(a+b)*(c+d) Infix To Postfix

Jasonbradley

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Jun 16, 2024

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Converting (a+b)*(c+d) from Infix to Postfix Notation

Infix notation is the way we typically write mathematical expressions, with operators placed between operands. Postfix notation, also known as Reverse Polish Notation (RPN), places operators after their operands.

Understanding Infix and Postfix

• Infix: (a + b) * (c + d)
• Postfix: a b + c d + *

Let's break down how to convert from infix to postfix using the given example:

Algorithm for Conversion

1. Initialize an empty stack and an empty output string.

2. Scan the infix expression from left to right.

3. For each token:

   • If the token is an operand (a, b, c, d), append it to the output string.
   • *If the token is an operator (+, ):
     • While the stack is not empty and the top element of the stack has a higher precedence than the current operator:
       • Pop the operator from the stack and append it to the output string.
     • Push the current operator onto the stack.
   • If the token is a left parenthesis '(', push it onto the stack.
   • If the token is a right parenthesis ')',
     • Pop operators from the stack and append them to the output string until a left parenthesis '(' is encountered. Discard both the left and right parentheses.

4. Once all tokens have been processed, pop any remaining operators from the stack and append them to the output string.

Applying the Algorithm

Let's walk through the conversion of (a + b) * (c + d):

Therefore, the postfix expression for (a + b) * (c + d) is: a b + c d + * .

Why Use Postfix Notation?

Postfix notation is advantageous for computer evaluation because it eliminates the need for parentheses and operator precedence rules. This simplifies parsing and allows for efficient evaluation using a stack-based approach.