Sonsuza Kadar Zeno's Dichotomy Paradox Yazdır (1 / (2 ^ n))

31

Vikipedi: Zeno Dikotomi Paradoksu

Sonsuz sayıda matematikçi bir bara girer. İlki bira siparişi veriyor. İkincisi yarım bira siparişi veriyor. Üçüncüsü dördüncü bira siparişi veriyor. Barmen onları durdurur, iki bira koyar ve "Hepiniz bir sürü aptalsınız" der.

Reddit

Aşağıdaki seriyi, program çalıştığı sürece, her bir maddenin paydası her seferinde iki ile çarpılarak yazdırın:

1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...

Olarak nsonsuza yaklaşan, bu dizinin toplam yaklaşır 2.

kurallar

Hayır, yazdıramayabilirsiniz 2.

1/1İlk öğe olarak yazdıramazsınız .

Boşlukları kaldırabilir 1+1/2+...veya 1 + 1 / 2 + ...istediğiniz kadar boşluk ekleyebilirsiniz .

Popüler talep nedeniyle boşluk yerine yeni satırları sınırlayıcı olarak kullanabilirsiniz.

Gerekirse, payda .artı bir artı 0s ekleyebilirsiniz .

"Sonsuz", gereksiz gecikmeler olmadığı ve mevcut (değişken) sistemin özellikleri tarafından sınırlandırıldığı, ancak geçerli dilinizle sınırlı olmadığı sürece anlamına gelir.

Standart boşluklar uygulanır.

Bu kod golf , bayt cinsinden en kısa cevap kazanır.

code-golf  math  rational-numbers 
— Stephen
kaynak
41
Şaka ile ilgili olarak, “Sizler kendi sınırlarınızı bilmelisiniz” versiyonunu daha çok seviyorum.
— Mart Ho,
14
Sadece ben miyim yoksa oradaki bir parabol mu?
— Adám
1
@StephenS Evet, onları da gördüm, ama bu çok daha net ve daha büyük.
— Adám
10
@ Adám: evet! Paydaların uzunlukları değişmediyse, +1/s'nin görsel düzeni sadece çapraz bir çizgi oluşturur. Bununla birlikte, paydaların uzunlukları doğrusal olarak değişmektedir (yuvarlamaya kadar): hanelerin sayısı 2^nyaklaşıkdır n log(2)/log(10). Bu lineer değişimin , her ikisinin nispi pozisyonunda , önceki pozisyona göre mutlak pozisyondaki ikinci dereceden bir değişiklikle aynı olan lineer bir değişime dönüşmesidir . +1/
— Greg Martin
3
@QPaysTaxes o zaman rekabet edemezsiniz - ancak birden fazla kişi rekabet eden C cevapları göndermek istiyorsa, birbirleriyle rekabet edebilirsin :)
— Stephen

Yanıtlar:

14

05AB1E , 10 9 bayt

Outgolfer Erik sayesinde 1 bayt kaydedildi

[No…+1/J?

Çevrimiçi deneyin!

açıklama

[           # loop over N infinitely [0 ...]
 No         # calculate 2^N
   …+1/J    # join with the string "+1/"
        ?   # print without newline
— Emigna
kaynak
Bunu golf oynayabilirsiniz:[No?…+1/?
— Outgolfer Erik
@EriktheOutgolfer: Doğru! İnterpolasyonun boşa gittiğini biliyordum: P
— Emigna
1
Teknik olarak kullanmak «yerine kullanmalısınız, Jama bu da işe yarıyor.
— Outgolfer Erik
13
@EriktheOutgolfer 'kullanmalı' bir golfçü sözlüğünde değildir.
— Okx,
6

APL (Dyalog Unicode) , 15 bayt

Daha fazla ise eğlence ⎕FR( F loating noktalı R ePresentation) 'dir 1287(128 bit ondalık) ve ⎕PP( P Rint P recision) olan 34.

{∇2×⊃⎕←⍵'+1/'}1

Çevrimiçi deneyin!

