Extract and Divide

Question

Challenge

For a given positive integer \$n\$:

Repeat the following until \$n < 10\$ (until \$n\$ contains one digit).
Extract the last digit.
If the extracted digit is even (including 0) multiply the rest of the integer by \$2\$ and add \$1\$ ( \$2n+1\$ ). Then go back to step 1 else move to step 4.
Divide the rest of the integer with the extracted digit (integer / digit) and add the remainder (integer % digit), that is your new \$n\$.

Note: In case n < 10 at the very beginning obviously you don't move to step 2. Skip everything and print \$[n, 0]\$.

Input

n: Positive integer.

Output

[o, r]: o: the last n, r: number of repeats.

Step-by-step example

For input n = 61407:

Repeat 1: 6140_7 -> 6140 / 7 = 877, 6140 % 7 = 1 => 877  + 1 = 878
Repeat 2: 87_8   -> 2 * 87 + 1 = 175 (even digit)
Repeat 3: 17_5   -> 17   / 5 = 3,   17   % 5 = 2 => 3    + 2 = 5 ( < 10, we are done )

The output is [5, 3] (last n is 5 and 3 steps repeats).

Rules

There are really no rules or restrictions just assume n > 0. You can either print or return the output.

I'm pretty sure that most answers from here can be trivially modified to answer this question. — Don Thousand, Sep 1 '18 at 16:00
@Arnauld No, the output needs to be two numbers (returned or printed). I guess you could convert the decimal number to string, replace . with whitespace and print it. — DimChtz, Sep 1 '18 at 16:06

duckmayr · Accepted Answer · 2018-09-01 19:28:04Z

6

R, 93 bytes

function(n,r=0,e=n%%10,d=(n-e)/10)"if"(n<10,c(n,r),"if"(e%%2,f(d%/%e+d%%e,r+1),f(d*2+1,r+1)))

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answered Sep 1 '18 at 19:28

duckmayr

4513 silver badges6 bronze badges

3

\$\begingroup\$ Save some bytes by getting rid of second "if", reversing n<10 condition and using %/% in d definition : TIO \$\endgroup\$
– Kirill L.
Sep 1 '18 at 20:24
\$\begingroup\$ agree with @KirillL. . Also unfortunately f= needs to be included in the bytecount since the function is called recursively. \$\endgroup\$
– JayCe
Sep 13 '18 at 17:03

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Mr. Xcoder · Accepted Answer · 2018-09-02 21:19:16Z

4

Python 2, 78 77 76 73 bytes

Recursive version. Saved 3 bytes thanks to Jonathan Frech.

f=lambda n,r=0:n>9and f(n%2*sum(divmod(n/10,n%10))or n/10*2+1,-~r)or[n,r]

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74 bytes

Full program.

n,i=input(),0
while n>9:i+=1;r,R=n/10,n%10;n=[r-~r,r/R+r%R][R&1]
print n,i

Try it online!

edited Sep 2 '18 at 21:19

answered Sep 1 '18 at 16:20

Mr. Xcoder

41.1k9 gold badges73 silver badges212 bronze badges

1

\$\begingroup\$ Since 2 divides 10, is n%10%2 not equivalent to n%2? \$\endgroup\$
– Jonathan Frech
Sep 1 '18 at 23:47
1

\$\begingroup\$ Great point by @JonathanFrech that will get you to 73 bytes. I think the following form would also work, and is also 73 bytes: def g(n,r=0):u,v=n/10,n%10;return u and g([u-~u,u/v+u%v][v&1],r+1)or(n,r) \$\endgroup\$
– mathmandan
Sep 2 '18 at 21:16
\$\begingroup\$ Somehow Jonathan's message did not appear in my inbox... Indeed, you're right, editing ASAP. \$\endgroup\$
– Mr. Xcoder
Sep 2 '18 at 21:17

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Community · Accepted Answer · 2020-06-17 09:04:33Z

JavaScript (ES6), 62 59 bytes

f=(n,r=0)=>(x=n/10|0)?f((n%=10)&1?x/n+x%n|0:x-~x,r+1):[n,r]

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Commented

f = (n, r = 0) =>         // n = input, r = number of iterations
  (x = n / 10 | 0) ?      // x = floor(n / 10); if x is not equal to 0:
    f(                    //   do a recursive call:
      (n %= 10) & 1 ?     //     n = last digit; if odd:
        x / n + x % n | 0 //       use quotient + remainder of x / n
      :                   //     else:
        x - ~x,           //       use x - (-x - 1) = x + x + 1 = 2x + 1
      r + 1               //     increment the number of iterations
    )                     //   end of recursive call
  :                       // else:
    [n, r]                //   return [ final_result, iterations ]

Okx · Accepted Answer · 2018-09-01 17:37:19Z

05AB1E (legacy), 19 bytes

[DgD–#ÁćDÈi\·>ë‰O]?

