Infix to Postfix Conversion

While working with mathematical expressions in programming or compiler design, you often have to deal with infix or postfix expressions. While it is easy for humans to understand infix expressions, the postfix expressions are often preferred by computers as they remove the need for parentheses and reduce ambiguity. In this blog, we will discuss Infix to Postfix Conversion, along with its algorithm, working, and implementation using a stack.

Table of Contents:

• What is Infix Notation?
• What is a Postfix Expression?
• Conversion of Infix to Postfix
  • Rules for Converting Infix to Postfix Expression
• Example for Converting an Infix Expression to Postfix
• Implementation of Infix to Postfix
  1. C Program to Convert Infix to Postfix
  2. C++ Program to Convert Infix to Postfix
  3. Java Program to Convert Infix to Postfix
  4. Python Program to Convert Infix to Postfix
  5. JavaScript Program to Convert Infix to Postfix
• Best Practices to Convert Infix to Postfix
• Conclusion

What is Infix Notation?

Infix Notation is the way of writing mathematical expressions. Here, the operator comes in between the operands. For example, A + B or X * Y are the infix expressions. It is easy for humans to read and understand, but computers may find it hard to understand and evaluate it directly.

Syntax of Infix Notation

The syntax for Infix notation is simple and easy to understand:

operand1 operator operand2

Here:

• operand1 and operand2 are the values or variables (like A, B, 5, 10)
• operator is basically a mathematical symbol (like +,  -,  *,  /)

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Problem with infix notation

The main problem behind the infix notation is that computers find it hard to evaluate it directly because of the operator precedence or parentheses. You also need extra rules in order to decide which operation you need to perform first, which makes the programming process tricky. This is why an Infix to Postfix converter is useful, as it helps to simplify the process of evaluation.

What is a Postfix Expression?

A Postfix Expression is also called Reverse Polish Notation. It is a way of writing mathematical expressions where the operator comes after the operands. For example, if the infix expression is X + Y, then the postfix version is X Y +.

Postfix expressions are easier for computers to evaluate. This is because they don’t need parentheses, and they follow operator precedence implicitly. This makes them more efficient than prefix expressions.

Syntax of Postfix Notation

The syntax for Postfix notation is different compared to the Infix notation because the operator comes after the operands.

operand1 operand2 operator

Here:

• operator is the mathematical symbol (like +, -, *, /, ^)
• operand1 and operand2 are the values or variables (like A, B, 5, 10)

Conversion of Infix to Postfix

It is important to know how to convert infix to postfix in order to evaluate expressions efficiently. To do this, you have to use an Infix to Postfix converter that is dependent on the stack data structure. The expressions that you want to convert might include operands, operators, and brackets ( or ). All of these are handled carefully while you convert infix to postfix using a stack. This process follows the algorithm to convert from infix to postfix step by step. This makes it easy for you to understand and implement.

Rules for Converting Infix to Postfix Expression

Given below are some of the basic rules that you need to follow when you convert from infix to postfix:

1. Operands go directly to the output: If you see a number or variable (like A, B, 5), you need to add it directly to the postfix expression.

2. Push ‘(‘ onto the stack: Whenever you see an opening bracket ‘(‘, you should put it on the stack so that you can use it later.

3. Pop until ‘(‘ for closing bracket: When you find a closing bracket ), you should take the operators out of the stack and add them to the output until you reach the same opening bracket ( . Then remove the bracket from the stack.

4. Operators are pushed based on precedence: If the stack is empty or the operator on the stack has a lower precedence than the current one, you have to push the current operator.

5. Pop operators with higher or equal precedence: If the operator present at the top of the stack has equal or higher precedence than the current operator, you need to pop it and add it to the output before you push the current operator.

6. Pop remaining operators at the end: After you have scanned the entire infix expression, you need to pop any remaining operators from the stack and then add them to the postfix expression.

Example for converting an Infix Expression to Postfix

In this section, we are going to do a dry run of an infix expression to find out its corresponding postfix expression.