{… }1 1 numaralı numaraya aşağıdaki işlevi uygulayın:

 ⎕←⍵'+1/' argümanı ve dizgeyi yazdırabilir

 ⊃ ilki seçin (yani argüman)

 2× ikiye katla

 ∇ bunun üzerine kuyruk çağrısı özyinelemesi (optimize edilmiş, böylece sonsuz tekrarlanabilir)

— Adem
kaynak
6

C (gcc) , 60 bayt

f(){for(long long n=1;n;n*=2)printf(&"+1/%llu"[n^1?0:3],n);}

İmzasız 64bit sınırını yükseltir.

Çevrimiçi deneyin!

Bu sonsuza dek sürecek; (alacağı kadar küçük)

C (tcc) , 312 264 255 251 233 231 208 204 195 190 188 170 bayt

l=4;c;main(i){for(char*t="*\b1+";puts(i=t),*++t=48;l=asprintf(&t,"1/%s",t+=*++t<49))for(t+=l-2;--t>i;)*t>52?*t=*t*2%58+c,c=*--t>52,*t=*t%48*2%10+49:(*t=*t*2-48+c+(c=0));}

Çevrimiçi deneyin!

İşte bu kadar golf versiyonu değil;

c;l=4;main(i){
    for(char*t="*\b1+";puts(i=t),*++t=48;l=asprintf(&t,"1/%s",t+=*++t<49))
        for(t+=l-2;--t>i;)
            *t>52?*t=*t*2%58+c,c=*--t>52,*t=*t%48*2%10+49:(*t=*t*2-48+c+(c=0));
}
— cleblanc
kaynak
5

Bash , 33 bayt

echo 1;yes|awk '{print"+1/"2^NR}'

Çevrimiçi deneyin!

Newline'dan kaçınmak printiçin printfve echoiçin değiştirinprintf

— marcosm
kaynak
1
printf 1Ayrıca bu yeni çizgiden de kaçınır, değil mi?
— Neil,
+1/infAwk'imde (GNU Awk 4.2.1), 1024'lük dönemden itibaren tekrarlanıyorum . :-(
— Toby Speight
5

dc, 19 18 bayt

1[rdp+[+1/]Prdx]dx

açıklama

Bu itme 1ve [rdp+[+1/]Prdx]yığına. Daha sonra kopyalayıp çalıştırıyoruz [rdp+[+1/]Prdx]. Yaptığı ilk şey r, değeri üstte olacak şekilde stack ( ) ' i döndürmektir . dp+değeri yazdırır ve kendini ekler (2 ile çarpmak için). [+1/]Pdeğişmezi basar +1/, sonra argümanları döndürerek kaydedilen makro tanımı en üstte olur, kopyalar ve tekrar başlar.

notlar

GNU dcnormalde 70 sütuna sarılacaktır. Bunu geçersiz kılmak ve sonsuz bir satır elde DC_LINE_LENGTH=0etmek için ortam değişkenlerinize ekleyin .

Çıktı (kısmi)

1
+1/2
+1/4
+1/8
+1/16
+1/32
+1/64
+1/128
+1/256
+1/512
+1/1024
+1/2048
+1/4096
+1/8192
+1/16384
+1/32768
+1/65536
+1/131072
+1/262144
+1/524288
+1/1048576
+1/2097152
+1/4194304
+1/8388608

...

+1/1042962419883256876169444192465601618458351817556959360325703910069443225478828393565899456512
+1/2085924839766513752338888384931203236916703635113918720651407820138886450957656787131798913024
+1/4171849679533027504677776769862406473833407270227837441302815640277772901915313574263597826048
+1/8343699359066055009355553539724812947666814540455674882605631280555545803830627148527195652096
+1/16687398718132110018711107079449625895333629080911349765211262561111091607661254297054391304192
+1/33374797436264220037422214158899251790667258161822699530422525122222183215322508594108782608384

...

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7029604801221984100983880306551144728065542617917554688

...

— Toby Speight
kaynak
15 dakika geç T_T kaldım, bir bayt kaydetmek dpyerine kullandımddn
— Felipe Nardi Batista
Yeni dnbir satır tanıtmaktan kaçınırdım, ancak düşündüm p(çirkin çıktı pahasına). Aslında, yansıma üzerine, sonuçta, çok çirkin değil.
— Toby Speight
4

Pyth, 10 bayt

#h~hyZ"+1/

Zsıfır olarak başlar. ~hyZdeğerini sonrası atar 2*Z+1için Z. Böylece Zolur 0, 1, 3, 7, 15, ...sürekli olarak yinelenir üzerinde. hdaha sonra bir büyük değeri yazdırır. #sonsuz döngüyü çalıştırır ve "+1/biçimlendirmeyi doğru yapar.

