Solved–Assignment 4: –Recursion, Graphs and SQL– Solution

Description

Marks: 35 marks.

Learning Goals:

At the end of this assignment you will be able to:

• Design, write and run a recursive function

• 15. Determine the basecase and recursive call

• Understand and apply the different algorithms for traversing a graph

• Determine the Big O efficiency of an algorithm

• Design and write basic SQL queries

Submission: (4 marks)

• This assignment must be done individually.

• The Python programming portion of the assignment must be attached to the

submission page on conneX as two files called concentricCircles.py and serpinskiFractals.py

• The online quiz on conneX under Tests&Quizzes must be completed before the deadline. You can repeat this quiz as many times as you want before the deadline and your highest score will be recorded.

• The SQL programming portion of the assignment must be attached to the submission page on conneX as a file called premierleague_queries.sql

TASK 1: Recursive algorithms (10 marks)

In this part of the assignment you will write two recursive functions in Python. As in the last assignment, you can do this online using: https://repl.it/languages/python3 but as last time, you will need to copy and save the code to .py files with the correct names to upload them to conneX.

1. Exercise to draw concentric circles:

1. 1. Download concentricCircles.py

1. 2. Start by uncommenting and running the tests of the concentric_loop

function one at a time to see what the output looks like

1. 3. Write the recursive version of this function in the file under the comments provided. Your function must be named concentric_recursive

1. 3. Test your function by uncommenting the tests of the concentric_recursive function one at a time to compare the output to that of concentric_loop

2. Exercise to draw Serpinski Fractals

   1. Download serpinskiFractals.py

2. 2. Start by uncommenting and running the tests of the stri function one at a time to see what the output looks like.

Notice, in the simplest case stri(24, 0, 0) with a CUTOFF of 25, no recursive calls are made, and the basecase draws one triangle with side length of 24:

The next testcase is a call to stri(50, 0, 0) with a CUTOFF of 25. This case, starts with an equilateral triangle with side length of 50. Inside of that triangle, three more Sierpinski triangles are drawn with a side length of 25 (two on the bottom and one above). The inner triangles are drawn in red to highlight the recursion:

With the later testcase stri(150, 0, 0) with a CUTOFF of 25. In this case, the outer triangle is drawn with side length 150, inside that triangle are 3 more Sierpinski triangles are drawn, and inside each of those 3 more Sierpinski triangles, and so on

If we were to lower the CUTOFF value it would take much more time to run the program, but a more detailed fractal would be drawn like this one from https://en.wikipedia.org/wiki/Sierpinski_triangle :

3. Write the recursive function scarpet in the file under the comments provided in serpinskiFractals.py. You are provided with a square function that you can call similarly to how the triangle function was called in the stri function provided. Test your function by uncommenting the tests of the scarpet function one at a time to compare the output to the images below.

In the simplest case scarpet(24, 0, 0) with a CUTOFF of 25, will draw one square:

The next testcase scarpet(75, 0, 0) with a CUTOFF of 25, will draw one square of side length 75. Inside this square, 8 inner Serpinski carpets of side length 25 (75/3) are drawn in 3 rows:

• 3 Serpinski carpets are drawn along the bottom row

• 2 Serpinski carpets are drawn on the second row, one on the far left and the other on the far right leaving a blank square in the middle

• 3 Serpinski carpets are drawn along the top row

The third testcase stri(100, 0, 0) with a CUTOFF of 25 will draw the outer square of side length 100, inside that outer square 8 more Serpinski carpets are drawn and inside each of those 8 carpets, 8 more Serpinski carpets are drawn:

The last testcase is stri(400, -200, -200) with a CUTOFF of 25 will draw an image like this:

If you want to generate a more detailed Serpinki Carpet you can reduce the CUTOFF value. This can take hours to complete if your CUTOFF is very small relative to your staring size so do not feel you need to do this to test your solution.

If you do test this, you will notice the accuracy of the turtle is not perfect when the square drawing gets really small, but it does produce a nice Serpinski carpet.

If you were to lower the CUTOFF value a more detailed fractal would be drawn like this one from https://commons.wikimedia.org/wiki/File:Sierpinski_carpet.png :

TASK 2: Graphs and BigO (11 marks)

Log into conneX and navigate to the Tests & Quizzes link on the sidebar. You will see an Assignment 4 quiz. You can use lab and lecture notes to help you answer these questions. You can submit your quiz as many times as you want, your highest score will be recorded.

You must complete and submit before the deadline. Late submissions will not be accepted for any reason.

TASK 3: SQL (10 marks)

Statistical data is available at our fingertips for almost anything we are interested in these days. In this assignment resources you have been provided with a file premierleague_data.sql which constructs an SQL database of English Premier League Soccer (https://www.premierleague.com) data from the 2017/2018 season. This data is set comprised of three separate tables is described below.

