In data structures and expression evaluation, what are the standard notations used when evaluating arithmetic expressions written in prefix and postfix forms?

Introduction / Context:
This question deals with arithmetic expression notation in data structures and algorithms. Prefix and postfix expressions are widely used in compiler design, stack based evaluation, and conversion between different forms of expressions. Understanding the names Polish notation and Reverse Polish notation is important when reading textbooks and technical documentation.

Given Data / Assumptions:

- The question asks about notations used for prefix and postfix forms.- Prefix expressions place operators before operands.- Postfix expressions place operators after operands.

Concept / Approach:
Polish notation is the historical term for prefix notation, while Reverse Polish notation refers to postfix notation. Both were introduced to remove the need for parentheses in expressions and to simplify expression evaluation by machines. The correct answer must therefore acknowledge that prefix and postfix notations correspond to these two forms. Infix notation is the common human readable form but is not specifically associated with prefix or postfix evaluation names.

Step-by-Step Solution:
Step 1: Recall that prefix notation, where an operator comes before its operands, is called Polish notation.Step 2: Recall that postfix notation, where an operator comes after its operands, is called Reverse Polish notation.Step 3: Note that both notations are designed to avoid parentheses by making the order of operations unambiguous.Step 4: Option C states that both Polish and Reverse Polish notations are used, which matches the association with prefix and postfix.Step 5: Options A and B mention only one of the two, which is incomplete.Step 6: Options D and E do not correctly describe the standard terminology for prefix or postfix notations.

Verification / Alternative check:
Standard algorithm textbooks and compiler design resources clearly define prefix as Polish notation and postfix as Reverse Polish notation. They show examples of evaluating such expressions using stacks, where operators and operands follow these formats. There is no reference to a separate notation name called binary tree notation for these expression formats, and infix notation is separate from Polish and Reverse Polish notation, which confirms the correct option.

Why Other Options Are Wrong:
Option A is wrong because it acknowledges only Polish notation and ignores Reverse Polish notation. Option B is wrong for similar reasons, focusing only on Reverse Polish notation. Option D is incorrect because infix notation is the usual human readable form, not the specific name for prefix or postfix evaluation. Option E is incorrect because while expressions can be represented as binary trees internally, that phrase is not the standard name for prefix or postfix expression notations.

Common Pitfalls:
Learners sometimes confuse the names or forget which notation is associated with which format. Another mistake is to assume that these notations are only theoretical, when in fact they are used in calculators and virtual machines. Remember that the word reverse in Reverse Polish notation hints at the operator being placed after operands, while simple Polish notation places it before.

Final Answer:
The notations used are both Polish notation for prefix and Reverse Polish notation for postfix.