— isaacg
kaynak
4

JavaScript (ES6) , 36 34 bayt

for(a=1;;a*=2)console.log(a+'+1/')

Çevrimiçi deneyin!

Jake Taylor'ın cevabından ilham aldı .

Bunun bir dilbilgisi adeğil, kayan nokta değişkeni olması nedeniyle dille sınırlı olduğunu unutmayın .

@Stefnotch sayesinde -2 bayt .

— eush77
kaynak
1
Console.log sonra parantez dışında bırakarak 2 bayt kaydedebilirsiniz. for(a=.5;;)console.log`${a*=2}+1/` Yine de, çözümünüz dille sınırlıdır, çünkü a bir değişkendir, büyük bir tamsayı değildir. (
— Zorluk
1
@Stefnotch Bu ne yazık ki işe yaramaz , çünkü enterpolasyonlu etiketli şablonlar tek bir argümandan daha fazlasını geçer. Sınırlılık ile ilgili notu da ekledim, teşekkür ederim.
— eush77
1
Kodumu test etmediğim için üzgünüm. Peki, bu kod 2 bayt tıraş ediyor:for(a=1;;a*=2)console.log(a+"+1/")
— Stefnotch
@Stefnotch Oh, ve bu da çok daha basit :) Teşekkürler.
— eush77
3

Java, 107 102 bayt

()->{for(java.math.BigInteger z=null,o=z.ONE,n=o;;n=n.add(n))System.out.print(n.max(o)==o?1:"+1/"+n);}

z=null12 bayt tasarrufu o=java.math.BigInteger.ONEiçine z=null,o=z.ONE, kısaltmak için var . z.ONEBir atmaz NullPointerExceptionbiz statik bir üyesi olup, bir örneği ise bir erişmek için.

Kullanımı intkodu kısaltır ancak 32 yinelemeden sonra uymaz.

kaydeder

  • : - 107> 102 bayt n.compareTo(o)>0dönüştü n.max(o)==o@Shufflepants tarafından verilen bir fikre, teşekkür
— Olivier Grégoire
kaynak
Bu, kurala uymaya çalışan tek girişlerden birine benziyor: "" Sınırsız ", gereksiz gecikmeler olmadığı ve mevcut (değişken) sistemin özellikleri tarafından sınırlandırıldığı, ancak geçerli dilinizle sınırlı olmadığı sürece." ancak yine de bunu yapmaz çünkü BigInteger hala maksimum 2 ^ değerine sahiptir (Integer.MAX_VALUE).
— Shufflepants
@Shufflepants Bu sınır nerede yazılır? Hiçbir yerde bu dilin bir sınırlama, ama sonra JVM, bir sınırlama değildir yani, ( "o aralık değerleri dışında destekleyebilir") olduğu sistem. Ayrıca, "bilgisayarımda çalışır", codegolf için yeterince iyi;)
— Olivier Grégoire
Bir dilin veya JVM'nin uygulamasının dilin değil sistemin bir parçası olduğu düşünülürse, BigInteger yerine int kullanabilirsiniz.
— Shufflepants
Hayır, çünkü intdiğer tüm ilkel türler dil düzeyinde sınırlıdır . Ayrıca, BigIntegerdoktor açıkça bir limitin zorunlu olmadığını, zorunlu olmadığını (ve varsayılan JVM uygulamasının bu limiti kullandığını) söyler.
— Olivier Grégoire
Bu fonksiyonda "BigInteger max (BigInteger val)" özelliği de belirtilmekte olup, mevcut uygulama limitinin ne olduğu gerekmemekle birlikte, limitin bir sonlu limit olması gerektiğini belirtir.
— Shufflepants
3

Vim, 22 , 21 bayt / tuş vuruşlarını

qqyiwA+1/<esc>p@"<C-a>@qqxX@q

Bunu test ederken, geçerli kayıt değerleri ile ilgili sorunlara rastlayabilirsiniz. Bunu düzeltmek için, koş

:let @q=''
:let @"=''

bunu çalıştırmadan önce veya ile vim 

vim -u NONE -i NONE
— DJMcMayhem
kaynak
1
Kesinlikle güzel.
— Tyrannosaur
3

R, 3534 bayt

cat(i<-1);repeat cat("+1/",i<-i*2)

Boşluk biraz serseri ama anladım ki sorun değil.

