General Algorithms (Edexcel International A Level Maths): Revision Note

Introduction to Algorithms

What is an algorithm?

• An algorithm is a set of precise instructions that, if strictly followed, will result in the solution to a problem

  • Algorithms are particularly useful for programming computers

    • Computers can process huge amounts of data and perform millions of calculations in very short time frames

  • Robots can be programmed to follow an algorithm in order to complete a task

    • E.g.  A robot vacuum cleaner or lawn mower

  • Algorithms can be performed by human beings too!

    • E.g.  The recipe and cooking instructions for a cake 

What does an algorithm look like?

• Algorithms may be presented in a variety of ways

  • A list of instructions, in order, written in words

  • Flow charts are a visual way of presenting the steps of an algorithm

    • These clearly show the order of instructions and any parts of an algorithm that may need repetition

What else do I need to know about algorithms?

• Some algorithms do not always provide an optimal (best) solution

  • However, they will give a solution that is sufficient for the purpose

• Modern real-life situations can be complex to analyse

  • A compromise between the efficiency of an algorithm and its accuracy is often required

  • E.g. An algorithm may produce a 'shortest route' result that is inaccurate by 200 miles
    

    • For a very long journey, the time saved using this algorithm may be more important than this inaccuracy 

• When using an algorithm with a small amount of data in an exam you must follow the algorithm precisely and accurately

  • This demonstrates understanding of the algorithm

  • Using common sense or intuition to 'see' the solution will not gain full marks

Flow Charts

What is a flow chart?

• A flow chart is a diagrammatic way of listing the instructions to an algorithm

• Flow charts lend themselves to algorithms that have

  • conditional instructions

    • E.g.  Is ?

    • If the answer is yes, the flow chart directs the user to one instruction

    • If the answer is no, the flow chart directs the user to a different instruction

  • repetitive parts or stages

What do the different shaped boxes in a flow chart mean?

• Each command in a flow chart is written inside a shape

  • The shape will depend on the type of command 
    

    • Ovals are used to represent the start and the end

    • Rectangles are used to represent instructions

    • Diamonds are used to represent questions

How do I work with a flow chart?

• Following a flow chart is generally straightforward but make sure you follow the instructions carefully

• Commands given in a flow chart are intuitive to follow

  • Examples include

    • 'Input ...' - The value(s)/data that the algorithm needs to be told

    • 'Let ...' - Assign or update a value for a variable

    • 'If ...' - A conditional statement, the outcome of which will lead to different parts of the algorithm

    • 'Output ...' or 'Print ...' -  Write down the answer

• Write down any values when instructed to

  • This will often involve completing a table of values

  • Sometimes there is a specific instruction to 'output' the final answer

    • Make sure the answer is separate to the table

• Some questions may ask for a description of what the flow chart/algorithm produces

Text-Based Algorithms

What are text-based algorithms?

• Text-based algorithms refer to instructions that are given in sentences

  • Each instruction may be labelled with 1, 2, 3, and so on

• The following text-based algorithm is for a very basic single player dice game

  • The aim of the game is to minimise the number of rolls of the dice needed to reach 'Stop'