Assignment 4: Recursion, Graphs and SQL Solution

Marks: 35 marks.




Learning Goals:




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




Design, write and run a recursive function



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.




Exercise to draw concentric circles:



Download concentricCircles.py



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

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



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
Exercise to draw Serpinski Fractals

Download serpinskiFractals.py



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 :




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:



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



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



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



players:

contains a record for each player in the league



columns include the player name, the name of the team they play for, their age, position they play and their nationality
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
collected from: https://www.kaggle.com/mauryashubham/english-premier-league-players-dataset
games:



contains a record for each game played in 2017/2018
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
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!



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.










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
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.



player_name




--------------------

Loris Karius

Simon Mignolet

Adrian

Darren Randolph

Claudio Bravo

Ederson Moraes

Joel Robles

Jordan Pickford

Maarten Stekelenburg

Ben Hamer

Kasper Schmeichel

Fraser Forster

Thibaut Courtois

Willy Caballero

Hugo Lloris




Michel Vorm




stadium_name




--------------------




Anfield

Anfield

Boleyn Ground

Boleyn Ground

Etihad Stadium

Etihad Stadium

Goodison Park

Goodison Park

Goodison Park

King Power Stadium

King Power Stadium

St Marys Stadium

Stamford Bridge

Stamford Bridge

White Hart Lane




White Hart Lane



Write a query to print the names of the referee, the number of games they have refereed and the number of red cards and yellow cards they award to the home team. The output should be in order of the number of red cards then by yellow cards.



referee
games_refereed
red_cards
yellow_cards
---------------
---------------
------------
------------
D Coote
1
0
1
S Hooper
1
0
1
K Friend
21
0
16
P Tierney
16
0
16
M Jones
12
0
20
L Mason
18
0
24
S Attwell
15
0
26
C Kavanagh
15
0
27
N Swarbrick
20
0
28
M Dean
25
0
48
L Probert
14
1
12
G Scott
20
1
21
R East
18
1
21
R Madley
18
1
26
A Taylor
27
1
49
J Moss
29
1
53
A Marriner
28
2
41
M Oliver
30
2
47
M Atkinson
28
3
52
C Pawson
24
4
33
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



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
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