— Masclins
kaynak
1
Bunun repeatyerine kullanabilirsiniz while(T): cat(i<-1);repeat cat("+1/",i<-i*2)1 bayt daha az.
— plannapus
2

Aseto , 20 bayt

 pL*
pd12<
p"M"
1+1/

Diziyi boşluksuz yazdırır. Çalıştırdığınızda, arabellek nedeniyle kısa bir süre hiçbir şey göremezsiniz, -Fhemen her şeyi görmek için birlikte çalıştırın .

  1. 1'e basıp yazdırır, sonra "+ 1 /" yazısını hızlı saklamaya (kayıt defterine) kaydeder.
  2. 1 iter.
  3. İki ile çarparak, kayıt cihazından yüklenir, yazdırılır, çoğaltılır ve yazdırılır.
  4. GOTO 3.
— L3viathan
kaynak
2

Git , 102 100 bayt

Görünüşe göre Go neredeyse Java kadar kötü olabilir.

import(."fmt"
."math/big")
func main(){n:=NewInt(1);for{Print(n.String()+"+1/");n.Mul(n,NewInt(2))}}

Çevrimiçi deneyin! ( Yerel olarak bunlardan herhangi birini çalıştırmaktan kaçınmak iyi bir fikir olacaktır .: P)

— totallyhuman
kaynak
Hayır, Java kadar kötü değil: Git 5 bayt daha kısa: P
— Olivier Grégoire
2

QBIC , 18 bayt

?1{q=q*2?@+1/`';`q

Her terimi yeni bir satıra yazdırır.

Açıklama:

?1       Prints 1
{        Infinite loop
q=q*2    Doubles q, starts at 1*2=2
?@+1/`  Prints the string +1/ 
  ';`      without tabs, newlines or other terminators (code literal, ; is a QBIC function)
q        Also prints q
         The infinite loop is auto-closed by QBIC at EOF.

Bir baytı daha liberal bir çıktı formatı ile kaydedebiliriz:

{?q,A,┘q=q*2#+1/
— steenbergh
kaynak
2

C #, ̶6̶8̶ 154 bayt

void A(int b=1){System.Console.Write($"1{(b>1?"/"+b:"")}+");A(b*2);}

İşte int tarafından kısıtlanmayan bir sürüm.

using System.Numerics;BigInteger b=new BigInteger(1);void A(){System.Console.Write($"1{(b>1?"/"+b:"")}+");b=BigInteger.Multiply(new BigInteger(2),b);A();}
— LiefdeWen
kaynak
Paydası vurduğunda çok hızlı çalışmayı durdururint.MaxValue
— Rob
@Rob davranış ne olmalı?
— LiefdeWen
— Rob
Tamam, teşekkürler, yeni sürüm yeterli olmalı.
— LiefdeWen
Olduğu gibi, hiçbir şey gerçekten yazdırılmıyor çünkü A () çağrısı yok; fonksiyonda özyinelemeli çağrının dışında. Ayrıca, BigIntegers ilkel sayısal türlerden ve yerleşik operatörlerden örtük dönüşümler yapar. Böylece ilk bildirimi değiştirerek BigInteger b=1;kısaltmayı kısaltarakb*=2;
— 54
2

JavaScript (ES6), 45 43 42 bayt

2 bayt kaydedildi, teşekkürler @DanielM! 1 bayt kurtarıldı, işaret ettiğin için teşekkürler @ eush77.

= console.log a 1 =; (1) (için;;) _ ( +1/${a*=2})

= console.log; (a = 1); ((;)) _ ( +1/${a*=2}) için

_=console.log;for(_(a=1);;)_(`+1/${a*=2}`)

İlk defa Codegolf'a git, kolay git!

