# Postfix to Prefix Conversion

Postfix: An expression is called the postfix expression if the operator appears in the expression after the operands. Simply of the form (operand1 operand2 operator).
Example : AB+CD-* (Infix : (A+B) * (C-D) )

Prefix : An expression is called the prefix expression if the operator appears in the expression before the operands. Simply of the form (operator operand1 operand2).
Example : *+AB-CD (Infix : (A+B) * (C-D) )

Given a Postfix expression, convert it into a Prefix expression.
Conversion of Postfix expression directly to Prefix without going through the process of converting them first to Infix and then to Prefix is much better in terms of computation and better understanding the expression (Computers evaluate using Postfix expression).

Examples:

```Input :  Postfix : AB+CD-*
Output : Prefix :  *+AB-CD
Explanation : Postfix to Infix : (A+B) * (C-D)
Infix to Prefix :  *+AB-CD

Input :  Postfix : ABC/-AK/L-*
Output : Prefix :  *-A/BC-/AKL
Explanation : Postfix to Infix : ((A-(B/C))*((A/K)-L))
Infix to Prefix :  *-A/BC-/AKL ```

Algorithm for Postfix to Prefix:

• Read the Postfix expression from left to right
• If the symbol is an operand, then push it onto the Stack
• If the symbol is an operator, then pop two operands from the Stack
Create a string by concatenating the two operands and the operator before them.
string = operator + operand2 + operand1
And push the resultant string back to Stack
• Repeat the above steps until end of Postfix expression.

Below is the implementation of the above idea:

## C++

 `// CPP Program to convert postfix to prefix``#include ``using` `namespace` `std;` `// function to check if character is operator or not``bool` `isOperator(``char` `x)``{``    ``switch` `(x) {``    ``case` `'+'``:``    ``case` `'-'``:``    ``case` `'/'``:``    ``case` `'*'``:``        ``return` `true``;``    ``}``    ``return` `false``;``}` `// Convert postfix to Prefix expression``string postToPre(string post_exp)``{``    ``stack s;` `    ``// length of expression``    ``int` `length = post_exp.size();` `    ``// reading from left to right``    ``for` `(``int` `i = 0; i < length; i++) {` `        ``// check if symbol is operator``        ``if` `(isOperator(post_exp[i])) {` `            ``// pop two operands from stack``            ``string op1 = s.top();``            ``s.pop();``            ``string op2 = s.top();``            ``s.pop();` `            ``// concat the operands and operator``            ``string temp = post_exp[i] + op2 + op1;` `            ``// Push string temp back to stack``            ``s.push(temp);``        ``}` `        ``// if symbol is an operand``        ``else` `{` `            ``// push the operand to the stack``            ``s.push(string(1, post_exp[i]));``        ``}``    ``}` `    ``string ans = ``""``;``    ``while` `(!s.empty()) {``        ``ans += s.top();``        ``s.pop();``    ``}``    ``return` `ans;``}` `// Driver Code``int` `main()``{``    ``string post_exp = ``"ABC/-AK/L-*"``;` `    ``// Function call``    ``cout << ``"Prefix : "` `<< postToPre(post_exp);``    ``return` `0;``}`

## Java

 `// Java Program to convert postfix to prefix``import` `java.util.*;` `class` `GFG {` `    ``// function to check if character``    ``// is operator or not``    ``static` `boolean` `isOperator(``char` `x)``    ``{` `        ``switch` `(x) {``        ``case` `'+'``:``        ``case` `'-'``:``        ``case` `'/'``:``        ``case` `'*'``:``            ``return` `true``;``        ``}``        ``return` `false``;``    ``}` `    ``// Convert postfix to Prefix expression``    ``static` `String postToPre(String post_exp)``    ``{``        ``Stack s = ``new` `Stack();` `        ``// length of expression``        ``int` `length = post_exp.length();` `        ``// reading from right to left``        ``for` `(``int` `i = ``0``; i < length; i++) {` `            ``// check if symbol is operator``            ``if` `(isOperator(post_exp.charAt(i))) {` `                ``// pop two operands from stack``                ``String op1 = s.peek();``                ``s.pop();``                ``String op2 = s.peek();``                ``s.pop();` `                ``// concat the operands and operator``                ``String temp``                    ``= post_exp.charAt(i) + op2 + op1;` `                ``// Push String temp back to stack``                ``s.push(temp);``            ``}` `            ``// if symbol is an operand``            ``else` `{` `                ``// push the operand to the stack``                ``s.push(post_exp.charAt(i) + ``""``);``            ``}``        ``}` `        ``// concatenate all strings in stack and return the``        ``// answer``        ``String ans = ``""``;``        ``for` `(String i : s)``            ``ans += i;``        ``return` `ans;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String args[])``    ``{``        ``String post_exp = ``"ABC/-AK/L-*"``;` `        ``// Function call``        ``System.out.println(``"Prefix : "``                           ``+ postToPre(post_exp));``    ``}``}` `// This code is contributed by Arnab Kundu`

