Infix to Postfix converter

1. Create an empty stack
2. Start scanning the infix expression from left to right
3. If the current character is an operand, append it to the result string
4. If the current character is an operator, push it onto the stack
5. If the current character is a left parentheses, push it onto the stack
6. If the current character is a right parentheses, pop operators from the stack and append them to the result string until you reach a left parentheses. Discard the left and right parentheses.
7. Repeat steps 2-6 until you have scanned the entire expression
8. Pop any remaining operators from the stack and append them to the result string

In the realm of computer science and programming, the conversion of mathematical expressions from infix notation to postfix notation is a fundamental concept. This article delves into the intricacies of the infix to postfix conversion process, providing a step-by-step guide, an algorithm, practical examples, and even a glimpse into coding this conversion in Java. We will also touch on relevant data structures and include a section on multiple-choice questions (MCQs) to test your understanding.

What is Infix and Postfix Notation?

Before we dive into the conversion process, let’s clarify what infix and postfix notations are:

• Infix Notation: This is the most common way of writing expressions, where operators are placed between operands. For example, the expression (A + B) is in infix notation.
• Postfix Notation: Also known as Reverse Polish Notation (RPN), in this format, operators follow their operands. The same expression (A + B) would be written as (AB+) in postfix notation.

The main advantage of postfix notation is that it eliminates the need for parentheses to dictate operation order, thus simplifying the process of expression evaluation.

Infix to Postfix Conversion Step by Step

The conversion from infix to postfix can be achieved through a systematic approach. Here’s a step-by-step breakdown of the process:

1. Initialize an empty stack for operators and an empty list for the output.
2. Read the infix expression from left to right.
3. Operands (like variables or numbers) are added directly to the output list.
4. Operators are pushed onto the stack, but first, the algorithm checks for operator precedence and associativity:

• If the stack is empty or contains a left parenthesis on top, push the operator onto the stack.
• If the incoming operator has higher precedence than the operator on top of the stack, push it onto the stack.
• If the incoming operator has lower or equal precedence, pop operators from the stack to the output list until this is no longer true. Then push the incoming operator onto the stack.

5. Left Parenthesis is pushed onto the stack to indicate that a subexpression is starting.
6. Right Parenthesis causes the stack to be popped to the output list until a left parenthesis is encountered.
7. After reading the entire expression, pop all operators from the stack to the output list.

Infix to Postfix Conversion Algorithm

Here’s a simple algorithm for converting an infix expression to postfix:

1. Initialize an empty stack and an empty output list.
2. For each token in the infix expression:
a. If the token is an operand, add it to the output list.
b. If the token is a left parenthesis, push it onto the stack.
c. If the token is a right parenthesis, pop from the stack to the output list until a left parenthesis is at the top of the stack.
d. If the token is an operator:
i. While there is an operator at the top of the stack with greater or equal precedence, pop from the stack to the output list.
ii. Push the current operator onto the stack.
3. Pop all operators from the stack to the output list.
4. The output list is the postfix expression.

Infix to Postfix Examples

Let’s illustrate the conversion process with a couple of examples:

Example 1: Simple Expression

Infix: (A + B)

Postfix: (AB+)

Example 2: Expression with Parentheses

Infix: ((A + B) * C)

Step-by-Step Conversion:

1. Read ‘(‘: push to stack.
2. Read ‘A’: add to output.
3. Read ‘+’: push to stack.
4. Read ‘B’: add to output.
5. Read ‘)’: pop ‘+’ to output, pop ‘(‘ (discard).
6. Read ‘*’: push to stack.
7. Read ‘C’: add to output.
8. End of expression: pop ‘*’ to output.

Postfix: (AB+C*)

Infix to Postfix Converter Code in Java

Here’s a simple Java implementation of the infix to postfix conversion algorithm:

import java.util.Stack;

public class InfixToPostfix {
public static int precedence(char op) {
switch (op) {
case '+':
case '-':
return 1;
case '*':
case '/':
return 2;
case '^':
return 3;
default:
return -1;
}
}

public static String infixToPostfix(String expression) {
Stack> stack = new Stack<>();
StringBuilder output = new StringBuilder();

for (char token : expression.toCharArray()) {
if (Character.isLetterOrDigit(token)) {
output.append(token);
} else if (token == '(') {
stack.push(token);
} else if (token == ')') {
while (!stack.isEmpty() && stack.peek() != '(') {
output.append(stack.pop());
}
stack.pop(); // pop '('
} else {
while (!stack.isEmpty() && precedence(token) <= precedence(stack.peek())) {
output.append(stack.pop());
}
stack.push(token);
}
}

while (!stack.isEmpty()) {
output.append(stack.pop());
}

return output.toString();
}

public static void main(String[] args) {
String infix = "(A+B)*C";
String postfix = infixToPostfix(infix);
System.out.println("Postfix: " + postfix);
}
}

Infix to Postfix Conversion Data Structure

The primary data structure utilized in the infix to postfix conversion is the stack. Stacks are ideal for this purpose because they follow the Last In First Out (LIFO) principle, which aligns perfectly with the need to manage operator precedence and parenthesis during the conversion process.

Infix to Postfix Conversion MCQ

1. What is the postfix of the expression (A + B * C)? a) (AB + C *) b) (ABC * +) c) (AB + C) d) (ABC + *)

Answer: b) (ABC * +)

2. Which data structure is primarily used in the infix to postfix conversion? a) Queue b) Stack c) Array d) Linked List

Answer: b) Stack

3. In the expression ((A + B) * C), what is the first operator to be added to the output list? a) + b) * c) A d) B

Answer: c) A

Conclusion

The conversion from infix to postfix notation is a critical skill in programming and algorithm design. By understanding the step-by-step conversion process, the underlying algorithm, and the relevant data structures, you can effectively implement this conversion in your code. The provided Java code serves as a solid foundation for your own infix to postfix converter. Whether you are preparing for exams or enhancing your programming skills, mastering this concept will undoubtedly benefit your computational prowess.