Latin Squares in reduced form/Randomizing using Jacobson and Matthews’ Technique: Difference between revisions

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

===The Functions===

// Jacobson and Matthews technique for generating Latin Squares. Nigel Galloway: August 5th., 2019

let R=let N=System.Random() in (fun n->N.Next(n))

 

let randLS α=Seq.unfold(fun g->Some(g,jmLS α g))(Array2D.init α α (fun n g->1+(n+g)%α))

===The Task===

;part 1

randLS 4 |> Seq.take 10000 |> Seq.map asNormLS |> Seq.countBy id |> Seq.iter(fun n->printf "%A was produced %d times\n\n" (fst n)(snd n))

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<pre>

</pre>

;part 2

randLS 5 |> Seq.take 10000 |> Seq.map asNormLS |> Seq.countBy id |> Seq.iteri(fun n g->printf "%d(%d) " (n+1) (snd g)); printfn ""

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<pre>

</pre>

;part 3

let q=Seq.item 749 (randLS 42)

for n in [0..41] do (for g in [0..41] do printf "%3d" q.[n,g]); printfn ""

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<pre>

;part 4

Generating 1000 Latin Squares of order 256 takes about 1.5secs

printfn "%d" (Array2D.length1 (Seq.item 999 (randLS 256)))

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<pre>

 

Part 4 is taking about 6.5 seconds on my Celeron @1.6 GHz but will be much faster on a more modern machine. Being able to compute random, uniformly distributed, Latin squares of order 256 reasonably quickly is interesting from a secure communications or cryptographic standpoint as the symbols of such a square can represent the 256 characters of the various extended ASCII encodings.

 

import (

elapsed := time.Since(start)

fmt.Printf("Generated in %s\n", elapsed)

 

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=={{header|Julia}}==

{{trans|Go}}

const Mat = Vector{Vector{Int}}

 

 

testJacobsenMatthews()

<pre>

PART 1: 10,000 latin Squares of order 4 in reduced form:

=={{header|Nim}}==

{{trans|Go}}

 

type

for _ in 1..1000:

c.shuffle()

 

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=={{header|Phix}}==

{{trans|Go}}

<span style="color: #008080;">function</span> <span style="color: #000000;">shuffleCube</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">rx</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ry</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rz</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>

<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>

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<pre>

=={{header|Raku}}==

{{trans|Go}}

 

#!/usr/bin/env raku

for ^100 { shuffleCube @c } # without hyper, will do only 100 cycles

say "Generated in { now - $snapshot } seconds."

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<pre>

{{libheader|Wren-fmt}}

{{libheader|Wren-seq}}

import "/fmt" for Fmt

import "/seq" for Lst

for (i in 1..1000) shuffleCube.call(c)

var elapsed = System.clock - start

 

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