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Champions League Round of 16 Draw
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|
//Declare some types
type Country =
|Germany |Italy |England |Spain
|France |Portugal |Turkey |Scotland
|Ukraine
type Group = |A|B|C|D|E|F|G|H
type Place = |First |Second
type Team = {
name : string;
country : Country;
group : Group;
place: Place;
}
//Declare all teams
let PSG = {name ="Paris Saint-Germain"; country=France; group=A;place=First}
let Porto = {name ="FC Porto"; country=Portugal; group=A; place=Second}
let Schalke = {name ="FC Schalke 04"; country=Germany; group=B;place=First}
let Arsenal = {name ="Arcenal FC"; country=England; group=B; place=Second}
let Malaga = {name ="Malaga CF"; country=Spain; group=C;place=First}
let Milan = {name ="AC Miland"; country=Italy; group=C; place=Second}
let Dortmund = {name ="Borussia Dortmund"; country=Germany; group=D;place=First}
let Real = {name ="Real Madrid CF"; country=Spain; group=D; place=Second}
let Juventus = {name ="Juventus"; country=Italy; group=E;place=First}
let Shakhtar = {name ="FC Shakhtar Donetsk"; country=Ukraine; group=E; place=Second}
let Bayern = {name ="FC Bayern München"; country=Germany; group=F;place=First}
let Valencia = {name ="Valemcia CF"; country=Spain; group=F; place=Second}
let Barcelona = {name ="FC Barcelona"; country=Spain; group=G;place=First}
let Celtic = {name ="Celtic FC"; country=Scotland; group=G; place=Second}
let ManchesterU = {name ="Manchester United FC"; country=England; group=H;place=First}
let Galatasaray = {name ="Galatasaray AŞ"; country=Turkey; group=H; place=Second}
//And put them in a list
let allTeams = [PSG; Porto; Schalke; Arsenal; Malaga; Milan; Dortmund; Real; Juventus;
Shakhtar; Bayern; Valencia; Barcelona;Celtic;ManchesterU; Galatasaray;]
//Partition the list in group winners and runner ups
let groupWinners, runnerUps =
let isGroupWinner team = (team.place = First)
List.partition isGroupWinner allTeams;
//I stole this function from stack overflow to generate all permutaions of a list
let rec perms =
let distrib e L =
let rec aux pre post =
seq {
match post with
| [] -> yield (L @ [e])
| h::t -> yield (List.rev pre @ [e] @ post)
yield! aux (h::pre) t
}
aux [] L
function
| [] -> Seq.singleton []
| h::t -> Seq.collect (distrib h) (perms t)
//Create all draws by using all permutations of the runner ups and pairing
//them with an unchanged list of gruop winners
let getDraws runnerUps groupWinners =
[for perm in (perms runnerUps) do
yield List.zip perm groupWinners
]
let draws = getDraws runnerUps groupWinners
//fnction to check if a match is valid
let isValidMatch (footballMatch: Team*Team) =
match footballMatch with
|(teamA,teamB) when teamA.group = teamB.group -> false
|(teamA,teamB) when teamA.country = teamB.country ->false
|_ -> true
//checks if all matches in a draw are valid
let isValidDraw (draw: (Team*Team) list) =
draw
|>List.map isValidMatch
|>List.fold (&&) true
//filter the draws so we only keep the valid ones
let validDraws = List.filter isValidDraw draws
//Calculates the probability of a match by looking how many of the draws
//contain the match and dividing by the total amount of matches
let matchProbability (footballMatch:Team*Team) =
let occurences =
validDraws
|> List.filter (List.exists (fun (x:Team*Team) -> x= footballMatch))
|> List.length
(float occurences)*100.0/(float <| List.length validDraws)
//Gets a list of tupples where each tuple consist of the match and it respective probability
let getProbabilities runnerUps groupWinners =
[for runnerUp in runnerUps do
for adversary in groupWinners do
let footbalMatch = (runnerUp,adversary)
yield (footbalMatch, matchProbability footbalMatch)
]
let probabilities = getProbabilities runnerUps groupWinners
//a function to print a probability
let printProbability probabilities =
match probabilities with
|((teamA,teamB),probability) -> printfn "%s \t %s \t %F%% " teamA.name teamB.name probability
//print all probabilities
List.iter printProbability probabilities
|
union case Country.Germany: Country
union case Country.Italy: Country
union case Country.England: Country
union case Country.Spain: Country
union case Country.France: Country
union case Country.Portugal: Country
union case Country.Turkey: Country
union case Country.Scotland: Country
union case Country.Ukraine: Country
type Group =
| A
| B
| C
| D
| E
| F
| G
| H
Full name: Script.Group
union case Group.A: Group
union case Group.B: Group
union case Group.C: Group
union case Group.D: Group
union case Group.E: Group
union case Group.F: Group
union case Group.G: Group
union case Group.H: Group
type Place =
| First
| Second
Full name: Script.Place
union case Place.First: Place
union case Place.Second: Place
type Team =
{name: string;
country: Country;
group: Group;
place: Place;}
Full name: Script.Team
Team.name: string
Multiple items
val string : value:'T -> string
Full name: Microsoft.FSharp.Core.Operators.string
--------------------
type string = System.String
Full name: Microsoft.FSharp.Core.string
