Un numero undulant è un numero in cui le sue cifre si alternano tra su e giù come il seguente numero: 461902 o 708143, o anche 1010101, ma non 123, perché 2 <3.

Scrivere un programma o una funzione che restituisce un valore truthy se un numero è ondulante , e un valore falsy altrimenti. Vince il codice più corto.

Nota : i numeri a una cifra sono un input valido ma non sono considerati udulanti , quindi isUndulantrestituiscono false per n <10.

J, 45

*./(n>9),(}:(=-)}.)(}:*@-}.)n#:~10$~>.10^.n=.

Esempio di utilizzo:

   *./(n>9),(}:(=-)}.)(}:*@-}.)n#:~10$~>.10^.n=. 461902
1
   *./(n>9),(}:(=-)}.)(}:*@-}.)n#:~10$~>.10^.n=. 708143
1
   *./(n>9),(}:(=-)}.)(}:*@-}.)n#:~10$~>.10^.n=. 1010101
1
   *./(n>9),(}:(=-)}.)(}:*@-}.)n#:~10$~>.10^.n=. 123
0
   *./(n>9),(}:(=-)}.)(}:*@-}.)n#:~10$~>.10^.n=. 5
0

Sono abbastanza sicuro che ci sia un modo migliore per torcere Insert /per fare più lavoro in un colpo solo, ma sono stato J-less per mesi, ho bisogno di tornare su di esso.

Rubino, 72 70 caratteri

Q=10;k=->n,v{(n%Q-n/Q%Q)*v<0?k[n/Q,-v]:n<Q};u=->n{n>9&&k[n,-1]|k[n,1]}

Utilizzo e test:

p u[10101]   # <= true
p u[708143]  # <= true
p u[2421]    # <= false
p u[1231]    # <= false
p u[873]     # <= false

Le cifre singole producono false :

p u[5]       # <= false

Anche le cifre identiche consecutive restituiscono false :

p u[66]      # <= false
p u[1221]    # <= false

J, 30 byte

*/0<(#,]*{.*1 _1$~#)2-/\a.i.":

Un approccio diverso rispetto all'altro J risponde.

   * / 0 <(#,] * {. * 1 _1 $ ~ #) 2 - / \ ai ": 461902
1
   * / 0 <(#,] * {. * 1 _1 $ ~ #) 2 - / \ ai ": 708143
1
   * / 0 <(#,] * {. * 1 _1 $ ~ #) 2 - / \ ai ": 1010101
1
   * / 0 <(#,] * {. * 1 _1 $ ~ #) 2 - / \ ai ": 123
0
   * / 0 <(#,] * {. * 1 _1 $ ~ #) (} .-} :) ai ": 5
0

Sarebbe più corto di 3 caratteri se 5 fossero considerati undulant.

(pdf) eTeX, 129 caratteri

\def\a#1#2{\if#2?\ifx\r\s\def\s{1}\else
True\end\fi\fi\edef\t{\pdfstrcmp{#2}{#1}}\ifx\s\t
False\end\fi\let\s\t\a#2}\expandafter\a

La compilazione con pdfetex filename.tex 1324?genera un output pdf. TeX è principalmente un linguaggio di composizione, e invece lo stdout invece richiederebbe circa 20 caratteri in più. Anche lo strano requisito per i numeri a una cifra (falso anziché vero) mi porta 26 caratteri.

Haskell, 88 77 73 65 caratteri

z=tail>>=zipWith compare
q[]=0>1
q s=all(/=EQ)$s++z s
u=q.z.show

Ciò richiede il pragma lingua comunemente utilizzata (o -Xbandiera): NoMonomorphismRestriction. Se non lo ammetti, dobbiamo aggiungere 4 caratteri e definire zcosì:

z s=zipWith compare s$tail s

Sage, 83 76 byte

f=lambda x:uniq(cmp(*`x`[i-2:i][::(-1)^i])for i in[2..len(`x`)])in[[1],[-1]]

Ho avuto l'idea di usare cmp (* [..]) da JBernardo. In Sage, uniq(...)è un alias per list(set(...)).

