Another update from ingydotnet^djgoku
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Ingy döt Net
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7604 changed files with 108452 additions and 22726 deletions
28
Task/Average-loop-length/Elixir/average-loop-length.elixir
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28
Task/Average-loop-length/Elixir/average-loop-length.elixir
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@ -0,0 +1,28 @@
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defmodule RC do
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def factorial(0), do: 1
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def factorial(n), do: Enum.reduce(1..n, 1, &(&1 * &2))
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def loop_length(n), do: loop_length(n, HashSet.new)
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defp loop_length(n, set) do
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r = :random.uniform(n)
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if Set.member?(set, r), do: Set.size(set),
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else: loop_length(n, Set.put(set, r))
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end
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def task(runs) do
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IO.puts " N average analytical (error) "
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IO.puts "=== ========= ========== ========="
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Enum.each(1..20, fn n ->
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sum_of_runs = Enum.reduce(1..runs, 0, fn _,sum -> sum + loop_length(n) end)
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avg = sum_of_runs / runs
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analytical = Enum.reduce(1..n, 0, fn i,sum ->
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sum + (factorial(n) / :math.pow(n, i) / factorial(n-i))
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end)
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:io.format "~3w ~9.4f ~9.4f (~6.2f%)~n", [n, avg, analytical, abs(avg/analytical - 1)*100]
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end)
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end
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end
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runs = 100_000
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RC.task(runs)
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@ -1,38 +1,37 @@
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/*REXX pgm computes avg loop length mapping a random field 1..N to 1..N*/
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parse arg runs tests seed .
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if runs ==',' | runs =='' then runs = 40 /*num of runs. */
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if tests ==',' | tests =='' then tests = 1000000 /*num of trials.*/
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if seed\==',' & seed\=='' then call random ,,seed /*repeatability?*/
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numeric digits 100000; !.=0; !.0=1 /*be able to calculate !(25000).*/
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numeric digits max(9,length(!(runs))) /*set NUMERIC digits for !(runs).*/
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say right( runs, 24) 'runs' /*display # of runs we're using*/
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say right( tests, 24) 'tests' /* " " " tests " " */
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say right( digits(), 24) 'digits' /* " " " digits " " */
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/*REXX pgm computes average loop length mapping a random field 1..N ───► 1..N */
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parse arg runs tests seed . /*obtain optional arguments from C.L. */
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if runs ==',' | runs =='' then runs = 40 /*number of runs. */
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if tests ==',' | tests =='' then tests= 1000000 /* " " trials. */
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if seed\==',' & seed\=='' then call random ,,seed /*RAND repeatability?*/
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numeric digits 100000; !.=0; !.0=1 /*be able to calculate 25,000! */
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numeric digits max(9,length(!(runs))) /*set the NUMERIC DIGITS for !(runs). */
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say right( runs, 24) 'runs' /*display number of runs we're using.*/
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say right( tests, 24) 'tests' /* " " " tests " " */
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say right( digits(), 24) 'digits' /* " " " digits " " */
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say
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say ' N average exact % error' /*headers & pad.*/
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h= ' ─── ───────── ───────── ─────────'; say h; pad=left('',3)
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do #=1 for runs; ##=right(#,9) /*## is used for indenting output*/
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avg = fmtD(exact(#)) /*use 4 digits past decimal point*/
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exa = fmtD(exper(#)) /* " " " " " " */
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err = fmtD(abs(exa-avg)*100/avg) /* " " " " " " */
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say ## pad exa pad avg pad err /*display a line of statistics. */
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end /*#*/
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say h /*display the final header bar. */
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exit /*stick a fork in it, we're done.*/
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/*──────────────────────────────────! subroutine────────────────────────*/
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!: procedure expose !.; parse arg z; if !.z\==0 then return !.z
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!=1; do j=1 for z; !=!*j; !.j=!; end; return !
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/*──────────────────────────────────EXACT subroutine────────────────────*/
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exact: parse arg x; s=0; do j=1 for x; s=s+!(x)/!(x-j)/x**j; end; return s
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/*──────────────────────────────────EXPER subroutine────────────────────*/
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exper: parse arg n
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k=0; do tests; $.=0 /*repeat TESTS times, reset FOUND*/
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do n; r=random(1,n); if $.r then leave
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$.r=1; k=k+1 /*bump the ctr. */
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end /*n*/
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end /*tests*/
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return k/tests
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/*──────────────────────────────────FMTD subroutine─────────────────────*/
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fmtD: parse arg y,d; d=word(d 4,1); y=format(y,,d); parse var y w '.' f
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if f=0 then return w || left('',d+1); return y
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say ' N average exact % error' /*◄──title,header►───┐*/
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h= ' ─── ───────── ───────── ─────────'; pad=left('',3) /*◄──────┘*/
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say h
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do #=1 for runs; ##=right(#,9) /*## is used for indenting the output.*/
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avg=fmtD(exact(#)) /*use four digits past decimal point. */
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exa=fmtD(exper(#)) /* " " " " " " */
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err=fmtD(abs(exa-avg)*100/avg) /* " " " " " " */
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say ## pad exa pad avg pad err /*display a line of statistics to term.*/
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end /*#*/
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say h /*display the final header (some bars).*/
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exit /*stick a fork in it, we're all done. */
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/*────────────────────────────────────────────────────────────────────────────*/
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!: procedure expose !.; parse arg z; if !.z\==0 then return !.z
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!=1; do j=1 for z; !=!*j; !.j=!; end; /*factorial*/ return !
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/*────────────────────────────────────────────────────────────────────────────*/
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exact: parse arg x; s=0; do j=1 for x; s=s+!(x)/!(x-j)/x**j; end; return s
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/*────────────────────────────────────────────────────────────────────────────*/
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exper: parse arg n; k=0; do tests; $.=0 /*do it TESTS times.*/
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do n; r=random(1,n); if $.r then leave
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$.r=1; k=k+1 /*bump the counter. */
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end /*n*/
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end /*tests*/
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return k/tests
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/*────────────────────────────────────────────────────────────────────────────*/
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fmtD: parse arg y,d; d=word(d 4,1); y=format(y,,d); parse var y w '.' f
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if f=0 then return w || left('', d+1); return y
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37
Task/Average-loop-length/Scala/average-loop-length.scala
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37
Task/Average-loop-length/Scala/average-loop-length.scala
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@ -0,0 +1,37 @@
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import scala.util.Random
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object AverageLoopLength extends App {
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val factorial: Stream[Double] = 1 #:: factorial.zip(Stream.from(1)).map(n => n._2 * factorial(n._2 - 1))
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def expected(n: Int) = (for (i <- 1 to n) yield factorial(n) / Math.pow(n, i) / factorial(n - i)).sum
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def trial(n: Int):Double = {
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var count = 0
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var x = 1
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var bits = 0
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while ((bits & x) == 0) {
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count = count + 1
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bits = bits | x
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x = 1 << Random.nextInt(n)
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}
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count
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}
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def tested(n: Int, times: Int) = (for (i <- 1 to times) yield trial(n)).sum / times
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val results = for (n <- 1 to 20;
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avg = tested(n, 1000000);
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theory = expected(n)
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) yield (n, avg, theory, (avg / theory - 1) * 100)
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println("n avg exp diff")
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println("------------------------------------")
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results foreach { n => {
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println(f"${n._1}%2d ${n._2}%2.6f ${n._3}%2.6f ${n._4}%2.3f%%")
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}
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}
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}
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