Explanation:

[                     Start infinite loop
 DgD                  Get the length
    –#                If it's 1, print the loop index and break.
      ÁćD             Extract: "hello" -> "hell", "o"
         Èi           if even,
           \·>        Double and increment
              ë       else,
               ‰O     Divmod, and sum the result (div and mod).
                 ]    End if statement & infinite loop
                  ?   Print

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Rustem B. · Accepted Answer · 2018-09-01 21:33:29Z

3

Julia 1.0, 81 80 79 bytes

function d(n,c=0)l,r=n÷10,n%10;n>9 ? d(r%2<1 ? 2l+1 : l÷r+l%r,c+1) : [n,c]end

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-1 (thanks Mr. Xcoder)

edited Sep 1 '18 at 21:33

answered Sep 1 '18 at 19:09

Rustem B.

513 bronze badges

\$\begingroup\$ Whis is my first golfcode :) \$\endgroup\$
– Rustem B.
Sep 1 '18 at 19:11
\$\begingroup\$ Welcome to PPCG! \$\endgroup\$
– Giuseppe
Sep 1 '18 at 19:45
\$\begingroup\$ @Giuseppe thanks \$\endgroup\$
– Rustem B.
Sep 1 '18 at 19:49
1

\$\begingroup\$ Save a byte using <1 rather than ==0. \$\endgroup\$
– Mr. Xcoder
Sep 1 '18 at 20:50

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Kirill L. · Accepted Answer · 2018-09-01 18:21:20Z

2

Ruby, 61 bytes

f=->n,r=0{n>9?(a=n%10;n/=10;f[a%2<1?n-~n:n/a+n%a,r+1]):[n,r]}

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edited Sep 1 '18 at 18:21

answered Sep 1 '18 at 18:10

Kirill L.

11.1k2 gold badges11 silver badges39 bronze badges

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Neil · Accepted Answer · 2018-09-01 20:50:59Z

Retina, 79 bytes

(\d+)[02468]$
;$.(_2*$1*
(\d+)(.)
$2*_;$1*
}`(_+);(\1)*(_*)
;$.($3$#2*
^;*
$.&;

Try it online! Explanation:

(\d+)[02468]$
;$.(_2*$1*

If the last digit is even, multiply the rest of the integer by 2 and add 1. This always results in an odd number, so we don't need to repeat this.

(\d+)(.)
$2*_;$1*

Split off the last digit and convert to unary for the divmod.

}`(_+);(\1)*(_*)
;$.($3$#2*

Divide the rest of the integer by the last digit and add the remainder. Then repeat the whole program until there's only one digit left.

^;*
$.&;

Count the number of operations performed.

nwellnhof · Accepted Answer · 2018-09-01 22:44:09Z

2

Perl 6, 61 bytes

{tail kv $_,{$1%2??$0/$1+$0%$1+|0!!$0*2+1}...{!/(.+)(.)/}: 2}

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Returns (r, o).

edited Sep 1 '18 at 22:44

answered Sep 1 '18 at 22:01

nwellnhof

10.4k1 gold badge16 silver badges37 bronze badges

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Kroppeb · Accepted Answer · 2018-09-02 09:10:03Z

2

Brachylog, 43 bytes

Feels messy and bad but here it is anyway

;0{hl1&|⟨{h⟨k{t%₂0&h×₂+₁|⟨÷+%⟩}t⟩}↰₁{t+₁}⟩}

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answered Sep 2 '18 at 9:10

Kroppeb

1,6186 silver badges11 bronze badges

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seadoggie01 · Accepted Answer · 2018-09-02 23:42:17Z

VBA (Excel), ~~145?, 142, 139,~~ 123 bytes

Condensed Form:

Sub t(n)
While n>10
e=Right(n, 1)
n=Left(n,Len(n)-1)
If e Mod 2=0Then n=n*2+1 Else n=Int(n/e)+n Mod e
c=c+1
wend
Debug.?n;c
End Sub

Expanded (with comments)

Sub test(n) 'For a given positive integer n
    'Repeat the following until n<10
    While n > 10
        'Extract the last digit
        e = Right(n, 1)
        'Remove the last digit
        n = Left(n, Len(n) - 1)
        'If the extracted digit is even...
        If e Mod 2 = 0 Then
            'Multiply the rest of the integer by 2 and add 1
            n = n * 2 + 1
        Else
            'Divide the rest of the integer with the extracted digit and add the remainder
            n = Int(n / e) + n Mod e
        End If
        'Keep count
        c = c + 1
    'End the Loop
    Wend
    'Give the output
    Debug.Print (n ; c)
End Sub

(Do excuse me, as this is my first post. I will happily edit! Right now, it looks like to test it you open the Immediate Window and type 't n' where n is your number to test :D)

