# Calculate ISBN-13 check digit

Write the shortest code that can calculate the check digit for an ISBN-13 from the first 12 digits.

Requirements:

• Must be a function that accepts a string
• Returns the full ISBN-13 as a string
• Uses the correct algorithm to calculate the digit (shown on the Wikipedia page)

Input
`978030640615`

Output
`9780306406157`

-
Are input and output supposed to contain dashes or only the digits? – sepp2k Feb 1 '11 at 19:57
Updated the description, the input and output are only the digits – Kevin Brown Feb 1 '11 at 20:06
Is outputting the full ISBN-13 acceptable as well? – Mr. Llama Mar 2 '12 at 19:43

## Golfscript - 25 chars

``````{...+(;2%+{+}*3-~10%`+}:f
``````

Whole program version is only 19 chars

``````...+(;2%+{+}*3-~10%
``````

Check back here for analysis later. Meanwhile check out my old uninspired answer

Golfscript - 32 chars

Similar to the luhn number calculation

``````{.{2+}%.(;2%{.+}%+{+}*~)10%`+}:f
``````

Analysis for 978030640615

``````{...}:f this is how you define the function in golfscript
.       store an extra copy of the input string
'978030640615' '978030640615'
{2+}%   add 2 to each ascii digit, so '0'=>50, I can get away with this instead
of {15&}% because we are doing mod 10 math on it later
'978030640615' [59 57 58 50 53 50 56 54 50 56 51 55]
.       duplicate that list
'978030640615' [59 57 58 50 53 50 56 54 50 56 51 55] [59 57 58 50 53 50 56 54 50 56 51 55]
(;      trim the first element off
'978030640615' [59 57 58 50 53 50 56 54 50 56 51 55] [57 58 50 53 50 56 54 50 56 51 55]
2%      select every second element
'978030640615' [59 57 58 50 53 50 56 54 50 56 51 55] [57 50 50 54 56 55]
{.+}%   double each element by adding to itself
'978030640615' [59 57 58 50 53 50 56 54 50 56 51 55] [114 100 100 108 112 110]
+       join the two lists together
'978030640615' [59 57 58 50 53 50 56 54 50 56 51 55 114 100 100 108 112 110]
{+}*    add up the items in the list
'978030640615' 1293
~       bitwise not
'978030640615' -1294
'978030640615' -1293
10%     mod 10
'978030640615' 7
`       convert to str
'978030640615' '7'
+       join the strings
'9780306406157'
``````
-
After running the code through an interpreter, I think you can save some characters (in your 32 character Luhn-based solution) by getting rid of the first `{` and the last three characters; `}:f`. I wonder if the same thing can be done for the first solution... – Rob Oct 1 '12 at 11:45
@MikeDtrick, those characters are how GS defines a function. The 19 char version does what you suggest, but the question asked for a "function" – gnibbler Oct 2 '12 at 3:45
Oh okay, thank you for the explanation. – Rob Oct 2 '12 at 21:40

## Python - 44 chars

``````f=lambda s:s+`-sum(map(int,s+s[1::2]*2))%10`
``````

Python - 53 chars

``````def f(s):d=map(int,s);return s+`-sum(d+d[1::2]*2)%10`
``````
-
I think f('9780306406159') outputs '97803064061598' instead of '9780306406157' – Eelvex Feb 2 '11 at 19:31
@Eelvex, the input string should always be 12 digits – gnibbler Feb 2 '11 at 20:47
Ah, somehow '9' sneaked in. Sorry... – Eelvex Feb 2 '11 at 21:19

## APL (27 characters)

``````F←{⍵,⍕10|10-(12⍴1 3)+.×⍎¨⍵}
``````

I'm using Dyalog APL as my interpreter. Here's a quick explanation, mostly from right to left (within the function definition, `F←{ ... }`):