Let us take an infix expression: K + L – M*N + (O^P) * W/U/V * T + Q. This expression is read from left to right. For each symbol, the current contents of the stack and the corresponding postfix expression are shown in the table:

The final Postfix expression is: 

K L + M N * - O P ^ W * U / V / T * + Q +

Explanation:

1. Step 1: K (Operand)

Since K is an operand, you need to add it directly to the postfix expression. Operands don’t need any checks for precedence; therefore, they go directly into postfix. At this step, the postfix expression is K, and the stack is empty.

2. Step 2: + (Operator)

The next symbol is the + operator. Since the stack is empty, you have to place + onto the stack. You can add operators directly to the postfix expression as you need to check their precedence at first. Therefore, the postfix expression is still K, and the + is now held by the stack.

3. Step 3: L (Operand)

L is another operand; therefore, you need to add it directly to the postfix expression. In the postfix form, operands are always placed right away. After this step, the postfix expression becomes K L, and the stack still contains the + in it.

4. Step 4: – (Operator)

The next symbol is –. Before you add it to the stack, you have to look at the top of the stack, which already has +. Since + and – have the same precedence, you need to remove + from the stack and include it in the postfix expression. The updated expression becomes K L +. Then the stack becomes empty, so push – onto the stack.

5. Continuing the Conversion

Continue this process for each element by adding operands directly to the postfix expression. Operators are always pushed or popped from the stack depending on their precedence compared to the operator present at the top of the stack. The opening brackets are pushed to indicate the start of a sub-expression, whereas the closing brackets cause popping from the stack until the matching opening bracket is removed.

6. Finalizing the Postfix Expression

Once you have read the whole infix expression, there may still be operators that are left in the stack. You need to pop all the remaining operators from the stack and append them to the postfix expression. The resultant postfix expression is:

K L + M N * - O P ^ W * U / V / T * + Q +

Implementation of Infix to Postfix

Here, we will discuss the various implementation methods of conversion of Infix to Postfix in different programming languages.

1. C Program to Convert Infix to Postfix

Here, a C program is given below, which shows the conversion of Infix to Postfix.

Code:

Output:

Explanation: The above C program is used to read an infix expression from the user and then convert it into a postfix expression using a stack.

2. C++ Program to Convert Infix to Postfix

Here, a C++ program is given below, which shows the conversion of Infix to Postfix.

Code:

Output:

Explanation: The above C++ program is used to take an infix expression as input and then convert it into a postfix expression. It uses a stack based on operator precedence and parentheses.

3.  Java Program to Convert Infix to Postfix

Here, a Java program is given below, which shows the conversion of Infix to Postfix.

Code:

Output:

Explanation: The above Java code is used to take an infix expression as input. After that, it converts the infix expression into a postfix expression using a stack based on operator precedence and parentheses handling.

4. Python Program to Convert Infix to Postfix

Here, a Python program is given below, which shows the conversion of Infix to Postfix.

Code:

Output:

Explanation:

The above Python program is used to read an infix expression. After that, it uses a stack to handle operators and parentheses. It then gives the output as the postfix expression following the operator precedence rules.

5.  JavaScript Program to Convert Infix to Postfix

Here, a JavaScript program is given below, which shows the conversion of Infix to Postfix.

Code:

Output:

Explanation: The above JavaScript code is used to read an infix expression. It uses a stack to manage operators and parentheses based on precedence. It then produces the corresponding output, which is the postfix expression.

Best Practices to Convert Infix to Postfix

1. While converting from Infix to Postfix, you should always keep your operators in a stack. This helps you to handle precedence and parentheses correctly.

2. Whenever you see a number or variable (operand), you should add it straight to the postfix expression.

3. Before you push a new operator onto the stack, you should always compare its precedence with the operator present at the top of the stack.

4. After reading the entire expression, you need to pop all the remaining operators from the stack in order to complete the postfix expression.

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Conclusion

Using an Infix to Postfix converter allows for much easier and more reliable processing of mathematical expressions. You can evaluate infix expressions easily and also resolve the precedence and errors in parentheses by converting the infix expressions to postfix. Having a good understanding of the conversion process and following the best practices will help you ensure that you can work with complex expressions in programming or calculations confidently.

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Infix to Postfix Conversion – FAQs