Euler’s Number

Posted on July 17, 2017 by Administrator Posted in Computer Science, Python - Advanced, Python Challenges, Solved Challenges

The number e is a famous irrational number called Euler’s number after Leonhard Euler a Swiss Mathematician (1707 – 1783). Number e is considered to be one of the most important numbers in mathematics.

The first few digits are: 2.7182818284590452353602874713527… It has an infinite number of digits with no recurring pattern. It cannot be written as a simple fraction.

Number e is the limit of (1 + ¹/_n)ⁿ as n approaches infinity:

Number e is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. Find out more on https://en.wikipedia.org/wiki/E_(mathematical_constant).

In this challenge we will use a Python script to calculate an approximation of e using three different approaches. The first approach as described above as already been implemented in the above Python trinket.

Calculating e using an iterative approach

Euler’s number, e, can also be calculated as the sum of the infinite series:

Complete your Python script to implement this infinite series using an iterative approach. (Method 2)

Calculating e using a continuous fraction (iterative approach)

A less common approach to calculate number e is to use a continued fraction based on the following sequence:

Continued Fraction:
$euler-continued-fraction$

Complete your Python script to implement this continued fraction. (Method 3)

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: iteration, recursion

Golden Angle

Posted on July 14, 2017 by Administrator Posted in Computer Science, Python - Intermediate, Python Challenges

In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio.

Golden Angle ≈ 137.5°

The golden angle plays a significant role in the theory of phyllotaxis; for example, the golden angle is the angle separating the florets or branches on some plants or flowers (e.g. sunflower).

Plants have their leaves spread all around the stem to soak up as much sun as possible. Using the golden angle between two consecutive leaves is the most effective approach to spread the leaves around the stem.

Let’s see how this work:
Leaf 1:

Leaf 2: Would be at an angle of around 137.5° (The Golden Angle) from leaf 1

Leaf 3: Would be at an angle of around 137.5° (The Golden Angle) from leaf 2

And so on for all new leaves…

etc…

Python Challenge

For this challenge we will apply the golden angle to position the first 50 branches of a tree using Python Turtle:

Sunflower using Python Turtle and the Golden Angle

Tagged with: Coordinates, iteration, Python Turtle

Graphing Algorithm

Posted on July 14, 2017 by Administrator Posted in Computer Science, Python - Advanced, Python Challenges

In this challenge we will write several procedures to graph different mathematical equations on screen using Python Turtle.

We will focus on:

Linear equations: y = ax + b
Quadratic equations: y = ax² + bx + c
Trigonometric functions: e.g. y = cos(x)

(x,y) coordinates using Python Turtle?

On the Python trinket used below the turtle screen is 400 pixels wide by 400 pixels high.

Look at the canvas below to understand how (x,y) coordinates work:

Linear Equation

y = ax + b

A linear equation produces a straight line when graphed on screen.

Your task:
Change the parameters used when calling the drawLine() procedure to graph the following equations:

y = 2x + 60
y = -x + 10
y = x
y = ¹/₂x

Quadratic Equation

y = ax² + bx + c

Add another procedure called drawQuadraticEquation() that will take three parameters: a, b and c and be used to graph and display the matching quadratic equation.

Use this new procedure to graph the following equations:

y = x² + 2x + 60
y = ¹/₂x² – 3x + 20
y = x²
y = -x² + 100

Trigonometric Functions

You can now add further procedures to draw the main trigonometric functions. To do so you will need to import the math library using an import statement.

import math

Here are the three main functions you will need to implement:

cosine: y = cos(x)
sine: y = sin(x)
tangent: y = tan(x)

Tagged with: Coordinates, iteration, Python Turtle, subroutine

Monopoly Quiz

Posted on July 12, 2017 by Administrator Posted in Computer Science, Python - Intermediate, Python Challenges, Solved Challenges

For this challenge you will create a quiz based on the game of Monopoly.

The computer will randomly display a street name from the list of streets used in the game and the user will have to guess the colour used in the game for the selected street.

The user will score one point per correct answer and will be asked to guess the colour of ten different streets, one at a time. At the end the user will be given their score out of ten.

To get you started with this challenge we have created three text files to cater for different audiences:

UK-monopoly.txt

US-monopoly.txt

French-monopoly.txt

To complete this challenge you will need to read more about how to read through a CSV file.

Complete the Code

We have started the code for you but you will need to complete it to meet all the requirements of this game.

Extension Task #1

Add a menu option at the beginning to ask the user if they want to play with the UK, US or French monopoly.

Extension Task #2

Ask the user to enter their name and store their name and final score in a leaderboard text file. See leaderboard challenge.

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Equalizer Animation Using JavaScript

Posted on July 10, 2017 by Administrator Posted in Computer Science, HTML, CSS & JavaScript, JavaScript, Solved Challenges

When your browser displays a webpage on screen it uses 3 different programming languages called HTML, CSS and JavaScript. We call the combination of these three languages “client-side web technologies”.