• `⍎¨⍵`: Execute/evaluate (`⍎`) each (`¨`) character given in the right argument (`⍵`).
• `(12⍴1 3)`: Reshape (`⍴`) the vector `1 3` into a `12`-element vector (repeating to fill the gaps).
• `+.×`: Take the dot product (`+.×`) of its left argument (`(12⍴1 3)`) and its right argument (`⍎¨⍵`).
• `10-`: Subtract from 10.
• `10|`: Find the remainder after division by `10`.
• `⍕`: Format the number (i.e., give a character representation).
• `⍵,`: Append (`,`) our calculated digit to the right argument.
-
Thanks for the explanation! – Felix Dombek Oct 2 '12 at 1:34

``````i s=s++show(sum[-read[c]*m|c<-s|m<-cycle[1,3]]`mod`10)
``````

This requires support for parallel list comprehensions, which is supported by GHC (with the `-XParallelListComp` flag) and Hugs (with the `-98` flag).

-

## PHP - 8685 82 chars

``````function c(\$i){for(\$a=\$s=0;\$a<12;)\$s+=\$i[\$a]*(\$a++%2?3:1);return\$i.(10-\$s%10)%10;}
``````

Re-format and explanation:

``````function c(\$i){                     // function c, \$i is the input

for(\$a=\$s=0;\$a<12;)             // for loop x12 - both \$a and \$s equal 0
// notice there is no incrementation and
// no curly braces as there is just one
// command to loop through

\$s+=\$i[\$a]*(\$a++%2?3:1);    // \$s (sum) is being incremented by
// \$ath character of \$i (auto-casted to
// int) multiplied by 3 or 1, depending
// wheter \$a is even or not (%2 results
// either 1 or 0, but 0 == FALSE)
// \$a is incremented here, using the
// post-incrementation - which means that
// it is incremented, but AFTER the value
// is returned

return\$i.(10-\$s%10)%10;         // returns \$i with the check digit
// attached - first it is %'d by 10,
// then the result is subtracted from
// 10 and finally %'d by 10 again (which
// effectively just replaces 10 with 0)
// % has higher priority than -, so there
// are no parentheses around \$s%10
}
``````
-
Exactly the approach I took in my C# answer. Seems PHP is ~9 characters more efficient! – Nellius Feb 2 '11 at 0:15

``````i s=s++(show\$mod(2-sum(zipWith(*)(cycle[1,3])(map fromEnum s)))10)
``````
-

## Ruby - 73 65 chars

``````f=->s{s+((2-(s+s.gsub(/.(.)/,'\1')*2).bytes.inject(:+))%10).to_s}
``````
-
`"\\1"` -> `'\1'`? – Nemo157 Feb 1 '11 at 22:42
@Nemo, thanks, my ruby is a bit rusty – gnibbler Feb 1 '11 at 23:24
Use Ruby 1.9 syntax `f=->s{...}`. Save 6 chars. Also write `s<<(...).to_s`instead of adding 48 and use `Fixnum#chr`. – Łukasz Niemier Mar 10 '12 at 16:58

C# (94 characters)

``````string I(string i){int s=0,j=0;for(;j<12;)s+=(i[j]-48)*(j++%2<1?1:3);return i+((10-s%10)%10);}
``````

``````string I(string i)
{
int s = 0, j = 0;
for (; j < 12; )
s += (i[j] - 48) * (j++ % 2 < 1 ? 1 : 3);
return i + ((10 - s % 10) % 10);
}
``````

Tested on several ISBNs from books on my shelf, so I know it's working!

-

## Perl, 53 chars

``````sub i{\$_=shift;s/(.)(.)/\$s+=\$1+\$2*3/ge;\$_.(10-\$s)%10}
``````
-

## Windows PowerShell, 57

``````filter i{\$_+(990-(\$_-replace'(.)(.)','+\$1+3*\$2'|iex))%10}
``````
-
Side note to the person suggesting an edit: Comment the next time please because I golf better than you ;-) – Joey Jun 1 '13 at 21:54

