Question

In C programming Language

Write a version of the infix-to-postfix conversion algorithm. Write a program that converts an ordinary infix arithmetic expression (assume a valid expression is entered) with single-digit integers

For Example: Infix expression (6 + 2) * 5 - 8 / 4 to a postfix expression is  62+5*84/-

The program should read the expression into character array infix and use the stack functions implemented in this chapter to help create the postfix expression in character array postfix. The algorithm for creating a postfix expression is as follows:

1 Push a left parenthesis '(' onto the stack.

2 Append a right parenthesis ')' to the end of infix.

3 While the stack is not empty, read infix from left to right and do the following:

• If the current character in infix is a digit, copy it to the next element of postfix.
• If the current character in infix is a left parenthesis, push it onto the stack.
• If the current character in infix is an operator,
  • Pop operators (if there are any) at the top of the stack while they have equal or higher precedence than the current operator, and insert the popped operators in postfix.
  • Push the current character in infix onto the stack.
• If the current character in infix is a right parenthesis
  • Pop operators from the top of the stack and insert them in postfix until a
    left parenthesis is at the top of the stack.
  • Pop (and discard) the left parenthesis from the stack.

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The following arithmetic operations are allowed in an expression:
+ (addition) , - (subtraction), * (multiplication), / (division), ^ (exponentiation) and
   % (remainder).

Answer 1

- Below is the C Programming code to convert from infix expression to postfix expression

#include <stdio.h>
#include <stdlib.h>
#define MAX 100
int top = -1;
char stck[MAX];
///////////////////////////Implement Stack//////////////////////////////
void push(char ch){
if(top < MAX-1)
stck[++top] = ch;
else
return;
}
char pop(){
if(top > -1)
return stck[top--];
}
char Top(){
if(top > -1)
return stck[top];
}
int isEmpty(){
if(top==-1)
return 1;
else
return 0;
}
///////////////////////////End Stack////////////////////////////////////

///////////////////////////Infix to postfix Implementation//////////////
int prec(char symbol){
switch(symbol){
case '+':
case '-':
return 1;
break;
case '*':
case '/':
case '%':
return 2;
break;
case '^':
return 3;
break;
default:
return 0;
break;
}
}
void infixTopostfix(char ch[],int n){
int i,j=0;
char res[MAX];
for(i=0; i<n; i++){
if(ch[i]=='0'||ch[i]=='1'||ch[i]=='2'||ch[i]=='3'||ch[i]=='4'||ch[i]=='5'
||ch[i]=='6'||ch[i]=='7'||ch[i]=='8'||ch[i]=='9')
res[j++]=ch[i];
else if(ch[i]=='(')
push(ch[i]);
else if(ch[i]==')'){
while(Top()!='(' && !isEmpty()){
res[j++] = pop();
}
if(!isEmpty() && Top() != '(')
return;
else
pop();
}else{
while(!isEmpty() && prec(ch[i]) <= prec(Top()))
res[j++]=pop();
push(ch[i]);
}
}
while(!isEmpty())
res[j++]=pop();
for(i=0; i<j; i++)
printf("%c",res[i]);
}
///////////////////////////End Infix to postfix ////////////////////////
int main()
{
char ch[] = "(6+2)*5-8/4"; //"(1+2)*(3+4)" , "1+2*3+4" insert string without space
int size = sizeof(ch);
infixTopostfix(ch,size);
return 0;
}