Average loop length: Difference between revisions
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Automated syntax highlighting fixup (second round - minor fixes)
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{{trans|Python}}
<syntaxhighlight lang="11l">F ffactorial(n)
V result = 1.0
L(i) 2..n
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=={{header|Ada}}==
<syntaxhighlight lang=
with Ada.Numerics.Generic_Elementary_Functions;
with Ada.Numerics.Discrete_Random;
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=={{header|BBC BASIC}}==
<syntaxhighlight lang="bbcbasic"> @% = &2040A
MAX_N = 20
TIMES = 1000000
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=={{header|C}}==
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdlib.h>
#include <math.h>
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=={{header|C sharp|C#}}==
{{trans|Java}}
<syntaxhighlight lang="csharp">public class AverageLoopLength {
private static int N = 100000;
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=={{header|C++}}==
Partial translation of C using stl and std.
<syntaxhighlight lang="cpp">#include <random>
#include <vector>
#include <iostream>
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=={{header|Clojure}}==
{{trans|Python}}
<syntaxhighlight lang="lisp">(ns cyclelengths
(:gen-class))
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=={{header|D}}==
{{trans|Raku}}
<syntaxhighlight lang="d">import std.stdio, std.random, std.math, std.algorithm, std.range, std.format;
real analytical(in int n) pure nothrow @safe /*@nogc*/ {
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{{libheader| System.Math}}
{{Trans|C}}
<syntaxhighlight lang=
program Average_loop_length;
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</pre>
=={{header|EchoLisp}}==
<syntaxhighlight lang="scheme">
(lib 'math) ;; Σ aka (sigma f(n) nfrom nto)
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{{trans|Ruby}}
{{works with|Elixir|1.1+}}
<syntaxhighlight lang="elixir">defmodule RC do
def factorial(0), do: 1
def factorial(n), do: Enum.reduce(1..n, 1, &(&1 * &2))
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{{trans|Scala}}
<p>But uses the Gamma function instead of factorials.</p>
<syntaxhighlight lang="fsharp">open System
let gamma z =
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The <code>loop-length</code> word is more or less a translation of the inner loop of C's <code>test</code> function.
{{works with|Factor|0.99 2020-01-23}}
<syntaxhighlight lang="factor">USING: formatting fry io kernel locals math math.factorials
math.functions math.ranges random sequences ;
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=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">Const max_N = 20, max_ciclos = 1000000
Function Factorial(Byval N As Integer) As Double
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=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
_nmax = 20
_times = 1000000
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=={{header|Go}}==
<syntaxhighlight lang="go">package main
import (
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=={{header|Haskell}}==
<syntaxhighlight lang=
import qualified Data.Set as S
import Text.Printf
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We can implement f as {&LIST where LIST is an arbitrary list of N numbers, each picked independently from the range 0..(N-1). We can incrementally build the described sequence using (, f@{:) - here we extend the sequence by applying f to the last element of the sequence. Since we are only concerned with the sequence up to the point of the first repeat, we can select the unique values giving us (~.@, f@{:). This routine stops changing when we reach the desired length, so we can repeatedly apply it forever. For example:
<syntaxhighlight lang=
0
(~.@, {&0 0@{:)^:_] 1
1 0</syntaxhighlight>
Once we have the sequence, we can count how many elements are in it.
<syntaxhighlight lang=
2</syntaxhighlight>
Meanwhile, we can also generate all possible values of 1..N by counting out N^N values and breaking out the result as a base N list of digits.
<syntaxhighlight lang=
0 0
0 1
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1 1</syntaxhighlight>
All that's left is to count the lengths of all possible sequences for all possible distinct instances of f and average the results:
<syntaxhighlight lang=
1
(+/ % #)@,@((#.inv i.@^~) ([: # (] ~.@, {:@] { [)^:_)"1 0/ i.)2
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2.77469</syntaxhighlight>
Meanwhile the analytic solution (derived by reading the Ada implementation) looks like this:
<syntaxhighlight lang=
ana"0]1 2 3 4 5 6
1 1.5 1.88889 2.21875 2.5104 2.77469</syntaxhighlight>
To get our simulation, we can take the exact approach and replace the part that generates all possible values for f with a random mechanism. Since the task does not specify how long to run the simulation, and to make this change easy, we'll use N*1e4 tests.
<syntaxhighlight lang=
sim"0]1 2 3 4 5 6
1 1.5034 1.8825 2.22447 2.51298 2.76898</syntaxhighlight>
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Finally, we can generate our desired results:
<syntaxhighlight lang=
+--+-------+--------+-----------+
|N |average|analytic|error |
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This uses a 0-based index (0, 1, ..., n-1) as opposed to the 1-based index (1, 2, ..., n) specified in the question, because it fits better with the native structure of Java.
