Catalan numbers: Difference between revisions

← Older edit

Catalan numbers (view source)

Revision as of 18:56, 1 May 2024

151 bytes removed , 27 days ago

→‎{{header|langur}}

Langurmonkey

889

edits

Revision as of 09:26, 6 May 2023 (view source) Ttmrichter (talk \| contribs) (→‎{{header\|Lua}}: Added a Logtalk implementation.) ← Older edit		Latest revision as of 18:56, 1 May 2024 (view source) Langurmonkey (talk \| contribs) (→‎{{header\|langur}})
(14 intermediate revisions by 7 users not shown)
Line 563: print n, " ", c[n] next n</syntaxhighlight> {{out\| Output}}<pre> 0 1 end</syntaxhighlight>▼ 1 1 2 2 3 5 4 14▼ 5 42▼ 6 132▼ 7 429▼ 8 1430▼ 9 4862▼ 10 16796▼ 11 58786▼ 12 208012▼ 13 742900▼ 14 2674440▼ 15 9694845 </pre>▼ ==={{header\|FreeBASIC}}=== Line 2,294 ⟶ 2,310: =={{header\|EasyLang}}== <syntaxhighlight lang="text"> func catalan n ~~. ans~~ . if n = 0 ~~ans~~ = return 1 ~~else~~ . return ~~call~~2 * (2 * n - 1) * catalan (n - 1) hdiv (1 + n) ~~ans = 2 * (2 * n - 1) * h div (1 + n)~~ . . for i = 0 to 14 ~~call~~ print catalan i h ~~print h~~ . </syntaxhighlight> ~~{{out}}~~ ~~<pre>~~ 1 1 2 5 ▲14 ▲42 ▲132 ▲429 ▲1430 ▲4862 ▲16796 ▲58786 ▲208012 ▲742900 ▲2674440 ▲</pre> =={{header\|EchoLisp}}== Line 2,958 ⟶ 2,953: =={{header\|Fōrmulæ}}== {{FormulaeEntry\|page=https://formulae.org/?script=examples/Catalan_numbers}} Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition. '''Solution''' Programs in Fōrmulæ are created/edited online in its [https://formulae.org website], However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used. '''Direct definition''' [[File:Fōrmulæ - Catalan numbers 01.png]] [[File:Fōrmulæ - Catalan numbers 02.png]] '''Direct definition (alternative)''' The expression <math>\frac{(2n)!}{(n+1)!\,n!}</math> turns out to be equals to <math>\prod_{k=2}^{n}\frac{n + k}{k}</math> [[File:Fōrmulæ - Catalan numbers 03.png]] (same result) '''No directly defined''' Recursive definitions are easy to write, but extremely inefficient (specially the first one). Because a list is intended to be get, the list of previous values can be used as a form of memoization, avoiding recursion. The next function make use of the "second" form of recursive definition (without recursion): [[File:Fōrmulæ - Catalan numbers 04.png]] [[File:Fōrmulæ - Catalan numbers 05.png]] (same result) ~~In '''[https://formulae.org/?example=Catalan_numbers this]''' page you can see the program(s) related to this task and their results.~~ =={{header\|GAP}}== <syntaxhighlight lang="gap">Catalan1 := n -> Binomial(2n, n) - Binomial(2n, n - 1); Line 3,756 ⟶ 3,778: =={{header\|langur}}== {{trans\|Perl}} <syntaxhighlight lang="langur">val .factorial = ffn(.x) { if(.x < 2: 1; .x x self(.x - 1)) } val .catalan = ffn(.n) { .factorial(2 x .n) / .factorial(.n+1) / .factorial(.n) } for .i in 0..15 { Line 3,821 ⟶ 3,844: <syntaxhighlight lang="logtalk"> % libraries▼ :- initialization(( ▲ % libraries logtalk_load(dates(loader)), logtalk_load(meta(loader)), logtalk_load(types(loader)), % application▼ ~~)).~~ ▲% application ~~:- initialization((~~ logtalk_load(seqp), logtalk_load(catalan), Line 3,850 ⟶ 3,868: :- end_protocol. ▲~~end~~</syntaxhighlight> The implementation of a Catalan sequence generator is in <code>catalan.lgt</code>: Line 3,856 ⟶ 3,875: :- object(catalan, implements(seqp)). :- private(catalan/2). :- dynamic(catalan/2). Line 6,150 ⟶ 6,170: {{libheader\|Wren-fmt}} {{libheader\|Wren-math}} <syntaxhighlight lang="~~ecmascript~~wren">import "./fmt" for Fmt import "./math" for Int var catalan = Fn.new { \|n\| Line 6,213 ⟶ 6,233: 15 9694845 </pre> =={{header\|XLISP}}== <syntaxhighlight lang="lisp">(defun catalan (n)