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Stack | Set 2 (Infix to Postfix)
• Difficulty Level : Medium
• Last Updated : 30 Oct, 2020

Prerequisite – Stack | Set 1 (Introduction)
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.
Why postfix representation of the expression?
The compiler scans the expression either from left to right or from right to left.
Consider the below expression: a op1 b op2 c op3 d
If op1 = +, op2 = *, op3 = +
The compiler first scans the expression to evaluate the expression b * c, then again scan the expression to add a to it. The result is then added to d after another scan.
The repeated scanning makes it very in-efficient. It is better to convert the expression to postfix(or prefix) form before evaluation.
The corresponding expression in postfix form is: abc*+d+. The postfix expressions can be evaluated easily using a stack. We will cover postfix expression evaluation in a separate post.
Algorithm
1. Scan the infix expression from left to right.
2. If the scanned character is an operand, output it.
3. Else,
1 If the precedence of the scanned operator is greater than the precedence of the operator in the stack(or the stack is empty           or the stack contains a ‘(‘ ), push it.
2 Else, Pop all the operators from the stack which are greater than or equal to in precedence than that of the scanned operator. After doing that Push the scanned operator to the stack. (If you encounter parenthesis while popping then stop there and push the scanned operator in the stack.)
4. If the scanned character is an ‘(‘, push it to the stack.
5. If the scanned character is an ‘)’, pop the stack and and output it until a ‘(‘ is encountered, and discard both the parenthesis.
6. Repeat steps 2-6 until infix expression is scanned.
7. Print the output
8. Pop and output from the stack until it is not empty.

Following is the implementation of the above algorithm

## C++

 `/* C++ implementation to convert `` ``infix expression to postfix*/``// Note that here we use std::stack  ``// for Stack operations``#include``using` `namespace` `std;`` ` `//Function to return precedence of operators``int` `prec(``char` `c)``{``    ``if``(c == ``'^'``)``    ``return` `3;``    ``else` `if``(c == ``'*'` `|| c == ``'/'``)``    ``return` `2;``    ``else` `if``(c == ``'+'` `|| c == ``'-'``)``    ``return` `1;``    ``else``    ``return` `-1;``}`` ` `// The main function to convert infix expression``//to postfix expression``void` `infixToPostfix(string s)``{``    ``std::stack<``char``> st;``    ``st.push(``'N'``);``    ``int` `l = s.length();``    ``string ns;``    ``for``(``int` `i = 0; i < l; i++)``    ``{``         ` `        ``// If the scanned character is ``        ``// an operand, add it to output string.``        ``if``((s[i] >= ``'a'` `&& s[i] <= ``'z'``) || ``           ``(s[i] >= ``'A'` `&& s[i] <= ``'Z'``))``        ``ns+=s[i];`` ` `        ``// If the scanned character is an ``        ``// ‘(‘, push it to the stack.``        ``else` `if``(s[i] == ``'('``)``         ` `        ``st.push(``'('``);``         ` `        ``// If the scanned character is an ‘)’, ``        ``// pop and to output string from the stack``        ``// until an ‘(‘ is encountered.``        ``else` `if``(s[i] == ``')'``)``        ``{``            ``while``(st.top() != ``'N'` `&& st.top() != ``'('``)``            ``{``                ``char` `c = st.top();``                ``st.pop();``               ``ns += c;``            ``}``            ``if``(st.top() == ``'('``)``            ``{``                ``char` `c = st.top();``                ``st.pop();``            ``}``        ``}``         ` `        ``//If an operator is scanned``        ``else``{``            ``while``(st.top() != ``'N'` `&& prec(s[i]) <= ``                                   ``prec(st.top()))``            ``{``                ``char` `c = st.top();``                ``st.pop();``                ``ns += c;``            ``}``            ``st.push(s[i]);``        ``}`` ` `    ``}``   ` `    ``// Pop all the remaining elements from the stack``    ``while``(st.top() != ``'N'``)``    ``{``        ``char` `c = st.top();``        ``st.pop();``        ``ns += c;``    ``}``     ` `    ``cout << ns << endl;`` ` `}`` ` `//Driver program to test above functions``int` `main()``{``    ``string ``exp` `= ``"a+b*(c^d-e)^(f+g*h)-i"``;``    ``infixToPostfix(``exp``);``    ``return` `0;``}``// This code is contributed by Gautam Singh`

