# Assignment 4: Recursion, Graphs and SQL Solution

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Marks: 35 marks.

Learning Goals:

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

• Design, write and run a recursive function

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

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

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

1. 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

1. Exercise to draw Serpinski Fractals

1. 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 :

1. 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.

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:

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

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

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

• players:

1. contains a record for each player in the league

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

1. 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

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

• games:

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

1. 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

1. 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!

1. 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.

1. 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

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

——————–

Anfield

Anfield

Boleyn Ground

Boleyn Ground

Goodison Park

Goodison Park

Goodison Park

Stamford Bridge

Stamford Bridge

White Hart Lane

White Hart Lane

1. 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
1. 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
1. 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
1. 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

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