Modifica: uniq(cmp(...)) == []ho appena notato che per x <10 , che non è attivo [[1],[-1]]. Se x fosse inserito come stringa, anziché come numero intero, potrei ottenere altri 4 caratteri!

Python: 101 100 caratteri

Prima della minificazione:

undulate = (lambda n: n > 9
            and all(cmp(*digits) == (i % 2) * 2 - 1
                    for i, digits
                    in enumerate(zip(min(`n`,`n`[1:]), 
                                     max(`n`,`n`[1:])))))

Dopo la minificazione:

a=lambda b:b>9and all(cmp(*c)==d%2*2-1 for d,c in enumerate(zip(min(`b`,`b`[1:]),max(`b`,`b`[1:]))))

Python, 134 129 caratteri

def f(x):d=[cmp(*i)for i in zip(`x`,`x`[1:])]if x>9 else[0];n=d[0]>0;return all(i<0 for i in d[n::2])&all(i>0 for i in d[n<1::2])

Ungolfed:

def f(x):
    if x>9:
        d = [cmp(*i)for i in zip(`x`,`x`[1:])] #difference of x[i] and x[i+1]
    else:
        d = [0]       #trick to return False if x<10 using less chars
    n = d[0]>0        #First digit is -1 or 1?
    neg = d[n::2]     #negative numbers if x is Undulant
    pos = d[not n::2] #positive numbers if x is Undulant

    #check if all negs are -1 and all pos are 1 and return value
    return all(i<0 for i in neg) and all(i>0 for i in pos)

JavaScript, 88 caratteri

function _(i){i+='';c=i[0];f=i[a=x=1];for(g=f<c;d=i[x++];c=d)g^=a&=g?d<c:d>c;return!f^a}

In sostanza, trasforma il numero in una stringa e confronta i caratteri adiacenti, ribaltando l'aspettativa per ciascuno.

K, 41 byte

{(x>9)&~max(=). 1_'-':'1_'(<':;>':)@\:$x}

Per esempio

{(x>9)&~max(=). 1_'-':'1_'(<':;>':)@\:$x}1212130659
1b

CoffeeScript, 98 67 53 byte

(n)->0!in((n[i]>=c^(n[0]<n[1])+i)%2for c,i in n[1..])

test:

[
    '01010101' # true
    '12345'    # false
    '1010101'  # true
    '887685'   # false
    '9120734'  # true
    '090909'   # true
]

Non compresso:

undulant = (n) ->
    direction = n[0] < n[1]
    return n.split('').every (cur, i) ->
        prev = arr[i-1] or 10 * direction
        +(prev >= cur) is (direction+i)%2

J, 44 39 36 31 byte

*/2(0<#@],0>*/\)*2-/\".;' ',.":

Utilizzo come prima.

Non avevo notato che la mia ultima modifica ha reso completamente inutile la disuguaglianza con 0 check. :-)

Risposta precedente (+ spiegazione):

(0=+/2=/\u)*(1<#u)**/2~:/\2<:/\u=.".;' ',.":

Uso:

    (0=+/2=/\u)*(1<#u)**/2~:/\2<:/\u=.".;' ',.":461902
1

La risposta ha quattro parti:

1. u=.".;' ',.": Questo legge il numero come una stringa ":, lo divide in un elenco di caratteri preceduto da spazi ' ',., lo ricucisce ;, lo converte in numeri ".e quindi memorizza il risultato. u=.Questo fondamentalmente trasforma 461902 in 4 6 1 9 0 2 che trovo più facile elaborare in J.