Each of the three language has its own syntax and purpose:

HTML uses <tags> and its purpose is to add content on the page such as text, pictures, and video clips.
CSS is used to customise the look and feel of the page by defining the position of each element on the page, defining the layout of the page as well as formatting text, pictures and other components on the page.
JavaScript is used to add user interaction to the page. JavaScript can be linked to HTML tags through various events such as the onClick event of a button.

In this challenge we are using JavaScript to create a frame-based animation. To do so we will use the setTimeOut() function to run our own javascript function called animate() every 50ms.

This is the line of code used to repeat the code used to refresh the equalizer every 50ms:

setTimeout(animate, 50);

Full Code

Edit this code in a new window using this button:

Your Challenge

Adapt this code to create a horizontal progress bar animation that expands from 0 to 100% progressively over 5 seconds. You can then make the animation loop by starting again at 0% when it reaches 100%.

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: animation, CSS, HTML, JavaScript

Defragmentation Algorithm

Posted on July 6, 2017 by Administrator Posted in Computer Science, Computing Concepts, Python - Advanced, Python Challenges

File Allocation Table (FAT System)

A file allocation table (FAT) is a table that an operating system maintains on a hard disk that provides a map of the clusters (the basic units of logical storage on a hard disk) that a file has been stored in. When you write a new file to a hard disk, the file is stored in one or more clusters that are not necessarily next to each other; they may be rather widely scattered over the disk. A typical cluster size is 2,048 bytes, 4,096 bytes, or 8,192 bytes.

Defragmentation?

When a file is accessed, the Operating System uses the FAT table to identify all the clusters that need to be accessed to retrieve the content of the file. The more scattered the clusters are the longer it will take for the Operating System and Hard drive to retrieve the content of the file. This is why, if you hard drive is based on a FAT systems, it is recommended to use a defragmentation utility to try to reorganise how all the files are stored by trying to move the content of clusters of a single file into consecutive clusters. Defragmenting your hard drive once every six months should hence have a positive impact on the performance of your computer.

On this graphic, each square represents a cluster of the hard drive and each colour represents a file.

Did you know?

With the introduction of more powerful computers and operating systems, as well as the development of more complex file systems for them, FAT is no longer the default file system for usage on Microsoft Windows computers.

FAT file systems are still commonly found on floppy disks, flash and other solid-state memory cards and modules (including USB flash drives), as well as many portable and embedded devices such as digital cameras.

Defragmentation Algorithm

The File Allocation Table is a linked list where each entry contains the cluster number, the file name and a pointer to identify the next cluster used by the file.

Cluster #	File Name	Pointer
0	File A	1
1	File A	2
2	File A	5
3	File B	4
4	File B	x
5	File A	6
6	File A	x
…	…	…

Let’s check this Python trinket to see how the File Allocation Table was implemented using a Python list of lists.

Challenge 1: Hard Drive Stats

Assuming that the standard cluster size is 4KB, complete the displayStats() procedure to:

Calculate and display the total size of the hard drive (in KB).
Calculate and display the total used space of the hard drive (in KB).
Calculate and display the total free space of the hard drive (in KB).
Calculate and display the total used space of the hard drive as a percentage of the total disk space.

Challenge 2: Defragmentation Algorithm

Your challenge consists of completing this code by writing the code for defragmentation() procedure that will group all the clusters of a file into consecutive clusters.

Tagged with: array, List

Catch Me If You Can

Posted on July 4, 2017 by Administrator Posted in Block Programming, Computer Science, Scratch

In this challenge we will create a three-player game using Scratch.

One player (the yellow ball) will be chased by two other players the red player and the blue player.

The red player will use the arrow keys to control their sprite.
The blue player will use the “WASD” keys to control their sprite.
The yellow player will use the mouse pointer to control their sprite.

The game will use two score variables one for the red player, one for the blue player. At the start of the game both scores will be initialized to 0. Every time a player collides with the ball their score will be incremented by 1. The ball will then be randomly moved on screen by resetting its x and y coordinates.

Scracth Code

To implement this game you will have to create three sprites and use the code provided below:

Red SpriteBlue SpriteYellow Sprite

The Red Sprite, called Red Dot, will be controlled using the arrow keys:

The Blue Sprite, called Blue Dot, will be controlled using the WASD keys:

The Yellow Sprite, called the Ball, will be controlled using the mouse pointer. it will also have a collision detection algorithm to detect if the ball has been caught by either the red sprite or the blue sprite.

Extension Task: Adding Walls/Platforms

To make this game more interesting we will add walls/obstacles that the red player, the blue player and the yellow ball will have to avoid when moving around.

Step 1: The StageRed SpriteBlue SpriteYellow Ball

Using a plain colour create a background for the stage by adding walls:

Adapt the script of your red sprite so that it cannot go through the walls:

Adapt the script of your yellow sprite so that it cannot go through the walls:

Tagged with: Block Programming, Scratch

Recursive Tree Challenge

Posted on June 30, 2017 by Administrator Posted in Computer Science, Python - Intermediate, Python Challenges

Look at the code provided below use to draw a tree using a recursive function.

