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Data Structure Prefix to Postfix Conversion

Prefix to Postfix Conversion

Prefix: As the name suggests if the operator placed before the operands called the prefix expression.  The form of prefix expression is (operator, operand1, operand2).

Example:  *+EF-GH (Infix: (E+F) * (F-H))

Postfix: In postfix expression, the operator placed after the operands and the form of postfix expression is (operand1, operand2, operator).

Example: EF+GH-* (Infix: (E+F * (G-H))


  • Firstly, we read input or prefix expression from right to left or we can say in reverse order.
  • If we encounter an operand, then we push it into the stack.
  • If we encounter an operator, then we pop two operands from the stack.
  • Then we are required to make a string which concatenate the two operands and the operator after them.
  • String = operand1 + operand2 + operator
  • Then we push the output or resultant string back to the stack.
  • We need to repeat above steps until the end of prefix expression.


Prefix:  * + E F – G H
Postfix: E F + G H - *
Explanation: Prefix to Infix: (E + F) * (G – H)
             Infix to Postfix:  E F + G H - *
Prefix:  * - E / F G - / E K L
Postfix: E F G / - E K / L - *
Explanation: Prefix to Infix: (E - ( F / G ) ) * ( ( E / K ) – L )
    Infix to Postfix :  E F G / - E K / L - * 

C- Program to covert prefix expression to postfix expression:

 #define BLANK ' '
 #define TAB '\t'
 #define MAX 50
 char *pop();
 char prefix[MAX];
 char stack[MAX][MAX];
 void push(char *str);
 int isempty();
 int white_space(char element);
 void prefix_to_postfix();
 int top;
 int main()
         top  =  -1;
         printf(" Enter Prefix Expression :  ");
 /* End of main() */
 void prefix_to_postfix()
         int i;
         char operand1[MAX], operand2[MAX];
         char element;
         char temp[2];
         char strin[MAX];
         for(i = strlen(prefix)-1; i >= 0; i--)
                 element = prefix[i];
                 temp[0] = element;
                 temp[1] = '\0';
                         case '+':
                         case '-':
                         case '*':
                         case '/':
                         case '%':
                         case '^':
 /* if an operand comes */
         printf("\nPostfix Expression :: ");
 /* End of prefix_to_postfix()  */
 void push(char *str)
         if(top  >  MAX)
                 printf("\nStack overflow\n");
                 top = top+1;
                 strcpy( stack[top], str);
 /* End of push() */
 char *pop()
         if(top  ==  -1 )
                 printf("\n Stack underflow \n");
                 return (stack[top--]);
 /*  End of pop()  */
 int isempty()
                 return 1;
                 return 0;
 int white_space(char element)
         if(element == BLANK || element == TAB || element == '\0')
                 return 1;
                 return 0;

Output: -

Time Complexity:  -  

The time complexity to convert prefix expression to postfix expression is O(n) and space complexity is also O(n).