26
Haskell, 35 bytes
x?y|isNaN$x/y=tanh x*tanh y|0<1=x/y
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The relevant function is (?), which takes two Doubles as input and returns a Double as output.
How?
The hyperbolic tangent is an amazing function (two bytes shorter than signum!).
x
tanh x
0.0
0.0
-0.0
-0.0
Infinity
1.0
-Infinity
-1.0
Haskell, 30 29 bytes
x?y|x/y<=1/0=x/y|0<...
19
Haskell, 320…236 230 bytes
length<$>iterate(\h->nub[r$x:y:u|u<-h,t<-u,x<-n t\\u,y<-n x\\u,([x,x,y]\\(u>>=n))/=[x,y]])[[l,0<$l]]
r u=minimum[sort$(!!i).p.map(*j).m a<$>u|a<-u,j<-l,i<-[0..5]]
n=(<$>p l).m
m=zipWith(-)
p=permutations
l=[-1..1]
import Data.List
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An infinite list whose \$n\$-th ...
13
J, 25 bytes
(%-.)~/@(10^#&>)#.10#.&>]
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Takes a boxed 2-item vector containing the digit vectors of \$x\$ and \$y\$, and returns a rational number. The digits must be given in extended precision. \$y\$ may be an empty vector. I guess it's pretty well golfed when Jelly is at 20 bytes :)
How it works
Uses the formula at the end of ...
12
Scratch 3.0, 45 blocks/254 bytes
As SB Syntax:
define(n)(d)
set[A v]to(0
set[D v]to(d
set[i v]to(0
repeat((n)+(1
set[j v]to(0
repeat((n)+(1
set[r v]to((i)/(j
if<(D)>([abs v]of((r)-(D)))>then
set[A v]to(join(i)(join(/)(j
set[D v]to([abs v]of((r)-(D
end
set[j v]to((j)+(1
end
set[i v]to((i)+(1
end
say(A
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Just wouldn't be right if I ...
12
JavaScript (ES6), 45 bytes
Expects (a)(b), as Numbers. Returns a Number.
a=>b=>a/b||+(b?1/a?a/b:a*b>0||-1:1/a/b<0&&-0)
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How?
Let \$\mathbb{R}^*\$ be \$\{x\in\mathbb{R}\mid x\neq0\}\$.
Direct answers when a/b is truthy
Whenever \$a/b\$ is neither NaN nor \$0\$, we know for sure that it is the expected answer. The cases that ...
11
Julia 0.7, 26 bytes
imaginary brownie points for using tanh instead of sign (thanks Delfad0r)
a$b=a/b<=Inf?a/b:tanh(a*b)
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10
Wolfram Language (Mathematica), 22 bytes
#!~IntegerExponent~#2&
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9
Husk, 12 10 bytes
◄oa-⁰´×/ŀ→
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≠ is absolute difference, but doesn't seem to work for floats. So oa- is used.
-2 bytes from Leo.
Explanation
◄oa-⁰´×/ŀ→ Inputs: decimal → ⁰, max denominator → implicit
ŀ→ range 0..denominator
´×/ convert all possible pairs to fractions
◄o min by
a-⁰ absolute difference with the ...
9
Wolfram Language (Mathematica), 25 bytes
$$n! \div \left( \sum ^n _{k=0} k!(n-k)! \right)$$
#!/Sum[k!(#-k)!,{k,0,#}]&
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-4 bytes from @ovs
9
J, 14 13 bytes
<[:>./2^/@p:]
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-1 byte thanks to @Jonah
A dyadic function. The right argument is \$n\$, the left argument is \$B\$. Returns 0 if \$n\$ is \$B\$-powersmooth, 1 otherwise.
How it works
<[:>./2^/@p:] NB. left arg = B, right arg = n
2 p:] NB. Prime factorization of n,
NB. given as a 2-row matrix ...
9
C++, Not competing
After spending so long on the golfing side of this challenge, I was curious to see what I could do from a fastest-code perspective. Here is my C++ attempt, which should be able to run up to \$n=8\$ on every computer, and \$n=9\$ if you have enough RAM and patience. The approach is the same as my other answer, but optimized for speed ...