## C

 `// C program to convert infix expression to postfix ``#include ``#include ``#include `` ` `// Stack type``struct` `Stack``{``    ``int` `top;``    ``unsigned capacity;``    ``int``* array;``};`` ` `// Stack Operations``struct` `Stack* createStack( unsigned capacity )``{``    ``struct` `Stack* stack = (``struct` `Stack*) ``           ``malloc``(``sizeof``(``struct` `Stack));`` ` `    ``if` `(!stack) ``        ``return` `NULL;`` ` `    ``stack->top = -1;``    ``stack->capacity = capacity;`` ` `    ``stack->array = (``int``*) ``malloc``(stack->capacity * ``                                   ``sizeof``(``int``));`` ` `    ``return` `stack;``}``int` `isEmpty(``struct` `Stack* stack)``{``    ``return` `stack->top == -1 ;``}``char` `peek(``struct` `Stack* stack)``{``    ``return` `stack->array[stack->top];``}``char` `pop(``struct` `Stack* stack)``{``    ``if` `(!isEmpty(stack))``        ``return` `stack->array[stack->top--] ;``    ``return` `'\$'``;``}``void` `push(``struct` `Stack* stack, ``char` `op)``{``    ``stack->array[++stack->top] = op;``}`` ` ` ` `// A utility function to check if ``// the given character is operand``int` `isOperand(``char` `ch)``{``    ``return` `(ch >= ``'a'` `&& ch <= ``'z'``) || ``           ``(ch >= ``'A'` `&& ch <= ``'Z'``);``}`` ` `// A utility function to return ``// precedence of a given operator``// Higher returned value means ``// higher precedence``int` `Prec(``char` `ch)``{``    ``switch` `(ch)``    ``{``    ``case` `'+'``:``    ``case` `'-'``:``        ``return` `1;`` ` `    ``case` `'*'``:``    ``case` `'/'``:``        ``return` `2;`` ` `    ``case` `'^'``:``        ``return` `3;``    ``}``    ``return` `-1;``}`` ` ` ` `// The main function that ``// converts given infix expression``// to postfix expression. ``int` `infixToPostfix(``char``* ``exp``)``{``    ``int` `i, k;`` ` `    ``// Create a stack of capacity ``    ``// equal to expression size ``    ``struct` `Stack* stack = createStack(``strlen``(``exp``));``    ``if``(!stack) ``// See if stack was created successfully ``        ``return` `-1 ;`` ` `    ``for` `(i = 0, k = -1; ``exp``[i]; ++i)``    ``{``         ` `        ``// If the scanned character is ``        ``// an operand, add it to output.``        ``if` `(isOperand(``exp``[i]))``            ``exp``[++k] = ``exp``[i];``         ` `        ``// If the scanned character is an ``        ``// ‘(‘, push it to the stack.``        ``else` `if` `(``exp``[i] == ``'('``)``            ``push(stack, ``exp``[i]);``         ` `        ``// If the scanned character is an ‘)’,``        ``// pop and output from the stack ``        ``// until an ‘(‘ is encountered.``        ``else` `if` `(``exp``[i] == ``')'``)``        ``{``            ``while` `(!isEmpty(stack) && peek(stack) != ``'('``)``                ``exp``[++k] = pop(stack);``            ``if` `(!isEmpty(stack) && peek(stack) != ``'('``)``                ``return` `-1; ``// invalid expression             ``            ``else``                ``pop(stack);``        ``}``        ``else` `// an operator is encountered``        ``{``            ``while` `(!isEmpty(stack) && ``                 ``Prec(``exp``[i]) <= Prec(peek(stack)))``                ``exp``[++k] = pop(stack);``            ``push(stack, ``exp``[i]);``        ``}`` ` `    ``}`` ` `    ``// pop all the operators from the stack``    ``while` `(!isEmpty(stack))``        ``exp``[++k] = pop(stack );`` ` `    ``exp``[++k] = ``'\0'``;``    ``printf``( ``"%s"``, ``exp` `);``}`` ` `// Driver program to test above functions``int` `main()``{``    ``char` `exp``[] = ``"a+b*(c^d-e)^(f+g*h)-i"``;``    ``infixToPostfix(``exp``);``    ``return` `0;``}`