2. */2~:/\2<:/\ Questo funziona sul valore memorizzato in u. Prende ogni coppia di caratteri e verifica se quella sinistra è inferiore o uguale a quella destra, 2<:/\quindi 4 6 1 9 0 2 diventa 1 0 1 0 1. Quindi prende il risultato di questo e controlla ogni coppia di numeri per la disuguaglianza 2~:/\così 1 0 1 0 1 diventa 1 1 1 1. Alla fine li moltiplica tutti insieme per ottenere uno 0 o un 1 */A questo punto potremmo restituire la risposta se non fosse per 2 cose: una singola cifra restituisce 1 quando il la domanda richiede uno 0; e numeri uguali sono trattati come 'meno di', quindi 461900 restituisce 1 invece di 0. Peccato. Andiamo ...

3. (1<#u) Verifica se il numero di elementi memorizzati in u #uè maggiore di 1 e restituisce false se si tratta di un solo numero a una cifra.

4. (0=+/2=/\u) Questo prende ogni coppia di numeri memorizzati in u e verifica l'uguaglianza 2=/\u. Quindi somma le risposte e controlla se ha 0.

I risultati delle parti 2, 3 e 4 vengono quindi moltiplicati insieme per (si spera) produrre un 1 quando il numero soddisfa i requisiti specificati nella domanda.

Haskell, 82 byte

c=cycle[(<),(>)]
l!n=n>9&&and(zipWith3($)l(show n)$tail$show n)
u n=c!n||((>):c)!n

Provalo online!

Python, 119 108 byte

def u(x):l=[cmp(i,j)for i,j in zip(`x`,`x`[1:])];print x>9and all([i*j<0 for i,j in zip(l,l[1:])])and l!=[0]

Python, 155 chars

g=lambda a,b:all(x>y for x,y in zip(a,b))
u=lambda D:g(D[::2],D[1::2])&g(D[2::2],D[1::2])
def U(n):D=map(int,str(n));return(n>9)&(u(D)|u([-d for d in D]))

C++, 94 chars

bool u(int N){int K,P,Q,U=1,D=1;while(N>9)P=N%10,Q=(N/=10)%10,K=D,D=U&Q<P,U=K&Q>P;return U^D;}

same method as my Erlang awnser with a for loop rather than recursion.

Python 105 101 100 chars

c=lambda r,t:len(r)<2 or(cmp(*r[:2])==t and c(r[1:],-t))
u=lambda x:x>9and c(`x`,cmp(*`x`[:2])or 1)

Recursive solution. c(r,t) checks if first char of r is less (t==-1) or greater (t==1) of second char, and call opposite check on shortened string.

Perl/re, 139 bytes

Doing everything in regex is kind of a bad idea.

/^(?:(.)(?{local$a=$1}))?(?:(?>((.)(?(?{$a lt$3})(?{local$a=$3})|(?!)))((.)(?(?{$a gt$5})(?{local$a=$5})|(?!))))*(?2)?)(?(?{pos>1})|(?!))$/

I'm using Perl 5.12 but I think this will work on Perl 5.10. Pretty sure 5.8 is out though.

for (qw(461902 708143 1010101 123 5)) {
    print "$_ is " . (/crazy regex goes here/ ? '' : 'not ') . "undulant\n";
}

461902 is undulant
708143 is undulant
1010101 is undulant
123 is not undulant
5 is not undulant

GolfScript, 48 bytes

[`..,(<\1>]zip{..$=\-1%.$=-}%(\{.@*0<*}/abs

Hoping to beat J, my first time using GolfScript. Didn't quite succeed.

JavaScript, 66 65 62 60 bytes

Takes input as a string, returns true for undulant numbers, an empty string (falsey) for single digit numbers and false otherwise.

([s,...a])=>a+a&&a.every(x=>eval(s+"<>"[++y%2]+x,s=x),y=s<a)

Try it

Run the Snippet below to test 0-9 and 25 random numbers <10,000,000.

f=
([s,...a])=>a+a&&a.every(x=>eval(s+"<>"[++y%2]+x,s=x),y=s<a)
tests=new Set([...Array(10).keys()])
while(tests.add(Math.random()*1e7|0).size<35);
o.innerText=[...tests].map(x=>(x=x+``).padStart(7)+` = `+JSON.stringify(f(x))).join`\n`

<pre id=o></pre>

Explanation

A few fun little tricks in this one so I think it warrants a rare explanation to a JS solution from me.