9
J, 17 15 bytes
1#.0&(]|.##\)&2
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-2 thanks to FrownyFrog!
On TIO, handles up to the 11th term 6837625106787 (where term 1 is 2).
how
J's "Copy" verb # is tailor made for this challenge:
1 2 3 # 'abc'
abbccc
The rest is just mechanics needed to reverse and iterate:
0&(...)&2 Iterate ... as many times as the input. ...
9
Wolfram Language (Mathematica), 37 33 bytes
d[#/d[0#-9]]~d~#2&
d=Fold[9#+##&]
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Input two lists of digits.
Fold[9#+##&] is longer than FromDigits, but has more flexibility with its input.
9
R, 98 95 89 88 bytes
-6 bytes thanks to Giuseppe
function(x,y=abs(scan(t=x)))cat("-"[!!sd(grepl("-",x))],c(z<-y[1]/y[2],!!y)[1+is.na(z)])
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Expects a vector of strings, as R cannot handle signed 0. Infinity will be input and output as Inf.
x contains the input as 2 strings, and y is the conversion to numeric in absolute ...
8
M, 7 6 bytes
cRİS‘İ
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M is Jelly's more mathematical (and out-of-date) sibling. While Jelly uses floating point maths, M uses rational numbers where possible.
Similarly to J42161217's Mathematica answer, we use the binomial coefficient. This calculates the exact value of
$$1 \div \left(1 + \sum ^n _{k=1} \frac 1 {\binom n k}\right)$$
How it ...
8
JavaScript (ES6), 72 68 67 bytes
Expects (max_denominator)(seq). Returns [numerator, denominator].
m=>g=([v,...a],n=0,d=1,N=1,D=0)=>(d+=D*v)<=m?g(a,N,D,N*v+n,d):[N,D]
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Commented
m => // outer function taking m = maximum denominator
g = ( // inner recursive function taking:
[v, // v = next ...
8
Husk, 10 bytes
►ȯLU¡oΠd↔ŀ
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Explanation
►ȯLU¡oΠd↔ŀ
↔ŀ reverse the range 0..n-1
►ȯ max-by, returning the last maximal element for the following:
¡o create an infinite list using:
Πd product of digits.
U longest unique prefix
L take its length
7
Factor + math.combinatorics math.unicode, 45 43 bytes
[ dup [0,b] [ nCk -1 ^ ] with map Σ -1 ^ ]
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This uses the formula graciously offered in the following M answer.
Edit: use -1 ^ instead of recip since it's 1 byte shorter.
Explanation:
It's a quotation (anonymous function) that takes an (0-indexed) integer as input and returns a number (...
7
Regex (ECMAScript), 61 bytes
^(?=(|x*)\1*(?=\1\b)(?!(((x+)x+)(?=\3+,)\3*\4)\2+,)(x*)).*,\5
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Takes \$n\$ and \$B\$ from input in unary as strings of xs whose length represents the number, separated by a ,.
Uses my prime power regex, and the same expression for cycling through divisors of N from largest to smallest as used in this problem.
# ...
7
JavaScript (Node.js), 63 bytes
f=(a,t=1)=>a.some(v=>t%v[1])?f(a,1+t):a.map(([p,q])=>[p*t/q,t])
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JavaScript (Node.js), 63 bytes
f=(a,t,b=a.map(([p,q])=>[m=p*t/q,o&=m%1||t],o=t))=>o?b:f(a,-~t)
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m=p*t/q cannot be changed to p*=t/q due to floating point errors. For example, 11*15/11 is 15, but 11*(15/11) is 14....
7
Vyxal, 15 bytes
L⁾₁I*₁L⁾⨪/₂I$-ƒ
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I spent roughly an hour on this, trying to arrange it to work properly. Took me a few re-reads of the specs, but I got there in the end.
Input taken as:
y
x
where y and x are strings (done by surrounding them with ""s), and if y isn't provided, [] is used.