Team.country: Country
type Country =
| Germany
| Italy
| England
| Spain
| France
| Portugal
| Turkey
| Scotland
| Ukraine
Full name: Script.Country
Team.group: Group
Team.place: Place
val PSG : Team
Full name: Script.PSG
val Porto : Team
Full name: Script.Porto
val Schalke : Team
Full name: Script.Schalke
val Arsenal : Team
Full name: Script.Arsenal
val Malaga : Team
Full name: Script.Malaga
val Milan : Team
Full name: Script.Milan
val Dortmund : Team
Full name: Script.Dortmund
val Real : Team
Full name: Script.Real
val Juventus : Team
Full name: Script.Juventus
val Shakhtar : Team
Full name: Script.Shakhtar
val Bayern : Team
Full name: Script.Bayern
val Valencia : Team
Full name: Script.Valencia
val Barcelona : Team
Full name: Script.Barcelona
val Celtic : Team
Full name: Script.Celtic
val ManchesterU : Team
Full name: Script.ManchesterU
val Galatasaray : Team
Full name: Script.Galatasaray
val allTeams : Team list
Full name: Script.allTeams
val groupWinners : Team list
Full name: Script.groupWinners
val runnerUps : Team list
Full name: Script.runnerUps
val isGroupWinner : (Team -> bool)
val team : Team
Multiple items
module List
from Microsoft.FSharp.Collections
--------------------
type List<'T> =
| ( [] )
| ( :: ) of Head: 'T * Tail: 'T list
interface IEnumerable
interface IEnumerable<'T>
member Head : 'T
member IsEmpty : bool
member Item : index:int -> 'T with get
member Length : int
member Tail : 'T list
static member Cons : head:'T * tail:'T list -> 'T list
static member Empty : 'T list
Full name: Microsoft.FSharp.Collections.List<_>
val partition : predicate:('T -> bool) -> list:'T list -> 'T list * 'T list
Full name: Microsoft.FSharp.Collections.List.partition
val perms : ('a list -> seq<'a list>)
Full name: Script.perms
val distrib : ('b -> 'b list -> seq<'b list>)
val e : 'b
val L : 'b list
val aux : ('b list -> 'b list -> seq<'b list>)
val pre : 'b list
val post : 'b list
Multiple items
val seq : sequence:seq<'T> -> seq<'T>
Full name: Microsoft.FSharp.Core.Operators.seq
--------------------
type seq<'T> = System.Collections.Generic.IEnumerable<'T>
Full name: Microsoft.FSharp.Collections.seq<_>
val h : 'b
val t : 'b list
val rev : list:'T list -> 'T list
Full name: Microsoft.FSharp.Collections.List.rev
module Seq
from Microsoft.FSharp.Collections
val singleton : value:'T -> seq<'T>
Full name: Microsoft.FSharp.Collections.Seq.singleton
val h : 'a
val t : 'a list
val collect : mapping:('T -> #seq<'U>) -> source:seq<'T> -> seq<'U>
Full name: Microsoft.FSharp.Collections.Seq.collect
val getDraws : runnerUps:'a list -> groupWinners:'b list -> ('a * 'b) list list
Full name: Script.getDraws
val runnerUps : 'a list
val groupWinners : 'b list
val perm : 'a list
val zip : list1:'T1 list -> list2:'T2 list -> ('T1 * 'T2) list
Full name: Microsoft.FSharp.Collections.List.zip
val draws : (Team * Team) list list
Full name: Script.draws
val isValidMatch : Team * Team -> bool
Full name: Script.isValidMatch
val footballMatch : Team * Team
val teamA : Team
val teamB : Team
val isValidDraw : draw:(Team * Team) list -> bool
Full name: Script.isValidDraw
val draw : (Team * Team) list
type 'T list = List<'T>
Full name: Microsoft.FSharp.Collections.list<_>
val map : mapping:('T -> 'U) -> list:'T list -> 'U list
Full name: Microsoft.FSharp.Collections.List.map
val fold : folder:('State -> 'T -> 'State) -> state:'State -> list:'T list -> 'State
Full name: Microsoft.FSharp.Collections.List.fold
val validDraws : (Team * Team) list list
Full name: Script.validDraws
val filter : predicate:('T -> bool) -> list:'T list -> 'T list
Full name: Microsoft.FSharp.Collections.List.filter
val matchProbability : Team * Team -> float
Full name: Script.matchProbability
val occurences : int
val exists : predicate:('T -> bool) -> list:'T list -> bool
Full name: Microsoft.FSharp.Collections.List.exists
val x : Team * Team
val length : list:'T list -> int
Full name: Microsoft.FSharp.Collections.List.length
Multiple items
val float : value:'T -> float (requires member op_Explicit)
Full name: Microsoft.FSharp.Core.Operators.float
--------------------
type float = System.Double
Full name: Microsoft.FSharp.Core.float
--------------------
type float<'Measure> = float
Full name: Microsoft.FSharp.Core.float<_>
val getProbabilities : runnerUps:seq<Team> -> groupWinners:seq<Team> -> ((Team * Team) * float) list
Full name: Script.getProbabilities
val runnerUps : seq<Team>
val groupWinners : seq<Team>
val runnerUp : Team
val adversary : Team
val footbalMatch : Team * Team
val probabilities : ((Team * Team) * float) list
Full name: Script.probabilities
val printProbability : (Team * Team) * float -> unit
Full name: Script.printProbability
val probabilities : (Team * Team) * float
val probability : float
val printfn : format:Printf.TextWriterFormat<'T> -> 'T
Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printfn
val iter : action:('T -> unit) -> list:'T list -> unit
Full name: Microsoft.FSharp.Collections.List.iter
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