Non-transitive dice: Difference between revisions

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=={{header|F_Sharp|F#}}==

// Non-transitive diceNigel Galloway: August 9th., 2020

// Find all 3(d1,d2,d3) four sided dice with faces valued 1,2,3,or 4 such that over a run d1 beats d2, d2 betas d3, but d3 beats d1.

let die=let g=[for n0 in [1..4] do for n1 in [n0..4] do for n2 in [n1..4] do for n3 in [n2..4]->[n0;n1;n2;n3]]

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// ~~Nigel~~ Galloway: August 9th., 2020

~~let~~ fN(n,g)~~=let~~ n=seq{for n in n do for g in g->compare n g}|>Seq.~~countBy id|>Map.ofSeq~~

[for n in g do for g in g->(n,g)]|>List.filter(fun(n,g)->seq{for n in n do for g in g->compare n g}|>Seq.sum<0)

match Map.tryFind -1 n,Map.tryFind 1 n with (Some n,Some g)->n>g |(Some _,_)->true |_->false

let e=[for n0 in ~~[1..4]~~ do for n1 in ~~[n0~~.~~.4]~~ do ~~for n2 in [n1.~~.4] do ~~for n3 in [n2..4]~~->~~[n0;n1;n2;n3]]~~

let n3=seq{for d1,d2 in die do for _,d3 in die|>List.filter(fun(n,g)->n=d2 && List.contains (g,d1) die)->(d1,d2,d3)}

let i=[for n in e do for g in e->(n,g)]|>List.filter fN

let n4=seq{for d1,d2 in die do for _,d3 in die|>List.filter(fun(n,_)->n=d2) do for _,d4 in die|>List.filter(fun(n,g)->n=d3 && List.contains (g,d1) die)->(d1,d2,d3,d4)}

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n3|>Seq.iter(fun((d1,d2),(_,d3))->printfn "%A<%A; %A<%A; %A>%A\n" d1 d2 d2 d3 d1 d3)

let l3=seq{for n in i do for g in i->(n,g)}|>Seq.filter(fun((a,n),(g,b))->n=g && List.contains (b,a) i)

l3|>Seq.iter(fun((n,g),(_,~~g')~~)->printfn "%A<%A; %A<%A; %A>%A\n" n g g g' n g')

n4|>Seq.iter(fun(d1,d2,d3,d4)->printfn "%A<%A; %A<%A; %A<%A; %A>%A" d1 d2 d2 d3 d3 d4 d1 d4)</lang>

let l4=seq{for n in i do for g in i do for i in i->(n,g,i)}|>Seq.filter(fun((a,n),(g,b),(x,y))->n=g && b=x && List.contains (y,a) i)

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l4|>Seq.iter(fun((n,g),(_,~~g'),(_,b~~))->printfn "~~%A<%A;~~ %A<%A; %A<%A; %A>%A" n g g g' ~~g' b n~~ b)

</lang>

<pre>

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[1; 3; 3; 3]<[1; 1; 4; 4]; [1; 1; 4; 4]<[2; 2; 2; 4]; [1; 3; 3; 3]>[2; 2; 2; 4]

[2; 2; 2; 4]<[1; 3; 3; 3]; [1; 3; 3; 3]<[1; 1; 4; 4]; [2; 2; 2; 4]>[1; 1; 4; 4]

Real: 00:00:00.830

[1; 1; 4; 4]<[2; 2; 2; 4]; [2; 2; 2; 4]<[2; 2; 3; 3]; [2; 2; 3; 3]<[1; 3; 3; 3]; [1; 1; 4; 4]>[1; 3; 3; 3]

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[2; 2; 2; 4]<[2; 2; 3; 3]; [2; 2; 3; 3]<[1; 3; 3; 3]; [1; 3; 3; 3]<[1; 1; 4; 4]; [2; 2; 2; 4]>[1; 1; 4; 4]

[2; 2; 3; 3]<[1; 3; 3; 3]; [1; 3; 3; 3]<[1; 1; 4; 4]; [1; 1; 4; 4]<[2; 2; 2; 4]; [2; 2; 3; 3]>[2; 2; 2; 4]

Real: 00:00:05.867

</pre>