Recursive Function

A recursive function is an alternative to using iteration. A function is a recursive function if:

It includes a call to itself,
It has a stopping condition to stop the recursion.

In the code given below the drawTree() function is a recursive function because:

It includes a call to itself (on line 10 and also on line 13)
It has a stopping condition on line 7 (it will stop recursing when level reaches 0)

Your Challenge

Tweak the code provided above to create different versions of recursive trees. You could investigate having three branches per node instead of two or using some random attributes so that the tree becomes less symmetrical.

Mixed Numbers Challenge

Posted on June 27, 2017 by Administrator Posted in Computer Science, Python - Intermediate, Python Challenges, Solved Challenges

Before completing this challenge we need to revise some Maths concepts.

Fraction = numerator / denominator

In Maths a fraction consists of two numbers: a numerator and a denominator.

What is an improper fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

For instance:
⁷⁄₄, ¹²⁄₁₀, ²¹⁄₃ are all improper fractions.

What is a proper fraction?

A proper fraction is a fraction where the numerator is lower than to the denominator.

For instance:
⁷⁄₉, ¹²⁄₂₁, ³⁄₄ are all proper fractions.

What is a mixed number?

A mixed number is a number consisting of a whole number and a proper fraction.

For instance:
3¹⁄₂, 1³⁄₁₀, 21³⁄₄ are all mixed numbers.

Converting improper fractions into mixed numbers

We can easily convert an improper fraction into a mixed number by calculating the quotient and the remainder from the improper fraction.

Mixed number = Quotient ^Remainder⁄_Denominator

For instance: Let’s convert ¹¹⁄₄ into a mixed number

Step 1: Quotient (Whole Division): 11 DIV 4 = 2
Step 2: Remainder: 11 MOD 4 = 3

¹¹⁄₄ = 2 ³⁄₄

Quotient & Remainder in Python?

In Python you can use the // operator to calculate the quotient of a fraction and the % operator to calculate the remainder of a fraction.

For instance:

quotient = 11 // 4
remainder = 11 % 4

Python Challenge #1

Complete the code given below to convert an improper fraction into a mixed number by:

Check that the user has entered a numerator and a denominator for an improper fraction. (The numerator should be greater or equal to the denominator).
Calculate and display the mixed number corresponding to the given fraction.

Python Challenge #2

Create a Python script to convert a mixed number into an improper fraction.

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
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Text Alignment Challenge

Posted on June 26, 2017 by Administrator Posted in Computer Science, Python - Intermediate, Python Challenges, Solved Challenges

This challenge focuses on the use of string manipulation techniques in order to format the output when printing text on the screen.

Step 1: Reverse Engineering

First look at the code provided above and use this code to answer the following questions:

Which line of code will be executed first by the computer when you run this code?
What data structure is used to store a selection of European capital cities?
What is the identifier of the procedure defined in this code?
How many parameters this procedure takes?
What programming construct is this procedure based on? Sequencing, Selection or Iteration?
What data will be stored in the itemLength variable?
What is the data type for this value: String, Boolean, Integer or Float?
What data will be stored in the spaces variable?
What is the data type for this value: String, Boolean, Integer or Float?
String concatenation is the act of joining two strings together (using the + sign). Which line of code is using string concatenation is this program?

Step 2: Complete the Code

Using a similar approach to the code given to implement the leftAlign procedure create two more procedures as follows:

rightAlign to display all the European capitals aligned to the right.
centerAlign to display all the European capitals centred on screen.

Step 3: Extension Task Task

-lorem ipsum.txt –
Write a Python program to read and display the content of the above text file:

Align to the left,
Align to the right,
Centred,
Justified,
Using Auto-hyphenation.

Solution...

The solution for this challenge is available to full members!
Find out how to become a member:
➤ Members' Area

Tagged with: String Manipulation

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Books Corner

Calculating e using an iterative approach

Calculating e using a continuous fraction (iterative approach)

Solution...

Python Challenge

Sunflower using Python Turtle and the Golden Angle

(x,y) coordinates using Python Turtle?

Linear Equation

Quadratic Equation

Trigonometric Functions

Complete the Code

Extension Task #1

Extension Task #2

Solution...

Full Code

Your Challenge

Solution...

File Allocation Table (FAT System)

Defragmentation?

Did you know?

Defragmentation Algorithm

Challenge 1: Hard Drive Stats

Challenge 2: Defragmentation Algorithm

Scracth Code

Extension Task: Adding Walls/Platforms

Recursive Function

Your Challenge

Fraction = numerator / denominator

What is an improper fraction?

What is a proper fraction?

What is a mixed number?

Converting improper fractions into mixed numbers

Quotient & Remainder in Python?

Python Challenge #1

Python Challenge #2

Solution...

Step 1: Reverse Engineering

Step 2: Complete the Code

Step 3: Extension Task Task

Solution...

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