What is a three-dimensional array?

A three-dimensional array is a static structure holding elements of one type that are located by three subscripts, so it behaves as a stack of two-dimensional tables.

How many elements does an array declared with bounds 0 to 2, 0 to 3 and 0 to 4 hold?

It holds 3 × 4 × 5 = 60 elements.

How is a single element of a three-dimensional array referred to in a program?

It is referred to by the array name followed by all three subscripts, such as sales[2][1][4].

Explain how a colour image is held in a three-dimensional array.

The first two subscripts give the row and column of the pixel and the third selects the red, green or blue component of that pixel.

WJEC A-Level Computer Science 601-5345-3

Hardware: Architecture, Memory and Storage

Topic overview Components of a computer system and how they connect Von Neumann architecture and the CPU The fetch-execute cycle Memory and caching Parallel processing Input and output devices and their uses Secondary storage, fragmentation and defragmentation

Networks and Data Transmission

Topic overview Serial and parallel transmission Simplex, half duplex and full duplex Multiplexing and switching Packets and the TCP/IP protocol stack Networks, standards and protocols Collisions and shared media Routing, addressing and the internet

Logic Gates and Boolean Algebra

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Data Representation and Data Types

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Data Structures

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Organisation of Data: Files and Records

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Database Systems

Topic overview Flat files and the relational model Relational and other contemporary database systems Primary, foreign, composite and candidate keys Indexes and links between tables Entity relationship modelling Normalisation to third normal form The database management system, queries and user views

The Operating System

Topic overview The need for an operating system The kernel and process management Memory protection and the backing store The user interface between user and hardware Directory structures and file attributes Utility software Batch, real time control and transaction processing

Algorithms and Programs

Topic overview Defining and designing algorithms Variables, constants and identifiers Scope, subprograms and parameter passing Sequence, selection and repetition Mathematical and logical operations Standard algorithms: sorting, searching and compression Dry running, trace tables and test data

Principles of Programming

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Systems Analysis

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Software Engineering and Program Construction

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Types of Software System

Topic overview Off-the-shelf, bespoke and custom software Open source and proprietary software Computers in weather forecasting Computer aided design and manufacture Robotics in industry Computer generated graphics and animation Expert systems

Practical Programming

Topic overview Designing data structures: fields, records and data types Key fields and methods of access Validation of input data Designing routines with pseudocode Tracing code and test data Prototyping and evaluating a solution Annotated listings and readable code

Data Security and Integrity

Topic overview Dangers of holding files of personal data Levels of permitted access and access control Passwords and authentication Clerical procedures and write-protection Threats to computer systems Malicious and accidental damage to data Contingency planning and disaster recovery

Computing, Society and the Law

Topic overview Social and economic change from computing Computers and the nature of employment The digital divide and cultural change Environmental cost of computing Data protection and freedom of information law The Computer Misuse Act 1990 and computer crime Copyright, surveillance and professional codes

Advanced Data Structures and Logic

Topic overview Arrays in three dimensions Stacks and queues using pointers and arrays Linked lists using pointers and arrays Binary trees using pointers and arrays Hash tables and collision resolution NAND, NOR and Boolean simplification Masking, clearing registers and encryption

Recursion, Sorting and Searching

Topic overview Recursion Quicksort and merge sort Comparing sorting algorithms Big O notation and algorithm complexity Searching and shortest-path algorithms Traversal of data structures Data compression and its efficiency

Programming Paradigms and Translators

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System Design and Human-Computer Interaction

Topic overview The waterfall approach Agile approaches Documentation and when it is produced Contemporary approaches to communicating with computers Natural language interfaces and spoken ambiguity Design review and validation Evaluating a computer based solution

Software Engineering Tools and Professional Practice

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Advanced Architecture and Assembly Language

Topic overview Components of contemporary architecture Von Neumann and Harvard architectures The fetch-execute cycle in detail Parallel processing and its limits Assembly language and instruction formats Voice input, command and recognition Mobile and wireless networking

Communication Networks and File Organisation

Topic overview Calculating data transfer rates Lowest-cost routing The internet as a global infrastructure Creating, organising and processing files Hashing algorithms Overflow and file reorganisation Choosing an organisation and a route

Number Representation and Floating Point

Topic overview Binary arithmetic Sign and magnitude representation Two's complement Floating point representation Converting between real numbers and floating point Truncation, rounding and accuracy Shifts, overflow and underflow

Databases and Distributed Systems

Topic overview Consistency, redundancy and data independence Relational organisation and normalisation Restructuring data into third normal form Entity relationship modelling Query languages and SQL Validation, verification and the DBMS Big Data, data warehousing and mining Distributed systems and distributed databases

Operating System Management

Topic overview Types of operating system Interrupts and interrupt handling Memory management and partitioning Buffering and data transfer Scheduling and process states Scheduling policies and priorities Evaluating operating system design

Software Systems and Applications

Topic overview The range of software system types Safety related and safety critical systems Computer control and automation The scope of automation in practice Expert systems The internet, intranets and search Selecting and evaluating a software system

Data Security, Cryptography and Attack

Topic overview Integrity problems in online updating The need for cryptography Symmetric and asymmetric techniques Classical ciphers and cryptographic algorithms Comparing cryptographic strength Biometric technologies Malicious software and its vectors Attacks, defence and penetration testing

Advanced Data Structures and Logic

Arrays in three dimensions

3 things to know
A2 Unit 3

Overview

Recall questions on what a three-dimensional array is, counting its elements, subscripting one, a colour image held as one, the row-major address formula worked through, the nested loops needed, and how quickly memory grows with a further dimension.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Give an application that suits a three-dimensional array.

Numbers

State the formula for the address of element [i][j][k] of a three-dimensional array stored in row-major order.

Key term

How many nested loops are needed to visit every element of a three-dimensional array exactly once?

Questions from this subtopic

Each one with the model answer underneath.

1
What is a three-dimensional array?
Model answer
A three-dimensional array is a static structure holding elements of one type that are located by three subscripts, so it behaves as a stack of two-dimensional tables.
2
How many elements does an array declared with bounds 0 to 2, 0 to 3 and 0 to 4 hold?
Model answer
It holds 3 × 4 × 5 = 60 elements.
3
How is a single element of a three-dimensional array referred to in a program?
Model answer
It is referred to by the array name followed by all three subscripts, such as sales[2][1][4].
4
Give an application that suits a three-dimensional array.
Model answer
Sales figures held by product, by region and by month suit a three-dimensional array, with one subscript for each of the three.
5
Explain how a colour image is held in a three-dimensional array.
Model answer
The first two subscripts give the row and column of the pixel and the third selects the red, green or blue component of that pixel.
6
State the formula for the address of element [i][j][k] of a three-dimensional array stored in row-major order.
Model answer
The address is base + ((i × D₂ + j) × D₃ + k) × w, where D₂ and D₃ are the sizes of the second and third dimensions and w is the width of one element.

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