Explained
L⁾₁I*₁L⁾⨪/₂I$-ƒ
L⁾ # ...
7
R, 118 116 108 103 98 92 bytes
function(x,y,`+`=nchar,B=10^+x-1,A=el(max(y,0):0)*B-x*10^+y,q=1:x)c(A,B)/max(q[!A%%q&!B%%q])
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Takes first input as integer and second as string (empty if no \$y\$).
GCD implementation borrowed from here: https://codegolf.stackexchange.com/a/48845/55372
-8 bytes thanks to @Kirill & @Dominic;
-5 and ...
7
R, 114 110 109 107 104 bytes
Edit: -4 and then -2 more bytes thanks to Giuseppe's comments on pajonk's answer, and then -3 bytes after copying a trick from Robin Ryder's answer here
function(s,z=10^nchar(s)-1:0,n=scan(t=pmax(s,0)),a=c(diff(n*z[2:1]),z[1]),c=1:z)a/max(c[!a%%c&!a[2]%%c])
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Input is a vector of two strings representing x and ...
7
Scratch, 310 bytes
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In scratchblocks4:
when gf clicked
ask()and wait
set[N v]to(answer
ask()and wait
set[D v]to(answer
set[Q v]to((N)/(D
if<(Q)=[NaN]>then
if<(A)contains(0)?>then
set[Q v]to(0
else
set[Q v]to(1
end
end
if<<(join(N)(D))contains(-)?>and<not<<(N)contains(-)?>and<(D)contains(-)?>>>>...
6
Factor + math.primes math.unicode, 38 33 bytes
[ dup length nprimes swap v^ Π ]
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Explanation:
dup duplicate the input (e.g.) { 0 1 2 3 } { 0 1 2 3 }
length find the length of a sequence { 0 1 2 3 } 4
nprimes generate primes given the number on top of the data stack { 0 1 2 3 } { 2 3 5 7 }
swap swap the top two objects on the data stack { 2 3 ...
6
Brachylog, 30 bytes
{s{h∧1|~cṪ↺₁hʰb=h↰ᶠ⌉+₁}ᵘ}ᶠcọtᵐ
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{s … }ᶠ for every substring:
{h∧1| …} on every non-empty string, return 1. Also try …
~c input split into groups, so that …
Ṫ↺₁…b= it unifies with [A,B,A] (this works, too, but is sadly longer).
hʰ B is non-empty
h↰ᶠ take A and call the predicate recursively, finding all results
⌉+₁ get the ...
6
05AB1E, 10 bytes
ÝD¦âΣ`/α}¬
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Explanation
Ý # [0 .. input]
D # Duplicate
¦ # Tail -> [1 .. input]
â # Cartesian product
Σ } # Sort by
α # Absolute difference between
# Input 2
`/ # and numerator / denominator
¬ # Head
6
APL (Dyalog Unicode), 41 bytes
(|40+⎕)+.×(|÷≢)1-1.8*1(-,+)⍨⍣(⎕-2)⊢1-3|⍳4
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A full program. Takes the number of people, then the initial temperature. TIO version is wrapped in a function for easier testing. As I pointed out in a comment, the initial and final units do not matter as long as they are equal.
The math
The code exploits the fact ...
6
J, 39 32 30 27 bytes
{.@".@]-".@[*(%<:)~&(10x^#)
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-5 thanks to Bubbler. Also go upvote his j answer, which is more creative and has delightful application of base #.
The wikipedia formula translated into J. The only part that might be of some interest is the calculation of z/w:
(%&x:<:)~&(10^#)
&(1>.10^#) ...
6
JavaScript (ES7), 80 76 bytes
Expects (x)(y) as strings (y may be an empty string) and returns [numerator, denominator].
x=>y=>(G=(a,b)=>b?G(b,a%b):[p/a,q/a])(q=1-10**x.length,p=y*q+x*10**y.length)
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Commented
x => // outer function taking x
y => // inner function taking y
( G = (a,...
Only top voted, non community-wiki answers of a minimum length are eligible