## Ruby - 80 characters

``````def f s;s+(10-s.bytes.zip([1,3]*6).map{|j,k|(j-48)*k}.inject(:+)%10).to_s[0];end
``````
-

Python - 91, 89

``````0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
|         |         |         |         |         |         |         |         |         |
def c(i):return i+`(10-(sum(int(x)*3for x in i[1::2])+sum(int(x)for x in i[::2]))%10)%10`
``````
-
Spaces are optional between the first argument and `for` (and `in` and the third) in a list comprehension so long as it can be split up by the parser (not using a variable name). -2 chars there. – Nick T Feb 3 '11 at 3:03
@Nick T, fixed. Thanks. – grokus Feb 3 '11 at 3:06

## J - 55 45

``````f=:3 :'y,":10|10-10|+/(12\$1 3)*(i.12)(".@{)y'
``````

eg

``````f '978030640615'
9780306406157
``````

old way:

``````f=:,":@(10(10&|@-)(10&|@+/@((12\$1 3)*(i.12)&(".@{))))
``````
-

## dc, 44 chars

``````[d0r[I~3*rI~rsn++lndZ0<x]dsxx+I%Ir-I%rI*+]sI
``````

Invoke as `lIx`, e.g:

``````dc -e'[d0r[I~3*rI~rsn++lndZ0<x]dsxx+I%Ir-I%rI*+]sI' -e '978030640615lIxp'
``````
-

# Q, 36 chars

``````{x,-3!10-mod[;10]sum(12#1 3)*"I"\$'x}
``````
-

## C# – 89 77 characters

``````string I(string s){return s+(9992-s.Sum(x=>x-0)-2*s.Where((x,i)=>i%2>0).Sum(x=>x-0))%10;}
``````

``````string I(string s)
{
return s +
(9992
- s.Sum(x => x - 0)
- 2 * s.Where((x, i) => i%2 > 0).Sum(x => x - 0)
) % 10;
}
``````

We do not multiply by one or three, we just add everything, plus we add all even-placed characters one more time, multiplied by two.

9992 is large enough so that the sum of all ASCII characters is less than that (so that we may mod by 10 and be sure the result is positive, no need to mod by 10 twice), and is not divisible by zero because we add up all those extra 2*12*48 (twelve ASCII digits, weighed by 1 and 3) == 1152, which allows us to spare one extra character (instead of twice subtracting 48, we subtract 0 just to convert from char to int, but instead of 990, we need to write 9992).

But then again, even though much less beautiful ;-), this old-school solution gets us to 80 characters (but this is almost C-compatible):

``````string T(string i){int s=2,j=0;for(;j<12;)s+=i[j]*(9-j++%2*2);return i+s%10;}
``````
-

D - 97 characters

``````auto f(string s){int n;foreach(i,c;s)n+=((i&1)*2+1)*(c-48);return s~cast(char)((10-n%10)%10+48);}
``````

Formatted more legibly:

``````auto f(string s)
{
int n;

foreach(i, c; s)
n += ((i & 1) * 2 + 1) * (c - 48);

return s ~ cast(char)((10 - n % 10) % 10 + 48);
}
``````

The verbosity of D's cast operator definitely makes it harder to write obsessively short code though.

-

Java - 161 Characters :(

``````int b[]=new int[a.length];
int d=0,n=0,j=1;
for(char c:a.toCharArray())b[d++]=Integer.valueOf(c+"");
for(int i:b)n+=(j++%2==0)?(i*3):(i*1);
return a+(10-(n%10));
``````
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This answer does not satisfy the first requirement, since it is not a function. – han Oct 3 '12 at 17:49

# Q (44 chars)

``````f:{x,string 10-mod[;10]0+/sum@'2 cut"I"\$/:x}
``````
-
This is actually incorrect I think – slackwear Mar 9 '12 at 19:53

## Scala 84

``````def b(i:String)=i+(10-((i.sliding(2,2).map(_.toInt).map(k=>k/10+k%10*3).sum)%10)%10)
``````

Testing:

``````val isbn="978030640615"
b(isbn)
``````

Result:

``````"9780306406157"
``````
-

# C, 80 79 characters

The function modifies the string in place, but returns the original string pointer to satisfy the problem requirements.

``````s;char*f(char*p){for(s=2;*p;s+=7**p++)s+=9**p++;*p++=48+s%10;*p=0;return p-13;}
``````