()=>

We start, simply, with an anonymous function which takes the integer string as an argument when called.

[s,...a]

That argument is immediately destructured into 2 parameters: s being the first character in the string and a being an array containing the remaining characters (e.g. "461902" becomes s="4" and a=["6","1","9","0","2"]).

a+a&&

First, we concatenate a with itself, which casts both occurrences to strings. If the input is a single digit number then a will be empty and, therefore, become and empty string; an empty string plus an empty string is still an empty string and, because that's falsey in JS, we stop processing at the logical AND and output our empty string. In all other cases a+a will be truthy and so we continue on to the next part of the function.

a.every(x=>)

We'll be checking if every element x in a returns true when passed through a function.

y=s<a

This determines what our first comparison will be (< or >) and then we'll alternate from there. We check if the string s is less than the array a, which gets cast to a string in the process so, if s is less than the first character in a, y will be true or false if it's not.

s+"<>"[++y%2]+x

We build a string with the current value of s at the beginning and x at the end. In between, we index into the string "<>" by incrementing y, casting its initial boolean value to an integer, and modulo by 2, giving us 0 or 1.

eval()

Eval that string.

s=x

Finally, we pass a second argument to eval, which it ignores, and use it to set the value of s to the current value of x for the next iteration.

PowerShell, 88

Naïve and trivial. I will golf later.

filter u{-join([char[]]"$_"|%{if($n){[Math]::Sign($n-$_)+1}$n=$_})-notmatch'1|22|00|^$'}

My test cases.

JavaScript, 112

function(n,d,l,c,f){while(l=n%10,n=n/10|0)d=n%10,c?c>0?d>=l?(f=0):(c=-c):d<=l?(f=0):(c=-c):(c=d-l,f=1);return f}

You only need to pass it one argument. I could probably golf this further with a for loop.

Erlang, 137 123 118 chars

u(N)->Q=N div 10,u(Q,N rem 10,Q>0,Q>0). u(0,_,D,U)->D or U;u(N,P,D,U)->Q=N rem 10,u(N div 10,Q,U and(Q<P),D and(Q>P)).

CJam, 30 bytes

CJam is newer than this challenge, so this does not compete for the green checkmark, but it's not a winner anyway (although I'm sure this can actually be golfed quite a bit).

l"_1=\+{_@-\}*;]"_8'*t+~{W>},!

Test it here.

How it works

Firstly, I'm doing some string manipulation (followed by eval) to save 5 bytes on duplicate code:

"..."_8'*t+~
"..."        "Push this string.":
     _       "Duplicate.";
      8'*t   "Replace the 8th character (the -) with *.";
          +~ "Concatenate the strings and evaluate.";

So in effect my code is

l_1=\+{_@-\}*;]_1=\+{_@*\}*;]{W>},!

First, here is how I deal with the weird special case of a single digit. I copy the digit at index 1 and prepend it to the number. We need to distinguish 3 cases:

• The first two digits are different, like 12..., then we get 212..., so the start is undulant, and won't affect whether the entire number is undulant.
• The first two digits are the same, like 11..., then we get 111.... Now the start is not undulant, but the number wasn't undulant anyway, so this won't affect the result either.
• If the number only has one digit, the digit at index 1 will be the first digit (because CJam's array indexing loops around the end), so this results in two identical digits, and the number is not undulant.

