Boustrophedon transform: Difference between revisions

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// Boustrophedon transform. Nigel Galloway:October 26th., 2023

let fG n g=let rec fG n g=[match g with h::[]->yield n+h |h::t->yield n+h; yield! fG (n+h) t] in [yield n; yield! fG n g]|>List.rev

let fG n g=let rec fG n g=[match n with h::[]->yield g+h |h::t->yield g+h; yield! fG t (g+h)] in [yield g; yield! fG n g]|>List.rev

let ~~rec~~ Boustrophedon n g=~~seq{yield List~~.~~head~~ g; ~~yield!~~ ~~Boustrophedon~~ n (fG (n()) ~~g)}~~

let Boustrophedon n=Seq.scan(fun n g->fG n g)[Seq.head n] (Seq.tail n)|>Seq.map(List.head)

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===The Task===

printfn "zeroes"; ~~Boustrophedon~~ (fun()->0I) [1I]|>Seq.take 15|>Seq.iter(printf "%A "); printfn ""

printfn "zeroes"; Seq.unfold(fun n->Some(n,0I))1I|>Seq.take 15|>Boustrophedon|>Seq.iter(printf "%A "); printfn ""

let n=sprintf $"%A{~~Boustrophedon~~ (fun()->0I) [1I]|>Seq.item 999}" in printfn "%s ... %s (%d digits)" n[0..19] n[n.Length-20..n.Length] (n.Length)

let n=sprintf $"%A{Seq.unfold(fun n->Some(n,0I))1I|>Boustrophedon|>Seq.item 999}" in printfn "%s ... %s (%d digits)" n[0..19] n[n.Length-20..n.Length] (n.Length)

printfn "ones"; ~~Boustrophedon~~ (fun()->1I) [1I]|>Seq.take 15|>Seq.iter(printf "%A "); printfn ""

printfn "ones"; Seq.unfold(fun n->Some(n,n))1I|>Seq.take 15|>Boustrophedon|>Seq.iter(printf "%A "); printfn ""

let n=sprintf $"%A{~~Boustrophedon~~ (fun()->1I) [1I]|>Seq.item 999}" in printfn "%s ... %s (%d digits)" n[0..19] n[n.Length-20..n.Length] (n.Length)

let n=sprintf $"%A{Seq.unfold(fun n->Some(n,n))1I|>Boustrophedon|>Seq.item 999}" in printfn "%s ... %s (%d digits)" n[0..19] n[n.Length-20..n.Length] (n.Length)

printfn "1,-1,1,-1....."; ~~Boustrophedon~~ (~~let mutable~~ n~~=1I in (fun()~~->n<- -n; n)) [1I]|>Seq.take 15|>Seq.iter(printf "%A "); printfn ""

printfn "1,-1,1,-1....."; Seq.unfold(fun n->Some(n,-n))1I|>Boustrophedon|>Seq.take 15|>Seq.iter(printf "%A "); printfn ""

let n=sprintf $"%A{~~Boustrophedon~~ (~~let mutable~~ n~~=1I in (fun()~~->n<- -n; n)) [1I]|>Seq.item 999}" in printfn "%s ... %s (%d digits)" n[0..19] n[n.Length-20..n.Length] (n.Length)

let n=sprintf $"%A{Seq.unfold(fun n->Some(n,-n))1I|>Boustrophedon|>Seq.item 999}" in printfn "%s ... %s (%d digits)" n[0..19] n[n.Length-20..n.Length] (n.Length)

printfn "factorials"; ~~Boustrophedon~~ (~~let mutable~~ n,g~~=1I,2I in (fun(~~)->~~let r=~~n ~~in n<-~~n*g~~; g<-~~g+1I~~; r~~)) [1I]|>Seq.take 15|>Seq.iter(printf "%A "); printfn ""

printfn "factorials"; Seq.unfold(fun(n,g)->Some(n,(n*g,g+1I)))(1I,1I)|>Boustrophedon|>Seq.take 15|>Seq.iter(printf "%A "); printfn ""

let n=sprintf $"%A{~~Boustrophedon~~ (~~let mutable~~ n,g~~=1I,2I in (fun(~~)->~~let r=~~n ~~in n<-~~n*g~~; g<-~~g+1I~~; r~~)) [1I]|>Seq.item 999}" in printfn "%s ... %s (%d digits)" n[0..19] n[n.Length-20..n.Length] (n.Length)

let n=sprintf $"%A{Seq.unfold(fun(n,g)->Some(n,(n*g,g+1I)))(1I,1I)|>Boustrophedon|>Seq.item 999}" in printfn "%s ... %s (%d digits)" n[0..19] n[n.Length-20..n.Length] (n.Length)

printfn "primes"; let p=~~primesI~~() in ~~Boustrophedon~~ (fun()->~~Seq.head~~ p) ~~[Seq.head p]~~|>Seq.take 15|>Seq.iter(printf "%A "); printfn ""

printfn "primes"; let p=primes() in Seq.initInfinite(fun _->bigint(p()))|>Boustrophedon|>Seq.take 15|>Seq.iter(printf "%A "); printfn ""

~~let p=primesI() in~~ let n=sprintf $"%A{~~Boustrophedon~~ ~~(fun~~()~~->Seq.head~~ p) [Seq.~~head~~ p]|>Seq.item 999}" in printfn "%s ... %s (%d digits)" n[0..19] n[n.Length-20..n.Length] (n.Length)

let n=sprintf $"%A{let p=primes() in Seq.initInfinite(fun _->bigint(p()))|>Boustrophedon|>Seq.item 999}" in printfn "%s ... %s (%d digits)" n[0..19] n[n.Length-20..n.Length] (n.Length)

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