波兰表示法（Polish notation，或波兰记法），是一种逻辑、算术和代数表示方法，其特点是操作符置于操作数的前面，因此也称做前缀表示法。如果操作符的元数（arity）是固定的，则语法上不需要括号仍然能被无歧义地解析。波兰记法是波兰数学家扬·武卡谢维奇1920年代引入的，用于简化命题逻辑。
举个例子：
(3 + 4)*8 用逆波兰表示法表示为：3 4 + 8 *
先引用下：
从左至右扫描表达式，遇到数字时，将数字压入堆栈（stack.c)，遇到运算符时，弹出栈顶的两个数，用运算符对它们做相应的计算（次顶元素 op 栈顶元素），并将结果入栈；重复上述过程直到表达式最右端，最后运算得出的值即为表达式的结果。
例如后缀表达式“3 4 + 5 × 6 -”：
(1) 从左至右扫描，将3和4压入堆栈；
(2) 遇到+运算符，因此弹出4和3（4为栈顶元素，3为次顶元素，注意与前缀表达式做比较），计算出3+4的值，得7，再将7入栈；
(3) 将5入栈；
(4) 接下来是×运算符，因此弹出5和7，计算出7×5=35，将35入栈；
(5) 将6入栈；
(6) 最后是-运算符，计算出35-6的值，即29，由此得出最终结果。
地址：https://blog.csdn.net/antineutrino/article/details/6763722
思路就是这样子的：
关于堆栈
就是定义一个外部数组（ double val[MAXVAL] ）,这个就是上面说的堆栈了，用来存操作数，再定义一个变量（ int sp；）来记录栈顶的位置，void push(double f)就是用来存操作数的，double pop(void) 用来返回栈顶的操作数，
#define MAXVAL 100 /* maxinum depth of val stack */
double pop(void);
int sp=0; /* next free stack position */
double val[MAXVAL]; /* value stack */
/*push: push f onto value stack */
void push(double f)
{
if (sp < MAXVAL)
val[sp++] = f;
else
printf("eorror: stack full,can not push %g\n",f);
}
/* pop: pop and return top value form stack */
double pop(void)
{
if( sp > 0)
return val[--sp];
else
{
printf("error : stack empty\n");
return 0.0;
}
}
然后怎么输入呢？
先看一下main函数
int main(void)
{
int type;
double op2;
char s[MAXOP]；
clearStacks(var);
while((type = getop(s)) != EOF)
{
switch(type)
{
case NUMBER: //NUMBER '0' 表示是s[]中存的是数字字符串
push(atof(s)); //atof(s)将数字字符串转换成对应的double型数值（10进制）
break；
case '+':
push(pop() + pop());
break;
case '*':
push(pop() * pop());
break;
case '-':
op2 = pop();
push(pop()- op2);
break;
case '/':
op2 = pop();
if(op2 != 0.0)
push(pop() / op2);
else
printf("error: zero divisor\n");
break;
case '\n':
printf("\t%.8g\n",pop());
break;
default :
printf("error: unknown command %s\n");
break;
}
}
return EXIT_SUCCESS;
}
int getch(void); /* in getch.c */
void ungetch(int c); /* in getch.c */
/*getop: get next character or numeric operand */
int getop(char s[])
{
int i = 0;
int c;
int next;
/* skip whitespace */
while((s[0] = c = getch()) == ' '|| c == '\t')
;
s[1] = '\0';
/* Not a number but may contain a unary minus. */
if (!isdigit(c) && c != '.' && c != '-')
return c; /* not a number */
if(c == '-')
{
next = getch();
if(!isdigit(next) && next != '.' )
{
return c;
}
c = next;
}
else
{
c = getch();
}
while(isdigit(s[++i] = c))
c = getch();
if(c == '.')
while(isdigit(s[++i] = c = getch()))
;
s[i] = '\0';
if( c != EOF)
ungetch(c);
return NUMBER;
}
char buf[BUFSIZE]; /* buffer for ungetch 缓存区 */
int bufp = 0;
int getch(void) /*get a (possibly pushed-back) charater */
{
return (bufp > 0) ? buf[--bufp] : getchar();
}
void ungetch(int c)
{
if(bufp >= BUFSIZE)
printf(" ungetch : too many characters \n");
else
buf[bufp++] = c;
}
这就是基本的框架了。
下面是扩展一些功能的代码：
/***********************
*** calcu.h ***
************************/
#define TURE 1
#define FLASE 0
#define IDENTIFIER 1
#define NUMBER '0' /*signal that a number was found */
#define MAX_ID_LEN 32
#define MAXVARS 30
struct varType{
char name[MAX_ID_LEN];
double val;
};
extern int pos;
extern struct varType last;
/***********************
*** main.c ***
************************/
#include<stdio.h>
#include<math.h>
#include<stdlib.h> /*for atof(), EXIT_SUCCESS*/
#include"calcu.h"
#define MAXOP 100 /*max size of operand or operator */
#define ENDSTRING 2
#define MAXVARS 30
#define MAX_ID_LEN 32
int getop(char []);
void push(double);
double pop(void);
void showtop(void);
void duplicate(void);
void swapitems(void);
void clearStacks(struct varType var[]);
void DealWithName(char s[],struct varType var[]);
struct varType last;
/* reverse Polish calculator */
int main(void)
{
int type;
double op2;
char s[MAXOP];
struct varType var[MAXVARS];
clearStacks(var);
while((type = getop(s)) != EOF)
{
switch(type)
{
case NUMBER:
push(atof(s));
break;
case IDENTIFIER:
DealWithName(s, var);
break;
case '+':
push(pop() + pop());
break;
case '*':
push(pop() * pop());
break;
case '-':
op2 = pop();
push(pop()- op2);
break;
case '/':
op2 = pop();
if(op2 != 0.0)
push(pop() / op2);
else
printf("error: zero divisor\n");
break;
case '%':
op2 = pop();
if(op2 != 0.0)
push(fmod(pop(),op2));
else
printf("error : zero divisor\n");
break;
case '#':
duplicate();
break;
case '!':
clearStacks(var);
break;
case '~':
swapitems();
break;
case '\n':
showtop();
break;
case ENDSTRING:
