Postfix to Infix


Infix expression: The expression of the form a op b. When an operator is in-between every pair of operands.
Postfix expression: The expression of the form a b op. When an operator is followed for every pair of operands.
Postfix notation, also known as reverse Polish notation, is a syntax for mathematical expressions in which the mathematical operator is always placed after the operands. Though postfix expressions are easily and efficiently evaluated by computers, they can be difficult for humans to read. Complex expressions using standard parenthesized infix notation are often more readable than the corresponding postfix expressions. Consequently, we would sometimes like to allow end users to work with infix notation and then convert it to postfix notation for computer processing. Sometimes, moreover, expressions are stored or generated in postfix, and we would like to convert them to infix for the purpose of reading and editing

Examples:

Input : abc++
Output : (a + (b + c))

Input  : ab*c+
Output : ((a*b)+c)

We have already discussed Infix to Postfix. Below is algorithm for Postfix to Infix.

Algorithm
1.While there are input symbol left
…1.1 Read the next symbol from the input.
2.If the symbol is an operand
…2.1 Push it onto the stack.
3.Otherwise,
…3.1 the symbol is an operator.
…3.2 Pop the top 2 values from the stack.
…3.3 Put the operator, with the values as arguments and form a string.
…3.4 Push the resulted string back to stack.
4.If there is only one value in the stack
…4.1 That value in the stack is the desired infix string.

Below is the implementation of above approach:

C++

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// CPP program to find infix for
// a given postfix.
#include <bits/stdc++.h>
using namespace std;
  
bool isOperand(char x)
{
   return (x >= 'a' && x <= 'z') ||
          (x >= 'A' && x <= 'Z');
}
  
// Get Infix for a given postfix
// expression
string getInfix(string exp)
{
    stack<string> s;
  
    for (int i=0; exp[i]!='\0'; i++)
    {
        // Push operands
        if (isOperand(exp[i]))
        {
           string op(1, exp[i]);
           s.push(op);
        }
  
        // We assume that input is
        // a valid postfix and expect
        // an operator.
        else
        {
            string op1 = s.top();
            s.pop();
            string op2 = s.top();
            s.pop();
            s.push("(" + op2 + exp[i] +
                   op1 + ")");
        }
    }
  
    // There must be a single element
    // in stack now which is the required
    // infix.
    return s.top();
}
  
// Driver code
int main()
{
    string exp = "ab*c+";
    cout << getInfix(exp);
    return 0;
}

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Java

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// Java program to find infix for
// a given postfix.
import java.util.*;
  
class GFG
{
      
static boolean isOperand(char x)
{
    return (x >= 'a' && x <= 'z') ||
            (x >= 'A' && x <= 'Z');
}
  
// Get Infix for a given postfix
// expression
static String getInfix(String exp)
{
    Stack<String> s = new Stack<String>();
  
    for (int i = 0; i < exp.length(); i++)
    {
        // Push operands
        if (isOperand(exp.charAt(i)))
        {
        s.push(exp.charAt(i) + "");
        }
  
        // We assume that input is
        // a valid postfix and expect
        // an operator.
        else
        {
            String op1 = s.peek();
            s.pop();
            String op2 = s.peek();
            s.pop();
            s.push("(" + op2 + exp.charAt(i) +
                    op1 + ")");
        }
    }
  
    // There must be a single element
    // in stack now which is the required
    // infix.
    return s.peek();
}
  
// Driver code
public static void main(String args[])
{
    String exp = "ab*c+";
    System.out.println( getInfix(exp));
}
}
  
