return '=';
if(ch1==' ')
return '<';

if(ch1=='+')
{
if(ch2=='+')
return '<';

if(ch2=='-')
return '>';

if(ch2=='*')
return '<';

if(ch2=='/')
return '<';

if(ch2=='(')
return '<';

if(ch2==')')
return '>';
}

else if(ch1=='-')
{
if(ch2=='+')
return '<';

if(ch2=='-')
return '>';

if(ch2=='*')
return '<';

if(ch2=='/')
return '<';

if(ch2=='(')
return '<';

if(ch2==')')
return '>';

}

else if(ch1=='*')
{
if(ch2=='+')
return '>';

if(ch2=='-')
return '>';

if(ch2=='*')
return '>';

if(ch2=='/')
return '>';

if(ch2=='(')
return '<';

if(ch2==')')
return '>';
}

else if(ch1=='/')
{
if(ch2=='+')
return '>';

if(ch2=='-')
return '>';

if(ch2=='*')
return '>';

if(ch2=='/')
return '>';

if(ch2=='(')
return '<';

if(ch2==')')
return '>';
}

else if(ch1=='(')
{
if(ch2=='+')
return '<';

if(ch2=='-')
return '<';

if(ch2=='*')
return '<';

if(ch2=='/')
return '<';

if(ch2=='(')
return '<';

if(ch2==')')
return '=';
}

else if(ch1==')')
{
if(ch2=='+')
return '>';

if(ch2=='-')
return '>';

if(ch2=='*')
return '>';

if(ch2=='/')
return '>';

if(ch2=='(')
return ' ';

if(ch2==')')
return '>';
}
}

int IsNum(char ch)
{
if(ch<='9' && ch>='0')
return TRUE;
return FALSE;
}

char calc(char a,char op,char b)
{

if(op=='+')
return a+b;
if(op=='-')
return a-b;
if(op=='*')
return a*b;
if(op=='/')
return a/b;
}

int EvalueateExpression(char *buf,int nlen)
{
char ch=0;
int i=0;
PStack opnd,optr;
InitStack(&opnd);//操作数
InitStack(&optr);//操作符
ElemType nd;
ElemType tr;
for(i = 0 ; i < nlen ; i++)
{
ch = buf[i];
//数字
if(IsNum(ch))
{
nd = ch-48;
Push(opnd,nd);
}
//操作符
else
{
tr = ' ';
GetTop(optr , &tr);
char cRet = Precede(tr , ch);

if(cRet =='<')
{
Push(optr,ch);
}

else if(cRet =='=')
{
Pop(optr,&tr);
}

else if(cRet=='>')
{
char op;
Pop(optr,&op);
char a1,a2;
Pop(opnd,&a1);
Pop(opnd,&a2);
char ret = calc(a2 , op , a1);
Push(opnd , ret);
i--;
}
}
}
while(!StackEmpty(optr))
{
char op;
Pop(optr,&op);
char a1,a2;
Pop(opnd,&a1);
Pop(opnd,&a2);
char ret = calc(a2 , op , a1);
//		printf("ret = %d",ret);
Push(opnd , ret);
}
if(!StackEmpty(opnd))
{
char cRet = 0;
Pop(opnd,&cRet);
printf("%-d\n",cRet);
}
return 0;

}

int main()
{
char buf[]="3*5";
int nlen = strlen(buf);
EvalueateExpression(buf , nlen);
printf("\n");
return 0;
}