<syntaxhighlight lang="java">import java.util.HashSet;
import java.util.Random;
import java.util.Set;
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=={{header|Julia}}==
{{trans|Python}}
<syntaxhighlight lang="julia">using Printf
analytical(n::Integer) = sum(factorial(n) / big(n) ^ i / factorial(n - i) for i = 1:n)
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=={{header|Kotlin}}==
{{trans|Go}}
<syntaxhighlight lang="scala">const val NMAX = 20
const val TESTS = 1000000
val rand = java.util.Random()
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=={{header|Liberty BASIC}}==
{{trans|BBC BASIC}}
<syntaxhighlight lang="lb">
MAXN = 20
TIMES = 10000'00
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=={{header|Lua}}==
<syntaxhighlight lang="lua">function average(n, reps)
local count = 0
for r = 1, reps do
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=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">Grid@Prepend[
Table[{n, #[[1]], #[[2]],
Row[{Round[10000 Abs[#[[1]] - #[[2]]]/#[[2]]]/100., "%"}]} &@
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=={{header|Nim}}==
{{trans|C}}
<syntaxhighlight lang="nim">import random, math, strformat
randomize()
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=={{header|Oberon-2}}==
<syntaxhighlight lang="oberon2">
MODULE AvgLoopLen;
(* Oxford Oberon-2 *)
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=={{header|PARI/GP}}==
{{trans|C}}
<syntaxhighlight lang="parigp">expected(n)=sum(i=1,n,n!/(n-i)!/n^i,0.);
test(n, times)={
my(ct);
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=={{header|Perl}}==
<syntaxhighlight lang="perl">use List::Util qw(sum reduce);
sub find_loop {
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=={{header|Phix}}==
<!--<syntaxhighlight lang=
<span style="color: #008080;">constant</span> <span style="color: #000000;">MAX</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">20</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">ITER</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000000</span>
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=={{header|Phixmonti}}==
{{trans|Phix}}
<syntaxhighlight lang=
20 var MAX
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=={{header|PicoLisp}}==
{{trans|Python}}
<syntaxhighlight lang=
(seed (in "/dev/urandom" (rd 8)))
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=={{header|PowerShell}}==
{{works with|PowerShell|2}}
<syntaxhighlight lang=
function Get-AnalyticalLoopAverage ( [int]$N )
{
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</syntaxhighlight>
Note: The use of the [pscustomobject] type accelerator to simplify making the test result table look pretty requires PowerShell 3.0.
<syntaxhighlight lang=
# Display results for N = 1 through 20
ForEach ( $N in 1..20 )
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=={{header|Python}}==
{{trans|C}}
<syntaxhighlight lang="python">from __future__ import division # Only necessary for Python 2.X
from math import factorial
from random import randrange
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=={{header|R}}==
<syntaxhighlight lang=
expected <- function(size) {
result <- 0
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=={{header|Racket}}==
<syntaxhighlight lang="racket">
#lang racket
(require (only-in math factorial))
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(formerly Perl 6)
{{Works with|rakudo|2016.08}}
<syntaxhighlight lang=
constant TRIALS = 100;
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Also note that the <big>'''!'''</big> (factorial function) uses memoization for optimization.
<syntaxhighlight lang="rexx">/*REXX program computes the average loop length mapping a random field 1···N ───► 1···N */
parse arg runs tests seed . /*obtain optional arguments from the CL*/
if runs =='' | runs =="," then runs = 40 /*Not specified? Then use the default.*/
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=={{header|Ruby}}==
Ruby does not have a factorial method, not even in it's math library.
<syntaxhighlight lang="ruby">class Integer
def factorial
self == 0 ? 1 : (1..self).inject(:*)
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=={{header|Rust}}==
{{libheader|rand}}
<syntaxhighlight lang="rust">extern crate rand;
use rand::{ThreadRng, thread_rng};
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=={{header|Scala}}==
<syntaxhighlight lang=
import scala.util.Random
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=={{header|Scheme}}==
<syntaxhighlight lang="scheme">
(import (scheme base)
(scheme write)
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=={{header|Seed7}}==
<syntaxhighlight lang="seed7">$ include "seed7_05.s7i";
include "float.s7i";
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=={{header|Sidef}}==
{{trans|Perl}}
<syntaxhighlight lang="ruby">func find_loop(n) {
var seen = Hash()
loop {
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=={{header|Simula}}==
<syntaxhighlight lang="simula">BEGIN
REAL PROCEDURE FACTORIAL(N); INTEGER N;
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=={{header|Tcl}}==
<syntaxhighlight lang="tcl"># Generate a list of the numbers increasing from $a to $b
proc range {a b} {
for {set result {}} {$a <= $b} {incr a} {lappend result $a}
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=={{header|Unicon}}==
{{trans|C}}
<syntaxhighlight lang="unicon">link printf, factors
$define MAX_N 20
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=={{header|VBA}}==
{{trans|Phix}}
<syntaxhighlight lang="vb">Const MAX = 20
Const ITER = 1000000
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=={{header|VBScript}}==
Ported from the VBA version. I added some precalculations to speed it up
<syntaxhighlight lang="vb">
Const MAX = 20
Const ITER = 100000
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=={{header|Vlang}}==
{{trans|Go}}
<syntaxhighlight lang="vlang">import rand
import math
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{{trans|Go}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascript">import "random" for Random
import "/fmt" for Fmt
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=={{header|zkl}}==
<syntaxhighlight lang="zkl">const N=20;
(" N average analytical (error)").println();
|