(a+b^c)*d+e^5 Convert Infix To Postfix

Jasonbradley

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Jun 16, 2024

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Converting Infix to Postfix: (a+b^c)*d+e^5

This article will guide you through the process of converting the infix expression *(a+b^c)d+e^5 to its postfix equivalent.

Understanding Infix and Postfix Notation

• Infix Notation: This is the standard way we write mathematical expressions, where operators are placed between their operands (e.g., 2 + 3).
• Postfix Notation: Also known as Reverse Polish Notation (RPN), operators are placed after their operands (e.g., 2 3 +).

Conversion Algorithm: Using a Stack

1. Initialization: Create an empty stack to store operators.
2. Scan the Infix Expression: Read the infix expression from left to right.
3. For each token:
   • Operand: Directly append the operand to the postfix expression.
   • Operator:
     • If the stack is empty or the top of the stack is a '(': Push the operator onto the stack.
     • If the operator has higher precedence than the top of the stack: Push the operator onto the stack.
     • If the operator has lower or equal precedence than the top of the stack: Pop operators from the stack and append them to the postfix expression until an operator with lower precedence is encountered or the stack becomes empty. Then, push the current operator onto the stack.
   • '(': Push '(' onto the stack.
   • ')': Pop operators from the stack and append them to the postfix expression until a '(' is encountered. Pop and discard the '('.
4. After processing the entire expression: Pop any remaining operators from the stack and append them to the postfix expression.

Applying the Algorithm to (a+b^c)*d+e^5

1. Initialization: Stack: []

2. Scan:

   Token	Postfix	Stack
   (		(
   a	a	(
   +	a	( +
   b	a b	( +
   ^	a b	( + ^
   c	a b c	( + ^
   )	a b c ^ +
   *	a b c ^ +	*
   d	a b c ^ + d	*
   +	a b c ^ + d	* +
   e	a b c ^ + d e	* +
   ^	a b c ^ + d e	* + ^
   5	a b c ^ + d e 5	* + ^

3. After scanning:

   | Postfix: a b c ^ + d * e 5 ^ + | Stack: [] |

Conclusion

The postfix expression for *(a+b^c)d+e^5 is a b c ^ + d * e 5 ^ +. This form is more convenient for evaluating expressions using a stack-based algorithm.