What is infix notation?

The ordinary way of writing an expression, with each binary operator placed between its two operands, as in 3 + 4. Because the order of evaluation is not shown by the layout, infix notation needs rules of operator precedence and brackets to say which operation is performed first.

Convert (3 + 4) * 5 to Reverse Polish notation.

3 4 + 5 *. The bracketed subexpression 3 + 4 becomes 3 4 +, and that result is then multiplied by 5, so the operands 3 4 + and 5 are followed by the operator *.

Convert 5 + 3 * 2 to Reverse Polish notation.

5 3 2 * +. Multiplication binds more tightly than addition, so 3 * 2 is evaluated first and becomes 3 2 *; that result is then added to 5, giving 5 3 2 * +.

Convert (a + b) * (c - d) to Reverse Polish notation.

a b + c d - *. Each bracketed subexpression is converted in turn — a + b becomes a b + and c - d becomes c d - — and the operator that joins them, *, is written after both.

Convert 7 2 3 * - from Reverse Polish notation to infix form and evaluate it.

Working left to right, 2 3 * means 2 * 3, and then 7 followed by that result and the operator - means 7 - (2 * 3). The infix form is 7 - 2 * 3, which evaluates to 7 - 6 = 1.

AQA A-Level Computer Science 7517

Fundamentals of Programming

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Topic overview Data Structures and Abstract Data Types Static and Dynamic Data Structures Queues and Linear Queues Circular and Priority Queues Stacks Graphs Trees Hash tables Dictionaries Vectors and Their Notation Vector Arithmetic and Geometry

Fundamentals of Algorithms

Topic overview Graph traversal Tree traversal Reverse Polish notation Searching algorithms Sorting algorithms Optimisation algorithms

Theory of Computation

Topic overview Logic Problems and Algorithm Constructs Pseudo-Code, Hand-Tracing and Program Correctness Representational Abstraction, Generalisation and Information Hiding Procedural and Functional Abstraction Data Abstraction and Problem Reduction Decomposition and Composition Automation and Finite State Machines Sets and Set Notation Subsets and Set Operations Regular expressions and regular languages Backus-Naur Form and syntax diagrams Comparing Algorithms and Functions Order of complexity and Big-O notation Limits of computation, tractability and heuristics Computable problems and the Halting problem Turing machines

Fundamentals of Data Representation

Topic overview Number systems and the sets of numbers Number bases: decimal, binary and hexadecimal Bits, bytes and units of information Unsigned binary and binary arithmetic Signed binary using two's complement Fixed point and floating point representation Normalisation of floating point numbers Rounding errors, accuracy, range and precision Character coding systems Error checking and correction Bit patterns, analogue and digital Bitmapped graphics Vector graphics Digital representation of sound MIDI and Data Compression Encryption

Fundamentals of Computer Systems

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Big Data

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Fundamentals of Algorithms

Reverse Polish notation

2 things to know
Paper 1

Overview

Recall questions on converting between infix and postfix, evaluating a postfix expression with a stack, and why the notation needs no brackets.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What is Reverse Polish notation?

Evaluation

Why is Reverse Polish notation used?

Questions from this subtopic

Each one with the model answer underneath.

1
What is Reverse Polish notation?
Model answer
A way of writing an expression in which each operator is written after the operands it applies to, rather than between them. It is also called postfix notation. For example the infix expression 3 + 4 is written 3 4 + in Reverse Polish.
2
What is infix notation?
Model answer
The ordinary way of writing an expression, with each binary operator placed between its two operands, as in 3 + 4. Because the order of evaluation is not shown by the layout, infix notation needs rules of operator precedence and brackets to say which operation is performed first.
3
Convert (3 + 4) * 5 to Reverse Polish notation.
Model answer
3 4 + 5 *. The bracketed subexpression 3 + 4 becomes 3 4 +, and that result is then multiplied by 5, so the operands 3 4 + and 5 are followed by the operator *.
4
Convert 5 + 3 * 2 to Reverse Polish notation.
Model answer
5 3 2 * +. Multiplication binds more tightly than addition, so 3 * 2 is evaluated first and becomes 3 2 *; that result is then added to 5, giving 5 3 2 * +.
5
Convert (a + b) * (c - d) to Reverse Polish notation.
Model answer
a b + c d - *. Each bracketed subexpression is converted in turn — a + b becomes a b + and c - d becomes c d - — and the operator that joins them, *, is written after both.
6
Convert 7 2 3 * - from Reverse Polish notation to infix form and evaluate it.
Model answer
Working left to right, 2 3 * means 2 * 3, and then 7 followed by that result and the operator - means 7 - (2 * 3). The infix form is 7 - 2 * 3, which evaluates to 7 - 6 = 1.

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