Data commit

Task/Permutations-Derangements/F-Sharp/permutations-derangements-1.fs

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+// Generate derangements. Nigel Galloway: July 9th., 2019
+let derange n=
+  let fG n i g=let e=Array.copy n in e.[i]<-n.[g]; e.[g]<-n.[i]; e
+  let rec derange n g α=seq{
+    match (α>0,n&&&(1<<<α)=0) with
+     (true,true)->for i in [0..α-1] do if n&&&(1<<<i)=0 then let g=(fG g α i) in yield! derange (n+(1<<<i)) g (α-1); yield! derange n g (α-1)
+    |(true,false)->yield! derange n g (α-1)
+    |(false,false)->yield g
+    |_->()}
+  derange 0 [|1..n|] (n-1)

Task/Permutations-Derangements/F-Sharp/permutations-derangements-2.fs

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+derange 4 |> Seq.iter(printfn "%A")

Task/Permutations-Derangements/F-Sharp/permutations-derangements-3.fs

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+let subFact n=let rec fN n g=match n with 0m->int64(round(g/2.7182818284590452353602874713526624978m))|_->fN (n-1m) (g*n) in if n=0 then 1L else fN (decimal n) 1m
+[1..9] |> Seq.iter(fun n->printfn "items=%d !n=%d derangements=%d" n (subFact n) (derange n|>Seq.length))