## Java

 `/* Java implementation to convert `` ``infix expression to postfix*/``// Note that here we use Stack class for Stack operations`` ` `import` `java.util.Stack;`` ` `class` `Test``{``     ` `    ``// A utility function to return ``    ``// precedence of a given operator``    ``// Higher returned value means ``    ``// higher precedence``    ``static` `int` `Prec(``char` `ch)``    ``{``        ``switch` `(ch)``        ``{``        ``case` `'+'``:``        ``case` `'-'``:``            ``return` `1``;``      ` `        ``case` `'*'``:``        ``case` `'/'``:``            ``return` `2``;``      ` `        ``case` `'^'``:``            ``return` `3``;``        ``}``        ``return` `-``1``;``    ``}``      ` `    ``// The main method that converts ``    ``// given infix expression``    ``// to postfix expression. ``    ``static` `String infixToPostfix(String exp)``    ``{``        ``// initializing empty String for result``        ``String result = ``new` `String(``""``);``         ` `        ``// initializing empty stack``        ``Stack stack = ``new` `Stack<>();``         ` `        ``for` `(``int` `i = ``0``; i

## Python

 `# Python program to convert infix expression to postfix`` ` `# Class to convert the expression``class` `Conversion:``     ` `    ``# Constructor to initialize the class variables``    ``def` `__init__(``self``, capacity):``        ``self``.top ``=` `-``1` `        ``self``.capacity ``=` `capacity``        ``# This array is used a stack ``        ``self``.array ``=` `[]``        ``# Precedence setting``        ``self``.output ``=` `[]``        ``self``.precedence ``=` `{``'+'``:``1``, ``'-'``:``1``, ``'*'``:``2``, ``'/'``:``2``, ``'^'``:``3``}``     ` `    ``# check if the stack is empty``    ``def` `isEmpty(``self``):``        ``return` `True` `if` `self``.top ``=``=` `-``1` `else` `False``     ` `    ``# Return the value of the top of the stack``    ``def` `peek(``self``):``        ``return` `self``.array[``-``1``]``     ` `    ``# Pop the element from the stack``    ``def` `pop(``self``):``        ``if` `not` `self``.isEmpty():``            ``self``.top ``-``=` `1``            ``return` `self``.array.pop()``        ``else``:``            ``return` `"\$"``     ` `    ``# Push the element to the stack``    ``def` `push(``self``, op):``        ``self``.top ``+``=` `1``        ``self``.array.append(op) `` ` `    ``# A utility function to check is the given character``    ``# is operand ``    ``def` `isOperand(``self``, ch):``        ``return` `ch.isalpha()`` ` `    ``# Check if the precedence of operator is strictly``    ``# less than top of stack or not``    ``def` `notGreater(``self``, i):``        ``try``:``            ``a ``=` `self``.precedence[i]``            ``b ``=` `self``.precedence[``self``.peek()]``            ``return` `True` `if` `a  <``=` `b ``else` `False``        ``except` `KeyError: ``            ``return` `False``             ` `    ``# The main function that ``    ``# converts given infix expression``    ``# to postfix expression``    ``def` `infixToPostfix(``self``, exp):``         ` `        ``# Iterate over the expression for conversion``        ``for` `i ``in` `exp:``            ``# If the character is an operand, ``            ``# add it to output``            ``if` `self``.isOperand(i):``                ``self``.output.append(i)``             ` `            ``# If the character is an '(', push it to stack``            ``elif` `i  ``=``=` `'('``:``                ``self``.push(i)`` ` `            ``# If the scanned character is an ')', pop and ``            ``# output from the stack until and '(' is found``            ``elif` `i ``=``=` `')'``:``                ``while``( (``not` `self``.isEmpty()) ``and` `                                ``self``.peek() !``=` `'('``):``                    ``a ``=` `self``.pop()``                    ``self``.output.append(a)``                ``if` `(``not` `self``.isEmpty() ``and` `self``.peek() !``=` `'('``):``                    ``return` `-``1``                ``else``:``                    ``self``.pop()`` ` `            ``# An operator is encountered``            ``else``:``                ``while``(``not` `self``.isEmpty() ``and` `self``.notGreater(i)):``                    ``self``.output.append(``self``.pop())``                ``self``.push(i)`` ` `        ``# pop all the operator from the stack``        ``while` `not` `self``.isEmpty():``            ``self``.output.append(``self``.pop())`` ` `        ``print` `"".join(``self``.output)`` ` `# Driver program to test above function``exp ``=` `"a+b*(c^d-e)^(f+g*h)-i"``obj ``=` `Conversion(``len``(exp))``obj.infixToPostfix(exp)`` ` `# This code is contributed by Nikhil Kumar Singh(nickzuck_007)`