// This code is contributed by Arnab Kundu

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Python3

# Python3 program to find infix for
# a given postfix.
def isOperand(x):
return ((x >= ‘a’ and x <= 'z') or (x >= ‘A’ and x <= 'Z')) # Get Infix for a given postfix # expression def getInfix(exp) : s = [] for i in exp: # Push operands if (isOperand(i)) : s.insert(0, i) # We assume that input is a # valid postfix and expect # an operator. else: op1 = s[0] s.pop(0) op2 = s[0] s.pop(0) s.insert(0, "(" + op2 + i + op1 + ")") # There must be a single element in # stack now which is the required # infix. return s[0] # Driver Code if __name__ == '__main__': exp = "ab*c+" print(getInfix(exp.strip())) # This code is contributed by # Shubham Singh(SHUBHAMSINGH10) [tabby title="C#"]

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// C# program to find infix for
// a given postfix.
using System;
using System.Collections;
  
class GFG
{
      
static Boolean isOperand(char x)
{
    return (x >= 'a' && x <= 'z') ||
            (x >= 'A' && x <= 'Z');
}
  
// Get Infix for a given postfix
// expression
static String getInfix(String exp)
{
    Stack s = new Stack();
  
    for (int i = 0; i < exp.Length; i++)
    {
        // Push operands
        if (isOperand(exp[i]))
        {
            s.Push(exp[i] + "");
        }
  
        // We assume that input is
        // a valid postfix and expect
        // an operator.
        else
        {
            String op1 = (String) s.Peek();
            s.Pop();
            String op2 = (String) s.Peek();
            s.Pop();
            s.Push("(" + op2 + exp[i] +
                    op1 + ")");
        }
    }
  
    // There must be a single element
    // in stack now which is the required
    // infix.
    return (String)s.Peek();
}
  
// Driver code
public static void Main(String []args)
{
    String exp = "ab*c+";
    Console.WriteLine( getInfix(exp));
}
}
  
// This code is contributed by Arnab Kundu

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PHP

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<?php 
   
class Stack {
    protected $stack;
    protected $limit;
  
   function CreateStack($limit){
        $this->stack = array();
        $this->limit = $limit;
    }
      
    function push($item) {
        // trap for stack overflow
        if (count($this->stack) < $this->limit) {
            // prepend item to the start of the array
            array_unshift($this->stack, $item);
        } else {
            throw new RunTimeException('Stack is full!'); 
        }
    }
  
     function pop() {
        if ($this->isEmpty()) {
            // trap for stack underflow
          throw new RunTimeException('Stack is empty!');
      } else {
            // pop item from the start of the array
            return array_shift($this->stack);
        }
    }
  
     function top() {
        return current($this->stack);
    }
  
     function isEmpty() {
        return empty($this->stack);
    }
      
    function Prec($ch
    
        switch ($ch
        
        case '+'
        case '-'
            return 1; 
  
        case '*'
        case '/'
            return 2; 
  
        case '^'
            return 3; 
        
        return -1; 
    
    function isOperand($ch
    
        return ($ch >= 'a' && $ch <= 'z') || ($ch >= 'A' && $ch <= 'Z'); 
    
      
    function isOperator($x) { 
      switch ($x) { 
      case '+'
      case '-'
      case '/'
      case '*'
        return true; 
      
      return false; 
    }
      
    public function  getInfix($exp
    
      
     $this->CreateStack(sizeof($exp));
          
    for ($i=0; $exp[$i]!= null; $i++) 
    
        // Push operands 
        if ($this->isOperand($exp[$i])) 
        
            $op = $exp[$i]; 
            $this->push($op);
        
    
        // We assume that input is 
        // a valid postfix and expect 
        // an operator. 
        else
        
                   $op1 = $this->top(); $this->pop();
                    $op2 = $this->top(); $this->pop();
                    $this->push("(". $op2 . $exp[$i] . $op1 . ")"); 
                    //$this->push($temp);
            
        
    
    
    // There must be a single element 
    // in stack now which is the required 
    // infix. 
    return $this->top(); 
}
$myExample = new Stack();
echo $input "ab*c+"
$exp str_split($input,sizeof($input));
echo '<br>'.$data = $myExample->getInfix($exp); 
?>

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Output:

((a*b)+c)


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