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Algorithms

Summary

Objectives

By the end of this session you should be able to:

  • Demonstrate performing basic arithmetic
  • Define an algorithm
  • Write and call functions in a program

Key Points

  • In most programming languages, arithmetic follows the BODMAS order of execution.
  • An algorithm is a set of steps used to complete a specific task.
  • Functions are a set of instructions bundled together to achieve a specific outcome.

Breakdown

Order of Operations

When calculating a mathematical equation you might expect to just move through each part in turn, calculating it and then moving on (usually from left to right) - however, this is not how computers (or mathematicians!) calculate. Instead, there is an order of operations - a set of rules that tell the computer what should be calculated first. That order is commonly remembered as BODMAS, an acronym which stands for:

  • Brackets
  • Order of powers or roots
  • Division and Multiplication
  • Addition and Subtraction

If you don't bear this in mind when writing calculations you may be caught out - for example, these two equations do not equal the same thing:

3 + 5 * 7 = 38
(3 + 5) * 7 = 56

The Algorithm

The word algorithm sounds like something complex and magical - indeed, many algorithms can be very complex (and seem like magic until you understand them). However, an algorithm is simply a set of instructions that describe how to get something done. An example of an algorithm might be a food recipe, or a guide to building some furniture. All computer programs are at least one algorithm, and we can expect them to have the following features:

  • Zero or more inputs - an algorithm often has an input, but doesn't have to. An example might be a random number generator.
  • A procedure - a process that must be followed.
  • One or more outputs - the end of the process must produce at least one output.

In programming we like to separate out our algorithms so that we can easily understand them and build them into more complex systems.

Functions

Functions are a great way to capture algorithms within a piece of code. A function is declared in a program - but not run until it is called. A function might be called many times, each with a different input. For example:

def more_than_ten(number):
    if number > 10:
        response = True
    else:
        response = False
    return response

This function has a single input (number), and when called will test that input to see if it's more than ten. It then returns an output (response), which is a boolean. If we call this function by typing more_than_ten(7), the function will respond False; if we call more_than_ten(11) it will respond True.

Built-in functions and Libraries

Programming languages have many built-in functions, which can be found in their documentation. Built-in functions come with the programming language and allow programmers to complete tasks they would otherwise have to write a function for themselves.

In addition to this, programmers publish modules of functions in *libraries which can be loaded into your code. This can be done within projects (to separate out code for ease of maintenance) or between projects (to share the burden of developing and maintaining generic algorithms). Many programming languages have repositories of libraries (e.g. PyPi for Python, npmjs for JavaScript) which you can use in your code to quickly get a project working.

::info Libraries contain modules, which themselves contain functions. However, since many libraries have only one module, these terms are often used interchangeably. :::