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Infix to Postfix conversion using Stack

This post is about conversion of Infix expression to Postfix conversion. For this conversion we take help of stack data structure, we need to push and pop the operators in and out of the stack.

Infix expressions are the expressions that we normally use,eg. 5+6-7; a+b*c etc. Postfix expressions are the expressions in which the 2 operands are followed by the operator eg. 56+7- , abc*+ etc.

 So inorder to convert an infix expression to a postfix expression we follow the below steps
(we have 2 string, 1st is the input infix expression string 2nd is the output string which is empty initially)

  1. We start by going through the characters of the infix expression one by one.
  2. If we come across an operand we simply copy it to the Postfix output string.
  3. If we come across any opening parenthesis we push it on the stack.
  4. If we come across any closing parenthesis we pop the stack till we find the corresponding opening parenthesis.
  5. If we come across an operator then we have 2 cases based on the precedence of the operators
    1. If the current operator has higher precedence than the stack top then we push the current operator on the stack.
    2. If the current operator has precedence less than or equal to the stack top then we pop the operator at the top and put it to the output string and then check the above condition again with the new stack top.
To see Simple Stack implementation program, click Here.

C Program

C++ Program

Sample input and output to check the program



You might also be interested in 

 Bubble Sort
Insertion Sort
Selection sort
Shell Sort
Hashing with Linear Probing
Hashing with Quadratic Probing
Double Hashing
4 methods to swap 2 numbers
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