## C#

 `using` `System;``using` `System.Collections.Generic;`` ` `/* c# implementation to convert ``infix expression to postfix*/``// Note that here we use Stack ``// class for Stack operations `` ` `public`  `class` `Test``{``     ` `    ``// A utility function to return ``    ``// precedence of a given operator ``    ``// Higher returned value means higher precedence ``    ``internal` `static` `int` `Prec(``char` `ch)``    ``{``        ``switch` `(ch)``        ``{``        ``case` `'+'``:``        ``case` `'-'``:``            ``return` `1;`` ` `        ``case` `'*'``:``        ``case` `'/'``:``            ``return` `2;`` ` `        ``case` `'^'``:``            ``return` `3;``        ``}``        ``return` `-1;``    ``}`` ` `    ``// The main method that converts given infix expression ``    ``// to postfix expression.  ``    ``public` `static` `string` `infixToPostfix(``string` `exp)``    ``{``        ``// initializing empty String for result ``        ``string` `result = ``""``;`` ` `        ``// initializing empty stack ``        ``Stack<``char``> stack = ``new` `Stack<``char``>();`` ` `        ``for` `(``int` `i = 0; i < exp.Length; ++i)``        ``{``            ``char` `c = exp[i];`` ` `            ``// If the scanned character is an ``            ``// operand, add it to output. ``            ``if` `(``char``.IsLetterOrDigit(c))``            ``{``                ``result += c;``            ``}`` ` `            ``// If the scanned character is an '(',``            ``// push it to the stack. ``            ``else` `if` `(c == ``'('``)``            ``{``                ``stack.Push(c);``            ``}`` ` `            ``//  If the scanned character is an ')', ``            ``// pop and output from the stack  ``            ``// until an '(' is encountered. ``            ``else` `if` `(c == ``')'``)``            ``{``                ``while` `(stack.Count > 0 && ``                        ``stack.Peek() != ``'('``)``                ``{``                    ``result += stack.Pop();``                ``}`` ` `                ``if` `(stack.Count > 0 && stack.Peek() != ``'('``)``                ``{``                    ``return` `"Invalid Expression"``; ``// invalid expression``                ``}``                ``else``                ``{``                    ``stack.Pop();``                ``}``            ``}``            ``else` `// an operator is encountered``            ``{``                ``while` `(stack.Count > 0 && Prec(c) <= ``                                  ``Prec(stack.Peek()))``                ``{``                    ``result += stack.Pop();``                ``}``                ``stack.Push(c);``            ``}`` ` `        ``}`` ` `        ``// pop all the operators from the stack ``        ``while` `(stack.Count > 0)``        ``{``            ``result += stack.Pop();``        ``}`` ` `        ``return` `result;``    ``}`` ` `    ``// Driver method  ``    ``public` `static` `void` `Main(``string``[] args)``    ``{``        ``string` `exp = ``"a+b*(c^d-e)^(f+g*h)-i"``;``        ``Console.WriteLine(infixToPostfix(exp));``    ``}``}`` ` `// This code is contributed by Shrikant13`

Output:

```abcd^e-fgh*+^*+i-
```

Quiz: Stack Questions

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