State the complexity of a linear search and explain why it has that complexity.

A linear search is O(n), because in the worst case every one of the n items has to be examined before the answer is known.

How many further comparisons does a binary search need when the list it is given is doubled in length?

Just one more, because that single extra comparison halves the doubled list back to its original length.

Under what conditions does a linear search beat a binary search?

A linear search wins on a very short list, on a list that is not in order, and wherever the cost of sorting the list first would outweigh the saving.

Why must a binary search be given a list held in an array rather than in a linked list?

A binary search has to jump straight to the midpoint, and only an array allows a position to be reached by calculation rather than by following pointers from the start.

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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Database Systems

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Algorithms and Programs

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Software Engineering and Program Construction

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Data Security and Integrity

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Advanced Data Structures and Logic

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Recursion, Sorting and Searching

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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

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Communication Networks and File Organisation

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Number Representation and Floating Point

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Databases and Distributed Systems

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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

Recursion, Sorting and Searching

Searching and shortest-path algorithms

3 things to know
A2 Unit 3

Overview

Recall questions on the complexity of linear and binary search and why, the comparisons needed on a million items, when linear beats binary, why binary needs an array, what Dijkstra's algorithm records and why it can finalise the smallest distance, negative weights, a worked shortest route, and A*.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

How does the A* algorithm differ from Dijkstra's algorithm?

Key term

State the complexity of a binary search and explain why it has that complexity.

Key term

State the greatest number of comparisons a binary search makes on a sorted list of 1,000,000 items.

Questions from this subtopic

Each one with the model answer underneath.

1
State the complexity of a linear search and explain why it has that complexity.
Model answer
A linear search is O(n), because in the worst case every one of the n items has to be examined before the answer is known.
2
State the complexity of a binary search and explain why it has that complexity.
Model answer
A binary search is O(log n), because every comparison discards half of the items still under consideration.
3
State the greatest number of comparisons a binary search makes on a sorted list of 1,000,000 items.
Model answer
2¹⁹ is 524,288 and 2²⁰ is 1,048,576, so at most 20 comparisons are needed.
4
How many further comparisons does a binary search need when the list it is given is doubled in length?
Model answer
Just one more, because that single extra comparison halves the doubled list back to its original length.
5
Under what conditions does a linear search beat a binary search?
Model answer
A linear search wins on a very short list, on a list that is not in order, and wherever the cost of sorting the list first would outweigh the saving.
6
Why must a binary search be given a list held in an array rather than in a linked list?
Model answer
A binary search has to jump straight to the midpoint, and only an array allows a position to be reached by calculation rather than by following pointers from the start.

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