Introduction
RPN stands for Reverse Polish Notation. It is a mathematical notation that is used to represent arithmetic expressions. It was developed by Jan Lukasiewicz in the early 20th century. RPN is also known as postfix notation as the operators appear after the operands.How does RPN work?
In RPN, the operators are written after the operands. For example, to add two numbers in RPN, we write the first number, then the second number, and finally the plus sign. The expression '3 4 +' in RPN represents the sum of 3 and 4.Advantages of RPN
One of the main advantages of RPN is that it eliminates the need for parentheses in mathematical expressions. This makes it easier to read and write complex expressions. Additionally, RPN is easier to implement in computer programs as the order of operations is well-defined.Applications of RPN
RPN is widely used in calculators, especially those designed for scientific and engineering purposes. It is also used in computer programming languages, such as Forth and HP-GL.Examples of RPN expressions
Here are some examples of RPN expressions: - 2 3 + 4 * = 20 (Add 2 and 3, then multiply by 4) - 5 6 7 * + = 47 (Multiply 6 and 7, then add 5) - 3 4 2 * 1 5 - 2 3 ^ ^ / + = 3.5 (Evaluate a complex expression)Comparison with infix notation
Infix notation is the standard notation used in mathematics, where operators are placed between the operands. For example, to add two numbers in infix notation, we write '3 + 4'. Infix notation can be ambiguous and requires the use of parentheses for complex expressions. In contrast, RPN notation is unambiguous and eliminates the need for parentheses.Conclusion
RPN is a mathematical notation that represents arithmetic expressions using operators that appear after the operands. It has several advantages over infix notation, including the elimination of parentheses and well-defined order of operations. RPN is widely used in calculators and computer programming languages.
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