## Python3

 `# Python3 Program to convert postfix to prefix` `# function to check if``# character is operator or not`  `def` `isOperator(x):` `    ``if` `x ``=``=` `"+"``:``        ``return` `True` `    ``if` `x ``=``=` `"-"``:``        ``return` `True` `    ``if` `x ``=``=` `"/"``:``        ``return` `True` `    ``if` `x ``=``=` `"*"``:``        ``return` `True` `    ``return` `False` `# Convert postfix to Prefix expression`  `def` `postToPre(post_exp):` `    ``s ``=` `[]` `    ``# length of expression``    ``length ``=` `len``(post_exp)` `    ``# reading from right to left``    ``for` `i ``in` `range``(length):` `        ``# check if symbol is operator``        ``if` `(isOperator(post_exp[i])):` `            ``# pop two operands from stack``            ``op1 ``=` `s[``-``1``]``            ``s.pop()``            ``op2 ``=` `s[``-``1``]``            ``s.pop()` `            ``# concat the operands and operator``            ``temp ``=` `post_exp[i] ``+` `op2 ``+` `op1` `            ``# Push string temp back to stack``            ``s.append(temp)` `        ``# if symbol is an operand``        ``else``:` `            ``# push the operand to the stack``            ``s.append(post_exp[i])` `   ` `    ``ans ``=` `""``    ``for` `i ``in` `s:``        ``ans ``+``=` `i``    ``return` `ans`  `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``post_exp ``=` `"AB+CD-"``    ` `    ``# Function call``    ``print``(``"Prefix : "``, postToPre(post_exp))` `# This code is contributed by AnkitRai01`

## C#

 `// C# Program to convert postfix to prefix``using` `System;``using` `System.Collections;` `class` `GFG {` `    ``// function to check if character``    ``// is operator or not``    ``static` `Boolean isOperator(``char` `x)``    ``{` `        ``switch` `(x) {``        ``case` `'+'``:``        ``case` `'-'``:``        ``case` `'/'``:``        ``case` `'*'``:``            ``return` `true``;``        ``}``        ``return` `false``;``    ``}` `    ``// Convert postfix to Prefix expression``    ``static` `String postToPre(String post_exp)``    ``{``        ``Stack s = ``new` `Stack();` `        ``// length of expression``        ``int` `length = post_exp.Length;` `        ``// reading from right to left``        ``for` `(``int` `i = 0; i < length; i++) {` `            ``// check if symbol is operator``            ``if` `(isOperator(post_exp[i])) {` `                ``// Pop two operands from stack``                ``String op1 = (String)s.Peek();``                ``s.Pop();``                ``String op2 = (String)s.Peek();``                ``s.Pop();` `                ``// concat the operands and operator``                ``String temp = post_exp[i] + op2 + op1;` `                ``// Push String temp back to stack``                ``s.Push(temp);``            ``}` `            ``// if symbol is an operand``            ``else` `{` `                ``// Push the operand to the stack``                ``s.Push(post_exp[i] + ``""``);``            ``}``        ``}` `        ``String ans = ``""``;``        ``while` `(s.Count > 0)``            ``ans += s.Pop();``        ``return` `ans;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``String post_exp = ``"ABC/-AK/L-*"``;``      ` `        ``// Function call``        ``Console.WriteLine(``"Prefix : "``                          ``+ postToPre(post_exp));``    ``}``}` `// This code is contributed by Arnab Kundu`

## Javascript

 ``

Output
`Prefix : *-A/BC-/AKL`

Time Complexity: O(N) // In the above-given approach, there is one loop for iterating over string which takes O(N) time in worst case. Therefore, the time complexity for this approach will be O(N).
Auxiliary Space: O(N) // we are using an empty stack as well as empty string to store the expression hence space taken is linear

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