If arity of operators is fixed, then which of the following notations can be used to parse expressions without parentheses? a) Infix Notation (Inorder traversal of a expression tree) b) Postfix Notation (Postorder traversal of a expression tree) c) Prefix Notation (Preorder traversal of a expression tree)a)b and cb)Only bc)a, b and cd)None of themCorrect answer is option 'A'. Can you explain this answer?

Question

Accepted Answer

Polish notation (PN), also known as normal Polish notation (NPN),[1] Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators precede their operands, in contrast to reverse Polish notation (RPN) in which operators follow their operands. It does not need any parentheses as long as each operator has a fixed number of operands. The description 'Polish' refers to the nationality of logician Jan Łukasiewicz,[2] who invented Polish notation in 1924.

The term Polish notation is sometimes taken (as the opposite of infix notation) to also include reverse Polish notation.[5]

When Polish notation is used as a syntax for mathematical expressions by programming language interpreters, it is readily parsed into abstract syntax trees and can, in fact, define a one-to-one representation for the same. Because of this, Lisp (see below) and related programming languages define their entire syntax in terms of prefix notation (and others use postfix notation).

Answer

Parsing Expressions with Fixed Arity Operators

In computer science, parsing is the process of analyzing a string of symbols to determine its grammatical structure. While parsing expressions, we may encounter expressions with fixed arity operators. Arity refers to the number of operands that an operator takes.

For example, the addition operator (+) takes two operands, so it has an arity of 2. Similarly, the multiplication operator (*) also takes two operands, so it also has an arity of 2.

Notations for Parsing Expressions without Parentheses

When parsing expressions with fixed arity operators, we can use the following notations to parse expressions without parentheses:

1. Infix Notation (Inorder traversal of an expression tree)
2. Postfix Notation (Postorder traversal of an expression tree)
3. Prefix Notation (Preorder traversal of an expression tree)

Out of these notations, only Infix Notation cannot be used to parse expressions without parentheses. This is because the Infix Notation requires the use of parentheses to determine the order of operations.

For example, consider the expression '2 + 3 * 4'. In Infix Notation, this expression is written as '2 + (3 * 4)', which uses parentheses to specify that the multiplication operation should be performed before the addition operation.

On the other hand, Postfix and Prefix Notation do not require the use of parentheses to determine the order of operations. This is because the order of operations is determined by the position of the operators in the expression.

For example, in Postfix Notation, the expression '2 3 4 * +' is equivalent to '2 + (3 * 4)'. Similarly, in Prefix Notation, the expression '+ 2 * 3 4' is equivalent to '2 + (3 * 4)'.

Conclusion

In summary, when parsing expressions with fixed arity operators, we can use Postfix or Prefix Notation to parse expressions without parentheses. However, Infix Notation requires the use of parentheses to determine the order of operations, and hence cannot be used to parse expressions without parentheses.

Answer

Polish notation (PN), also known as normal Polish notation (NPN),^[1] Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which

operators

precede their

operands

, in contrast to the more common

infix notation

, in which operators are placed between operands, as well as

reverse Polish notation

(RPN), in which operators follow their operands. It does not need any parentheses as long as each operator has a fixed

number of operands

. The description 'Polish' refers to the

nationality

of

logician

Jan Łukasiewicz

,^[2] who invented Polish notation in 1924.^[3]^[4]

The term Polish notation is sometimes taken (as the opposite of infix notation) to also include reverse Polish notation.^[5]

When Polish notation is used as a syntax for mathematical expressions by

programming language

interpreters

, it is readily parsed into

abstract syntax trees

and can, in fact, define a

one-to-one representation

for the same. Because of this,

Lisp

(

see below

) and related programming languages define their entire syntax in prefix notation (and others use postfix notation).

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