Now looking at the code in detail:

l_1=\+{_@-\}*;]_1=\+{_@*\}*;]{W>},!
l                                   "Read input.";
 _1=\+                              "Prepend second digit.";
      {_@-\}*                       "This fold gets the differences of consecutive elments.";
             ;]                     "Drop the final element and collect in an aray.";
               _1=\+                "Prepend second element.";
                    {_@*\}*         "This fold gets the products of consecutive elments.";
                           ;]       "Drop the final element and collect in an aray.";
                             {W>},  "Filter out non-negative numbers.";
                                  ! "Logical not.";

I'm sure there is a shorter way to actually check digits (of length greater 1) for whether they are undulant (in particular, without using two folds), but I couldn't find it yet.

Prolog 87 bytes

u(X) :- number_codes(X,C),f(C).
f([_,_]).
f([A,B,C|L]) :- (A<B,B>C;A>B,B<C),f([B,C|L]).

To run it, just save it as golf.pl, open a prolog interpreter (e.g. gprolog) in the same directory then do:

consult(golf).
u(101010).

It will give true if the number is undulant, otherwise just no.

Mathematica, 46 bytes

#!=Sort@#&&#!=Reverse@Sort@#&[IntegerDigits@n]

Examples (spaces are not required):

# != Sort@# && # != Reverse@Sort@# &[IntegerDigits@5]
# != Sort@# && # != Reverse@Sort@# &[IntegerDigits@123]
# != Sort@# && # != Reverse@Sort@# &[IntegerDigits@132]
# != Sort@# && # != Reverse@Sort@# &[IntegerDigits@321]

(*  out *)
False  False  True  False

Scala, 141 133 129 97 bytes

def u(n:Int):Boolean=n>9&&{
val a=n%10
val b=(n/10)%10
a!=b&&n<99||(a-b*b-(n/100)%10)<0&&u(n/10)}

With a = n % 10, b = (n/10) % 10, c = (n/100) % 10

if a > b and b < c or 
   a < b and b > c

Then a-b * b-c is either x*-y or -x*y with x and y as positive numbers, and the product is in both cases negative, but for -x*-y or x*y (a < b < c or a > b > c) the product is always positive.

The rest of the code is handling special cases: one digit, two digits, two identical digits.

Perl, 78 bytes

sub u{@_=split//,$_=shift;s/.(?=.)/($&cmp$_[$+[0]])+1/ge;chop;$#_&&!/00|1|22/}

Q, 71 bytes

{$[x>9;any all a=#[;(1 -1;-1 1)](#)a:1_signum(-':){"I"$x}each -3!x;0b]}

Sample usage:

q){$[x>9;any all a=#[;(1 -1;-1 1)](#)a:1_signum(-':){"I"$x}each -3!x;0b]} 5
0b
q){$[x>9;any all a=#[;(1 -1;-1 1)](#)a:1_signum(-':){"I"$x}each -3!x;0b]} 10101
1b
q){$[x>9;any all a=#[;(1 -1;-1 1)](#)a:1_signum(-':){"I"$x}each -3!x;0b]} 01010
1b
q){$[x>9;any all a=#[;(1 -1;-1 1)](#)a:1_signum(-':){"I"$x}each -3!x;0b]} 134679
0b
q){$[x>9;any all a=#[;(1 -1;-1 1)](#)a:1_signum(-':){"I"$x}each -3!x;0b]} 123456
0b
q){$[x>9;any all a=#[;(1 -1;-1 1)](#)a:1_signum(-':){"I"$x}each -3!x;0b]} 132436
1b

Julia 0.6, 62 bytes

f(x,a=sign.(diff(digits(x))))=x>9&&-a*a[1]==(-1).^(1:endof(a))

Takes in a number, returns true for Undulant, and false for not. Eg f(163) returns true.

f(x,a=sign.(diff(digits(x))))=x>9&&-a*a[1]==(-1).^(1:endof(a))
f(x,                        )                                   # function definition
    a=sign.(diff(digits(x)))                                    # default 2nd argument is array of differences of signs of digits
                              x>9&&                             # short circuiting and to catch cases under 10
                                   -a*a[1]                      # make the first element of a always -1
                                          ==(-1).^(1:endof(a))  # check that a is an array of alternating -1 and 1 of correct length

Try it online!