# Postfix to Infix

• Difficulty Level : Easy
• Last Updated : 24 May, 2022

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++

 `// CPP program to find infix for``// a given postfix.``#include ``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 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;``}`

## Java

 `// 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 s = ``new` `Stack();` `    ``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`

## 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)`

## C#

 `// 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`

## PHP

 `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` `'
'``.``\$data` `= ``\$myExample``->getInfix(``\$exp``);``?>`

## Javascript

 ``

Output:

`((a*b)+c)`

Time Complexity: O(N) where N is the length of the string

Auxiliary Space: O(N) where N is the stack size.

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