Some explanation: Instead of subtracting 48 (the ASCII value of the digit `0`) from each input character, the accumulator `s` is initialized so that it is modulo 10 equal to 48+3*48+48+3*48...+48+3*48 = 24*48 = 1152. The step `10-sum` can be avoided by accumulating `s` by subtraction instead of addition. However, the module operator `%` in C would not give a usable result if `s` was negative, so instead of using `s-=` the multipliers 3 and 1 are replaced by -3=7 modulo 10 and -1=9 modulo 10, respectively.

Test harness:

``````#include <stdio.h>
#define N 12
int main()
{
char b[N+2];
fgets(b, N+1, stdin);
puts(f(b));
return 0;
}
``````
-

# Groovy 75, 66 chars

``````i={int i;it+(10-it.inject(0){t,c->t+(i++&1?:3)*(c as int)}%10)%10}
``````

use:

``````String z = "978030640615"
println i(z)

-> 9780306406157
``````
-

# MATLAB - 82 chars

``````function c(i)
[i num2str(mod(10-mod(sum(str2num(i(:)).*repmat([1;3],6,1)),10),10))]
``````
-

## R, 147 characters

``````f=function(v){s=as.numeric(strsplit(v,"")[[1]]);t=0;for(i in 1:12)if(i%%2==0)t=t+s[i]*3 else t=t+s[i];paste(v,(10-(t%%10))%%10,collapse="",sep="")}
``````

Usage:

``````f("978030640615")
[1] "9780306406157"
``````
-

# J, 25

``````,[:":10|0(-+/)"."0*1 3\$~#
``````
```   f =: ,[:":10|0(-+/)"."0*1 3\$~#
f '978030640615'
9780306406157
```
-

### APL (25)

``````{⍵,⍕10-10|+/(⍎¨⍵)×12⍴1,3}
``````
-

Javascript: 73 71 chars

``````function _(b){for(i=s=0;12>i;)s+=((i*2&2)+1)*b[i++];return b+(10-s%10)}
``````

Usage:

``````_('978030640615') //"9780306406157"
``````
-

## Python

``````>>>r=input()
>>>a=0
>>>for x in r[::2]:
a+=int(x)
>>>for x in r[1::2]:
a+=int(x)*3
>>>a=(10-(a%10))%10
print(r+str(a))
``````
-
I've added the language name to your answer; I was going to add a character count too but it looks like you've cut and paste from the REPL. Could you change this so it's a function as requested in the question and add a character count? – Gareth Oct 29 '12 at 12:53

Clojure 264 -> 241 characters:

``````(defn s [a b] (let [c (count a)] (if (= 0 c) b (s (rest a) (+ b (* (if (= 0 (m c 2)) 1 3) (first a)))))))
(defn m [a b] (let [f (mod a b)] (if (= f 10) 0 f)))
(defn c [a] (str a (m (- 10 (m (s (map #(read-string %) (map str a)) 0) 10)) 10)))
``````

Usage

``````(c "978030640615")
``````

Non minified:

``````(defn sum [collection total]
(let [len (count collection)]
(if (= 0 len)
total
(sum (rest collection)
(+ total
(* (if (= 0 (mod len 2)) 1 3)
(first collection)))))))

(defn mods [a b]
(let [f (mod a b)]
(if (= f 10)
0
f)))

(defn create [isbn]
(str isbn
(mods (- 10 (mods (sum (map #(read-string %) (map str isbn)) 0) 10)) 10)))
``````

Usage:

``````(create "978030640615")
``````

New to Clojure so I have to believe that can be knocked down.

-

# Tcl, 79

``````proc f c {lmap a\ b [split \$c {}] {incr d [expr \$a+3*\$b]};list \$c[expr -\$d%10]}
``````
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