Look in premierleague_data.sql to get exact column names for your queries:

• stadiums:

• 15. contains a record for each home stadium that a team in the league plays at

• 15. columns include the name of the home team that plays there, the city it is in, the name of the stadium and its capacity

• 15. collected from: https://opisthokonta.net/?p=619

• players:

  15. contains a record for each player in the league

15. columns include the player name, the name of the team they play for, their age, position they play and their nationality

15. a position is one of (value = definition):

    • GK = Goalkeeper

    • AM = Attacking Midfielder

    • CB = Center Back

    • CF = Center Forward

    • CM = Center Midfielder

    • LB = Left Back

    • RB = Right Back

    • LM = Left Midfielder

    • RM = Right Midfielder

    • SS = Second Striker

    • DM = Defensive Midfielder

    • RW = Right Wing

    • LW = Left Wing

15. collected from: https://www.kaggle.com/mauryashubham/english-premier-league-players-dataset

• games:

15. contains a record for each game played in 2017/2018

15. there are many columns in this table including but not limited to:

the home team name, away team name, winner of the game (one of H, A or D

• home team, away team or draw/tie game), the number of fouls, red cards, yellow cards given to the home and away teams

15. you will not need to use all of the columns provided but feel free to come up with your own queries on the data besides those you are asked to do!

15. collected from: https://datahub.io/sports-data/english-premier-league#resource-season-1718

Write the SQL queries for each of the questions below in the space provided in premierleague_queries.sql. Do not modify any of the existing code in the files given, only add your queries below each question heading.

Your query outputs must match the sample outputs given below exactly including: column names, the data in each row and the ordering of the data. Your column widths can be different. A given query may only need to use one table or possibly multiple tables.

1. Write a query to print the team name, city, stadium name and capacity of all stadiums in the league in order of decreasing capacity.

team_name	city	stadium_name	capacity
——————–	——————–	——————–	———-
Man United	Stretford	Old Trafford	75811
Arsenal	London	Emirates Stadium	60361
Newcastle	Newcastle upon Tyne	Sports Direct Arena	52409
Man City	Manchester	Etihad Stadium	47405
Liverpool	Liverpool	Anfield	45276
Chelsea	London	Stamford Bridge	42449
Everton	Liverpool	Goodison Park	40157
Tottenham	London	White Hart Lane	36230
West Ham	London	Boleyn Ground	35303
Southampton	Southampton	St Marys Stadium	32689
Leicester City	Leicester	King Power Stadium	32500
West Brom	West Bromwich	The Hawthorns	27877
Stoke	Stoke-on-Trent	Britannia Stadium	27740
Crystal Palace	London	Selhurst Park	26309
Huddersfield	Huddersfield	The John Smiths Stad	24500
Watford	Watford	Vicarage Road	23500
Burnley	Burnley	Turf Moor	22546
Brighton	Brighton	American Express Com	22374
Swansea	Swansea	Liberty Stadium	20520
Bournemouth	Bournemouth	Goldsands Stadium	12000

2. Write a query to print the names of the players that are goal keepers that play at a home stadium with a capacity between 30,000 and 50,000. You should print this in alphabetical order of the name of the stadium they play at, then in alphabetical order of the name of the player.

4. Write a query to print the nationality and the number of players of that nationality. Print those nationalities with either 1 player or more than 10 players in the league. The data should be sorted by increasing number of players of a given nationality.

nationality	num_players
——————–	————–
Armenia	1
Benin	1
Bermuda	1
Canada	1
Colombia	1
Croatia	1
Curacao	1
Estonia	1
Finland	1
Greece	1
Kenya	1
New Zealand	1
Norway	1
Romania	1
Slovenia	1
The Gambia	1
Trinidad and Tobago	1
Tunisia	1
Uruguay	1
Venezuela	1
Brazil	12
Wales	12
Scotland	14
Germany	16
Argentina	17
Ireland	17
Belgium	18
Netherlands	20
France	25
Spain	28
England	156

5. Write a query to print the number of wins that each home team had. Print the result in decreasing order of wins.

team_name	num_wins
——————–	————–
Man City	16
Arsenal	15
Man United	15
Tottenham	13
Liverpool	12
Chelsea	11
Everton	10
Newcastle	8
Bournemouth	7
Brighton	7
Burnley	7
Crystal Palace	7
Leicester	7
Watford	7
West Ham	7
Huddersfield	6
Swansea	6
Stoke	5
Southampton	4
West Brom	3

6. OPTIONAL: Write a query to print the names of players on most winning team

ordered by nationality then by player name. Tip: You will need to find the team with the maximum number of wins and join that result with the players table.

player_name	team_name	nationality
——————–	————–	————
Nicolas Otamendi	Man City	Argentina
Sergio Aguero	Man City	Argentina
Kevin De Bruyne	Man City	Belgium
Vincent Kompany	Man City	Belgium
Ederson Moraes	Man City	Brazil
Fernandinho	Man City	Brazil
Fernando	Man City	Brazil
Gabriel Jesus	Man City	Brazil
Claudio Bravo	Man City	Chile
Yaya Toure	Man City	Cote dIvoire
Fabian Delph	Man City	England
John Stones	Man City	England
Kyle Walker	Man City	England
Raheem Sterling	Man City	England
Ilkay Gundogan	Man City	Germany
Leroy Sane	Man City	Germany
Kelechi Iheanacho	Man City	Nigeria
Bernardo Silva	Man City	Portugal
Aleksandar Kolarov	Man City	Serbia
David Silva	Man City	Spain