Infix to Prefix and Postfix Converter

FAQs

How do you convert an infix to a postfix and prefix?

To convert an infix expression to postfix and prefix, you typically use a stack and follow a series of steps. Here’s a high-level overview:

1. Infix to Postfix:
   • Initialize an empty stack and an output list.
   • Scan the infix expression from left to right.
   • If the scanned character is an operand, add it to the output list.
   • If the scanned character is an operator and the stack is empty or has an operator of lower precedence at the top, push it onto the stack.
   • If the scanned character is an operator with lower or equal precedence than the top of the stack, pop from the stack and add to the output list until this is no longer true, then push the scanned operator onto the stack.
   • If the scanned character is a left parenthesis, push it onto the stack.
   • If the scanned character is a right parenthesis, pop from the stack and add to the output list until a left parenthesis is encountered. Discard the pair of parentheses.
   • After the entire expression has been scanned, pop any remaining operators from the stack and add them to the output list.
2. Infix to Prefix:
   • Reverse the infix expression.
   • Replace every ‘(‘ with ‘)’ and every ‘)’ with ‘(‘.
   • Obtain the postfix expression of the modified expression.
   • Reverse the postfix expression to get the prefix expression.

How do you convert an infix to a prefix?

To convert an infix expression to a prefix expression:

1. Reverse the infix expression.
2. Replace every ‘(‘ with ‘)’ and every ‘)’ with ‘(‘.
3. Convert the modified expression to postfix.
4. Reverse the postfix expression to obtain the prefix expression.

What is the prefix notation of a + ( B * C )?

The prefix notation of the expression a + (B * C) is + a * B C.

How to convert infix to postfix step by step?

Step-by-step conversion of infix to postfix:

1. Input: A + B * C
2. Initialize an empty stack and an empty output list.
3. Read A – output list: A
4. Read + – stack: +
5. Read B – output list: A B
6. Read * – stack: + *
7. Read C – output list: A B C
8. End of expression, pop remaining operators from the stack to output list – output list: A B C * +

Why convert infix to postfix?

Infix expressions can be ambiguous and difficult to evaluate using a simple left-to-right scan, especially without parenthesis. Converting to postfix removes ambiguity and allows for straightforward, stack-based evaluation without the need for parenthesis.

How to convert infix to postfix and evaluate postfix expression?

1. Convert the infix expression to postfix using the algorithm described above.
2. Evaluate the postfix expression:
   • Initialize an empty stack.
   • Read the postfix expression from left to right.
   • If an operand is encountered, push it onto the stack.
   • If an operator is encountered, pop the necessary number of operands from the stack, apply the operator, and push the result back onto the stack.
   • The final result will be the only value left in the stack.

How to convert infix to prefix manually?

1. Reverse the infix expression.
2. Replace every ‘(‘ with ‘)’ and every ‘)’ with ‘(‘.
3. Convert the modified expression to postfix.
4. Reverse the postfix expression to obtain the prefix expression.

How to do prefix conversion?

Convert the infix expression to prefix by following the steps: reverse the infix expression, swap parentheses, convert to postfix, and then reverse the result.

What is an example of a prefix infix and suffix?

• Prefix: + A B
• Infix: A + B
• Postfix: A B +

How to convert prefix to postfix?

To convert prefix to postfix:

1. Reverse the prefix expression.
2. Convert the reversed expression to infix.
3. Reverse the infix expression to obtain the postfix expression.

Why is postfix better than prefix?

Postfix notation is often considered better for evaluation because it allows for a simple left-to-right scan and uses a stack to evaluate expressions without the need for parentheses, making it less error-prone in practical use.

What is an example of an infix?

Example of infix: A + B * C

What is an example of a postfix notation?

Example of postfix: A B C * +