🔁 Reverse Polish Notation (RPN)
Definition:
Reverse Polish Notation (RPN), also called postfix notation, is a mathematical notation in which operators follow their operands. There are no parentheses needed to dictate order of operations.
Example:
- Infix:
3 + 4 - Postfix (RPN):
3 4 +
✅ Advantages of Postfix over Infix
- No Need for Parentheses:
- In postfix, the order of operations is explicit, eliminating the need for brackets.
- Simple Evaluation:
- Postfix expressions are easy to evaluate using a stack, avoiding the complexity of operator precedence.
- Efficient for Computers:
- Computers and compilers can process postfix notation faster and more reliably than infix.
- Easy to Implement in Code:
- Algorithmically simpler to parse and evaluate.
🧮 Evaluation of Postfix Expressions Using a Stack
Algorithm:
- Initialize an empty stack.
- Scan the postfix expression left to right:
- If the token is an operand, push it to the stack.
- If the token is an operator, pop the top two operands, apply the operator, and push the result back.
- The result will be the single element remaining on the stack.
Example:
Postfix expression: 5 3 2 * +
Steps:
- Push 5
- Push 3
- Push 2
*: Pop 2 and 3 → 3 × 2 = 6 → Push 6+: Pop 6 and 5 → 5 + 6 = 11 → Push 11
Result: 11
🔧 Applications in Calculators and Compilers
1. Calculators:
- Many scientific and HP calculators use RPN for efficient and accurate computation.
- Users enter operands before operators, reducing ambiguity and errors.
2. Compilers:
- During expression parsing, compilers often convert infix expressions to postfix (RPN) using the Shunting Yard algorithm.
- Makes code generation and evaluation simpler in intermediate code.
📘 What is Parsing?
Parsing means analyzing a sequence of symbols (like a sentence or expression) to understand its structure and meaning according to a set of rules, typically a grammar.
🧠 In Simple Words:
Parsing = Understanding the structure of input
🧮 In Programming/Compilers:
- When a compiler parses code, it breaks it into parts (like variables, operators, etc.) and checks if the code follows the rules of the programming language (syntax).
- Parsing helps in building an internal tree-like structure (syntax tree) that represents how the code should be understood and executed.
Example:
Expression: 3 + 4 * 2
- A parser will break it into:
3→ operand+→ operator4,*,2→ another sub-expression
It then decides:
4 * 2happens first (due to precedence),- then add
3.
🧾 Parsing in Natural Language:
In English, parsing the sentence:
“The cat sat on the mat.”
Means:
- Identifying “The cat” as the subject
- “sat” as the verb
- “on the mat” as a prepositional phrase
✅ Uses of Parsing:
- Compilers (to convert code into machine-understandable form)
- Interpreters
- Calculators using RPN
- Web browsers (to parse HTML, CSS)
- Natural language processing (NLP)
💻 What is Intermediate Code?
Intermediate Code is a kind of temporary, simplified code generated by a compiler between the source code and machine code.
Think of it as a bridge between high-level language (like C++, Java, Python) and low-level machine instructions.
- It’s not machine-specific, meaning it can be used for different computer architectures.
- Helps in optimizing and analyzing the program before turning it into final machine code.
- Acts as a universal format that simplifies the compiler design.
📌 Why RPN (Postfix) is Useful in Intermediate Code
When a compiler translates an expression like:
It first parses it into a structure (like a syntax tree), then often converts it to postfix (RPN):
This postfix form becomes easier to translate into intermediate instructions, such as:
These t1, t2 are temporary variables in intermediate code, often represented in:
- Three-address code
- Postfix notation (RPN)
- Quadruples, or
- Stack-based instructions
🛠️ Applications Recap
1. ✅ Calculators:
- HP and scientific calculators use RPN to let users enter operands first, which simplifies real-time computation and avoids the need for parentheses.
2. 🧠 Compilers:
- Compilers use RPN/postfix notation during the intermediate code generation phase.
- It simplifies:
- Operator precedence handling
- Code optimization
- Final machine code generation
🔁 Summary
| Concept | Role |
|---|---|
| Parsing | Understanding and breaking down expressions |
| RPN (Postfix) | A simpler, unambiguous expression format |
| Intermediate Code | A simplified version of source code, easier for the machine to process |
| Compilers | Use RPN to generate efficient intermediate code |