— Jake Taylor
kaynak
3
Sizin için bir pasajı düzenleyecektim, ama sonra tarayıcımı kırdım ve bunun sonsuz bir döngü sorusu olduğunu hatırladım xD
— Stephen
2
Evet, aletimi birkaç kez baştan başlatmak zorunda kaldım!
— Jake Taylor
Kutu a=1, for'un ilk bölümüne gidebilir, for(a=1;;)size ekstra noktalı virgülle bir bayt kazandırır.
— DanielM
_(a=1), iş DanielM'in önerisiyle de
— Felipe Nardi Batista
@ eush77 Bu doğru çıktı imo oluşturmaz. Her zaman bir ize sahip olacak +1/, bir kesir değil.
— Jake Taylor
2

AWK , 37 32 bayt

BEGIN{for(;;)printf 2^i++"+1/"}

Çevrimiçi deneyin!

BEGINGirdiye izin verildiyse kaldırılabilir ve 5 bayt kaydedilebilir. Üstlerin kullanılması kesinlikle çarpmadan ziyade bayt bakımından daha ucuzdur. :)

Umarım 2 ^ 1023 (iş bilgisayarımda) sonsuza kadar yakındır. Ne yazık ki, TIO bağlantısı bundan daha erken kesiliyor (yaklaşık 921). Ama 17726622920963562283492833353875882150307419319860869157979152909707315649514250439943889552308992750523075148942386782770807567185698815677056677116184170553481231217950104164393978236130449019315710017470734562946173533283208371259654747728689409291887821024109648618981425152 oldukça yakın sonsuza görünüyor. :)

— Robert Benson
kaynak
2

Haskell- 66 62 60 51 49 karakter

import Data.List
main=print$intercalate" + 1/"$map(show.(2^))[0..]

Bu, dize ile ayrılmış, 1'den başlayan ikisinin güçlerinin dize temsillerini yazdırarak oluşturulan dizeyi yazdırır " + 1/".

Kodun kendisi 49 bayttır, import ve newline bunu 66'ya çıkarır

Düzenleme: (62)

İthalatı keserek ve çok daha kısa bir adla ortalamayı tanımlayarak 4 bayt tıraş edildi

f(x:xs)s=x++s++xs`f`s
main=print$map(show.(2^))[0..]`f`" + 1/"

Düzenleme 2: (60)

(X: xs) list kuralını kullanmaya gerek olmadığımı fark ederek 2 karakter daha kazandınız:

f(x:y)s=x++s++y`f`s
main=print$map(show.(2^))[0..]`f`" + 1/"

Düzenleme 3: (51)

9 karakter daha kazanmak için f ve haritanın bir katlama gövdesi olarak tanımlanması yeniden uygulandı.

main=print$foldr((++).(++" + 1/").show.(2^))""[0..]

Düzenleme 4: (49)

Laokoni tarafından belirtildiği gibi, toplamda 2 baytı daha kesmek için boşlukları kaldırabilirim:

main=print$foldr((++).(++"+1/").show.(2^))""[0..]
— archaephyrryx
kaynak
Zorluk, çıktıdaki boşlukların isteğe bağlı olduğunu belirtir, böylece iki bayttan tasarruf edebilirsiniz.
— Laikoni
Ayrıca, en son sürümün, eğer "birbiriyle birleşmek" Haskell temel kütüphanesinde olsaydı, orijinalin kullandığı bayt sayısının aynı olduğuna dikkat çekti.
— archaephyrryx
1

Braingolf , 41 37 bayt

4 bayt kurtardı çünkü boşluklara ihtiyacım olmadığının farkına vardım, her zaman özellikleri tamamen okudum.

1!_V"+/">!@R.[<!_>2*v<!@>R!_v!@R<1+>]

Çevrimiçi deneyin!

Muhtemelen daha iyi golf olabilir, ama işe yarıyor.

— Skidsdev
kaynak
1

Fourier, 20 bayt

1~io(43a1o47ai*2~io)

Çevrimiçi deneyin!

Bunun yalnızca Python ve Javascript’in büyük sayıları kullanma biçimindeki farklılıkları nedeniyle Çevrimiçi Çalışabileceğini düşünüyorum.

Açıklama Psuedocode:

i = 1
Print i
While i != 0
    Print "+1/"
    i = i * 2
    Print i
End While
— Beta Bozulması
kaynak
Eğer Kıpırdayamıyorum Print ibaşlangıcına Whiledöngü?
— Neil,
@ Neil olabilir, ama herhangi bir bayt demez
— Beta Decay
Oh, şimdi anlıyorum, aslında baskı yapmıyorsun i.
— Neil,
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