If you use an inline if statement ( IIf(..) ), integer division (\ ), and change the n>10 to n>9, then you can get this down to an immediate window function worth 97 bytes. n=[A1]:While n>9:e=Right(n,1):n=Left(n,Len(n)-1):n=IIf(e/2=e\2,n*2+1,n\e+n Mod e):c=c+1:Wend:?n;c — Taylor Raine, Feb 15 '19 at 19:28

paper1111 · Accepted Answer · 2018-09-04 12:27:14Z

2

Swift 4, 112 104 100 93 bytes

var n=Int(readLine()!)!,r=0,p=n%10;while n>9{n=[n/10*2+1,n/10/p+n/10%p][n%2];r+=1};print(n,r)

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Prints n r

-7 (Thanks to Mr. Xcoder)

edited Sep 4 '18 at 12:27

answered Sep 2 '18 at 7:52

paper1111

1214 bronze badges

\$\begingroup\$ Very nice first answer (+1)! var n=Int(readLine()!)!,r=0,p=n%10;while n>9{n=[n/10*2+1,n/10/p+n/10%p][n%2];r+=1};print(n,r) should save you 7 bytes (golfing the conditional). \$\endgroup\$
– Mr. Xcoder
Sep 3 '18 at 12:24

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Erik the Outgolfer · Accepted Answer · 2018-09-01 21:08:49Z

1

Jelly, 19 bytes

dd/Sɗ:Ḥ‘ɗḂ?Ƭ⁵ṖṖṪ,LƊ

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answered Sep 1 '18 at 21:08

Erik the Outgolfer

39.5k5 gold badges36 silver badges118 bronze badges

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score 1 · Accepted Answer · 2018-09-02 06:56:37Z

1

Common Lisp, 145 bytes

A function which takes the n provided and returns the list (n r). Lisp syntax is fun.

(defun f(n &optional(r 0))(if(< n 10)`(,n,r)(let((h(floor n 10))(l(mod n 10)))(if(evenp l)(f(1+(* 2 h))(1+ r))(f(+(mod h l)(floor h l))(1+ r)))))

edited Sep 2 '18 at 6:56

answered Sep 2 '18 at 6:50

user82200

1

\$\begingroup\$ Welcome to the site =D \$\endgroup\$
– Luis felipe De jesus Munoz
Sep 2 '18 at 12:48
\$\begingroup\$ Thankyou very much, Luis. \$\endgroup\$
– user82200
Sep 3 '18 at 8:46

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nimi · Accepted Answer · 2018-09-02 20:48:42Z

1

Haskell, 78 bytes

f n|n<10=(n,0)|(d,m)<-divMod n 10=(1+)<$>f(last$2*d+1:[div d m+mod d m|odd n])

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answered Sep 2 '18 at 20:48

nimi

35k3 gold badges30 silver badges94 bronze badges

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user5434231 · Accepted Answer · 2018-09-03 03:24:47Z

8086 machine code, 35 bytes

00000000  31 c9 31 d2 bb 0a 00 f7  f3 85 c0 74 14 f6 c2 01  |1.1........t....|
00000010  75 05 d1 e0 40 e2 eb 89  d3 88 f2 f7 f3 01 d0 e2  |u...@...........|
00000020  e1 f7 d9                                          |...|
00000023

Input: AX = n
Output: DX = o, CX = r

Assembled from:

        xor cx, cx
next:   xor dx, dx
        mov bx, 10
        div bx
        test ax, ax
        jz done
        test dl, 1
        jnz odd
        shl ax, 1
        inc ax
        loop next
odd:    mov bx, dx
        mov dl, dh
        div bx
        add ax, dx
        loop next
done:   neg cx

Galen Ivanov · Accepted Answer · 2018-09-04 09:13:37Z

1

Red, 131 bytes

func[n][s: 0 while[n > 9][r: do form take/last t: form n t: do t
n: either r % 2 = 1[t / r +(t % r)][2 * t + 1]s: s + 1]print[n s]]

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Extract and Divide

Challenge

Input

Output

Step-by-step example

Rules

16 Answers 16

R, 93 bytes

Python 2, 78 77 76 73 bytes

74 bytes

JavaScript (ES6), 62 59 bytes

Commented

05AB1E (legacy), 19 bytes

Julia 1.0, 81 80 79 bytes

Ruby, 61 bytes

Retina, 79 bytes

Perl 6, 61 bytes

Brachylog, 43 bytes

Swift 4, 112 104 100 93 bytes

Jelly, 19 bytes

Common Lisp, 145 bytes

Haskell, 78 bytes

8086 machine code, 35 bytes

Red, 131 bytes

More readable:

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Extract and Divide

Challenge

Input

Output

Step-by-step example

Rules

16 Answers 16

R, 93 bytes

Python 2, 78 77 76 73 bytes

74 bytes

JavaScript (ES6), 62 59 bytes

Commented

05AB1E (legacy), 19 bytes

Julia 1.0, 81 80 79 bytes

Ruby, 61 bytes

Retina, 79 bytes

Perl 6, 61 bytes

Brachylog, 43 bytes

Swift 4, 112 104 100 93 bytes

Jelly, 19 bytes

Common Lisp, 145 bytes

Haskell, 78 bytes

8086 machine code, 35 bytes

Red, 131 bytes

More readable:

Your Answer

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