break;
case '=':
var[pos].val = pop();
last.val = var[pos].val;
push(last.val);
break;
default :
printf("error: unknown command %s\n");
break;
}
}
return EXIT_SUCCESS;
}
/**************************
*** stack.c ***
***************************/
#include<stdio.h>
#include"calcu.h"
#define MAXVAL 100 /* maxinum depth of val stack */
double pop(void);
int sp=0; /* next free stack position */
double val[MAXVAL]; /* value stack */
/*push: push f onto value stack */
void push(double f)
{
if (sp < MAXVAL)
val[sp++] = f;
else
printf("eorror: stack full,can not push %g\n",f);
}
/* pop: pop and return top value form stack */
double pop(void)
{
if( sp > 0)
return val[--sp];
else
{
printf("error : stack empty\n");
return 0.0;
}
}
void showtop(void)
{
double item = pop();
printf("Top of stack contains: %.8g\n",item);
push(item);
}
void duplicate(void)
{
double temp = pop();
push(temp);
push(temp);
}
void swapitems(void)
{
double temp1 = pop();
double temp2 = pop();
push(temp1);
push(temp2);
}
/* pop only returns a value if sp is greater than zero. So setting the
stack pointer to zero will cause pop to return its error */
/* Altered to clear both the main stack and that of the variable
structure */
void clearStacks(struct varType var[])
{
int i;
/* Clear the main stack by setting the pointer to the bottom. */
sp = 0;
/* Clear the variables by setting the initial element of each name
to the terminating character. */
for( i = 0;i < MAXVARS; ++i)
{
var[i].name[0] = '\0';
var[i].val = 0.0;
}
}
/**********************************
****getch.c ***
***********************************/
#include<string.h>
#include<stdio.h>
#define BUFSIZE 100
char buf[BUFSIZE]; /* buffer for ungetch */
int bufp = 0;
int getch(void) /*get a (possibly pushed-back) charater */
{
return (bufp > 0) ? buf[--bufp] : getchar();
}
void ungetch(int c)
{
if(bufp >= BUFSIZE)
printf(" ungetch : too many characters \n");
else
buf[bufp++] = c;
}
void ungets(const char *s)
{
int i = strlen(s);
while(i > 0)
{
ungetch(s[--i]);
}
}
/************************************
**** getop.c ***
*************************************/
#include<stdio.h>
#include<ctype.h>
#include"calcu.h"
int getch(void); /* in getch.c */
void ungetch(int c); /* in getch.c */
/*getop: get next character or numeric operand */
int getop(char s[])
{
int i = 0;
int c;
int next;
/* skip whitespace */
while((s[0] = c = getch()) == ' '|| c == '\t')
;
s[1] = '\0';
if(isalpha(c))
{
i=0;
while(isalpha(s[i++] = c))
c = getch();
s[i-1] = '\0';
if(c != EOF)
ungetch(c);
return IDENTIFIER;
}
/* Not a number but may contain a unary minus. */
if (!isdigit(c) && c != '.' && c != '-')
return c; /* not a number */
if(c == '-')
{
next = getch();
if(!isdigit(next) && next != '.' )
{
return c;
}
c = next;
}
else
{
c = getch();
}
while(isdigit(s[++i] = c))
c = getch();
if(c == '.')
while(isdigit(s[++i] = c = getch()))
;
s[i] = '\0';
if( c != EOF)
ungetch(c);
return NUMBER;
}
/***********************************
*** dealwith.c ***
************************************/
#include"calcu.h"
#include<string.h>
#include<math.h>
#define MAXVARS 30
int pos = 0;
extern struct varType last;
void DealWithVar(char s[],struct varType var[]);
int pop(void);
void push(double f);
/* deal with a string/name this may be either a maths function or for
future exercises: a variable */
/* a string/name may be either a maths function or a variable */
void DealWithName(char s[],struct varType var[])
{
double op2;
if(0 == strcmp(s ,"sin"))
push(sin(pop()));
else if(0 == strcmp(s ,"cos"))
push(cos(pop()));
else if(0 == strcmp(s ,"exp"))
push(exp(pop()));
else if(0 == strcmp(s ,"pow"))
{
op2 = pop();
push(pow(pop() ,op2));
}
/* Finally if it isn't one of the supported maths functions we have a
variable to deal with. */
else
{
DealWithVar(s,var);
}
}
/* Our identifier is not one of the supported maths function so we have
to regard it as an identifier. */
void DealWithVar(char s[],struct varType var[])
{
int i = 0;
while(var[i].name[0] != '\0' && i < MAXVARS-1)
{
if(!strcmp(s, var[i].name))
{
strcpy(last.name, s);
last.val = var[i].val;
push(var[i].val);
pos = i;
return;
}
i++;
}
/* variable name not found so add it */
strcpy(var[i].name, s);
/* and save it to last variable*/
strcpy(last.name, s);
push(var[i].val);
pos = i;
}