栈的应用实例——中缀表达式转换为后缀表达式

声明：本程序读入一个中缀表达式，将该中缀表达式转换为后缀表达式并输出后缀表达式。


注意：支持+、-、*、/、（），并且输入时每输入完一个数字或符号都要加一个空格，特别注意的是在整个表达式输入完成时也要加一个空格后再回车。这是该程序的一个不足之处，有待改进。

/* infix_to_postfix.c */

#include <stdio.h>
#include <errno.h>
#include <stdlib.h>
#include <unistd.h>

struct op_node
{
char op;
int level;
};
struct stack_record
{
int capacity;
int top_of_stack;
struct op_node *array;
};

struct stack_record *
create_stack( int max_elements )
{
struct stack_record *s;

if(max_elements < 5)
{
printf(" stack size is too samll\n");
exit(0);
}

s = malloc(sizeof(struct stack_record));
if(s == NULL)
{
perror("malloc");
exit(1);
}

s->array = malloc(sizeof(struct op_node) * max_elements);
if(s->array == NULL)
{
perror("malloc");
exit(1);
}

s->capacity = max_elements;
s->top_of_stack = -1;

return s;
}

void
push( struct op_node x, struct stack_record *s)
{
if(s->top_of_stack + 1 == s->capacity)
{
printf("full stack\n");
exit(0);
}
else
{
s->array[++s->top_of_stack] = x;
}
}

struct op_node
top( struct stack_record *s)
{
if(s->top_of_stack == -1)
{
printf("top : empty stack\n");
exit(1);
}
else
{
return s->array[s->top_of_stack];
}
}

void
pop( struct stack_record *s)
{
if(s->top_of_stack == -1)
{
printf("pop : empty stack\n");
exit(1);
}
else
{
s->top_of_stack--;
}
}

struct op_node
top_and_pop( struct stack_record *s)
{
if(s->top_of_stack == -1)
{
printf("top_and_pop : empty stack\n");
exit(1);
}
else
{
return s->array[s->top_of_stack--];
}
}

int
main(void)
{
int i;
static int j;
char c;
char data_string[100];
char postfix_expression[100];
struct stack_record *op_stack;
struct op_node op1, op2;
int flag;

op_stack = create_stack(100);

printf("Please input an infix-expression end with a space: \n");

i = 0;
j = 0;
for(c = getchar(); c != '\n'; c = getchar())
{
switch(c)
{
case '0':
case '1':
case '2':
case '3':
case '4':
case '5':
case '6':
case '7':
case '8':
case '9':
case '.':
flag = 1;
data_string[i++] = c;
break;
case ' ':
if(flag == 1)
{
data_string[i] = '\0';
i = 0;
while(data_string[i] != '\0')
{
postfix_expression[j++] = data_string[i++];
}
postfix_expression[j++] = ' ';

i = 0;
data_string[0] = '\0';
}
break;
case '+':
flag = 0;
op1.op = c;
op1.level = 1;
if(op_stack->top_of_stack == -1)
{
push( op1, op_stack );
}
else
{
op2 = top( op_stack );
while( op1.level <= op2.level )
{
if(op2.op != '(')
{
pop( op_stack );
postfix_expression[j++] = op2.op;
postfix_expression[j++] = ' ';
}
else
{
break;
}
if(op_stack->top_of_stack == -1)
{
break;
}
else
{
op2 = top( op_stack );
}
}
push( op1, op_stack );
}
break;

case '-':
flag = 0;
op1.op = c;
op1.level = 1;
if(op_stack->top_of_stack == -1)
{
push( op1, op_stack );
}
else
{
op2 = top( op_stack );
while( op1.level <= op2.level )
{
if(op2.op != '(')
{
pop( op_stack );
postfix_expression[j++] = op2.op;
postfix_expression[j++] = ' ';
}
else
{
break;
}
if(op_stack->top_of_stack == -1)
{
break;
}
else
{
op2 = top( op_stack );
}
}
push( op1, op_stack );
}
break;

case '*':
flag = 0;
op1.op = c;
op1.level = 2;
if(op_stack->top_of_stack == -1)
{
push( op1, op_stack );
}
else
{
op2 = top( op_stack );
while( op1.level <= op2.level )
{
if(op2.op != '(')
{
pop( op_stack );
postfix_expression[j++] = op2.op;
postfix_expression[j++] = ' ';
}
else
{
break;
}
if(op_stack->top_of_stack == -1)
{
break;
}
else
{
op2 = top( op_stack );
}
}
push( op1, op_stack );
}
break;

case '/':
flag = 0;
op1.op = c;
op1.level = 2;
if(op_stack->top_of_stack == -1)
{
push( op1, op_stack );
}
else
{
op2 = top( op_stack );
while( op1.level <= op2.level )
{
if(op2.op != '(')
{
pop( op_stack );
postfix_expression[j++] = op2.op;
postfix_expression[j++] = ' ';
}
else
{
break;
}

if(op_stack->top_of_stack == -1)
{
break;
}
else
{
op2 = top( op_stack );
}
}
push( op1, op_stack );
}
break;
case '(':
flag = 0;
op1.op = c;
op1.level = 3;
push( op1, op_stack );
break;
case ')':
flag = 0;
op2 = top_and_pop( op_stack );
while(op2.op != '(')
{
postfix_expression[j++] = op2.op;
postfix_expression[j++] = ' ';
op2 = top_and_pop( op_stack );
}
break;

}
}

while(!(op_stack->top_of_stack == -1))
{
op2 = top_and_pop( op_stack );
postfix_expression[j++] = op2.op;
postfix_expression[j++] = ' ';
}
postfix_expression[j] = '\0';

printf("postfix_expression is: %s\n", postfix_expression);

}

测试结果如下：


再次提醒：输入中缀表达式时一定要以空格结尾，比如下面的输入中输入完7后需要再输入一个空格，然后再按回车。