Lookup tables or arrays can simplify algorithm implementations - save many lines of code - and with that increase performance... if the calculation of the lookup index is simple - or simpler - and the array's memory footprint is affordable.
On the other hand, understanding how the particular lookup array or data structure came to be can at times be quite difficult, because the related algorithm implementation may look - at first sight - quite different from the original algorithm specification or description.
Indication to use lookup tables are number oriented algorithms with simple arithmetics, simple comparisons, and equally structured repetition patterns - and of course - of quite finite value sets.
The many answers in this thread go for different lookup tables and with that for different algorithms to implement the very same Luhn algorithm. Most implementations use the lookup array to avoid the cumbersome figuring out of the value for doubled digits:
var luhnArr = [0, 2, 4, 6, 8, 1, 3, 5, 7, 9];
//
// ^ ^ ^ ^ ^ ^ ^ ^ ^ ^
// | | | | | | | | | |
//
// - d-igit=index: 0 1 2 3 4 5 6 7 8 9
// - 1st
// calculation: 2*0 2*2 2*2 2*3 2*4 2*5 2*6 2*7 2*8 2*9
// - intermeduate
// value: = 0 = 2 = 4 = 6 = 8 =10 =12 =14 =16 =18
// - 2nd
// calculation: 1+0 1+2 1+4 1+6 1+8
//
// - final value: 0 2 4 6 8 =1 =3 =5 =7 =9
//
var luhnFinalValue = luhnArray[d]; // d is numeric value of digit to double
An equal implementation for getting the luhnFinalValue looks like this:
var luhnIntermediateValue = d * 2; // d is numeric value of digit to double
var luhnFinalValue = (luhnIntermediateValue < 10)
? luhnIntermediateValue // (d ) * 2;
: luhnIntermediateValue - 10 + 1; // (d - 5) * 2 + 1;
Which - with the comments in above true and false terms - is of course simplified:
var luhnFinalValue = (d < 5) ? d : (d - 5) * 2 + 1;
Now I'm not sure if I 'saved' anything at all... ;-) especially thanks the value-formed or short form of if-then-else. Without it, the code may look like this - with 'orderly' blocks
and embedded in the next higher context layer of the algorithm and therefore luhnValue:
var luhnValue; // card number is valid when luhn values for each digit modulo 10 is 0
if (even) { // even as n-th digit from the the end of the string of digits
luhnValue = d;
} else { // doubled digits
if (d < 5) {
luhnValue = d * 2;
} else {
lunnValue = (d - 5) * 2 + 1;
}
}
Or:
var luhnValue = (even) ? d : (d < 5) ? d * 2 : (d - 5) * 2 + 1;
Btw, with modern, optimizing interpreters and (just in time) compilers, the difference is only in the source code and matters only for readability.
Having come that far with explanation - and 'justification' - of the use of lookup tables and comparison to straight forward coding, the lookup table looks now a bit overkill to me. The algorithm without is now quite easy to finish - and it looks pretty compact too:
function luhnValid(cardNo) { // cardNo as a string w/ digits only
var sum = 0, even = false;
cardNo.split("").reverse().forEach(function(dstr){ d = parseInt(dstr);
sum += ((even = !even) ? d : (d < 5) ? d * 2 : (d - 5) * 2 + 1);
});
return (sum % 10 == 0);
}
What strikes me after going through the explanation exercise is that the initially most enticing implementation - the one using reduce() from @kalypto - just lost totally its luster for me... not only because it is faulty on several levels, but more so because it shows that bells and whistles may not always 'ring the victory bell'. But thank you, @kalypto, it made me actually use - and understand - reduce():
function luhnValid2(cardNo) { // cardNo as a string w/ digits only
var d = 0, e = false; // e = even = n-th digit counted from the end
return ( cardNo.split("").reverse().reduce(
function(s,dstr){ d = parseInt(dstr); // reduce arg-0 - callback fnc
return (s + ((e = !e) ? d : [0,2,4,6,8,1,3,5,7,9][d]));
} // /end of callback fnc
,0 // reduce arg-1 - prev value for first iteration (sum)
) % 10 == 0
);
}
To be true to this thread, some more lookup table options have to be mentioned:
- how about just adjust varues for doubled digits - as posted by @yngum
- how about just everything with lookup tables - as posted by @Simon_Weaver - where also the values for the non-doubled digits are taken from a look up table.
- how about just everything with just ONE lookup table - as inspired by the use of an offset as done in the extensively discussed luhnValid() function.
The code for the latter - using reduce - may look like this:
function luhnValid3(cardNo) { // cardNo as a string w/ digits only
var d = 0, e = false; // e = even = n-th digit counted from the end
return ( cardNo.split("").reverse().reduce(
function(s,dstr){ d = parseInt(dstr);
return (s + [0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,1,3,5,7,9][d+((e=!e)?0:10)]);
}
,0
) % 10 == 0
);
}
And for closing lunValid4() - very compact - and using just 'old fashioned' (compatible) JavaScript - with one single lookup table:
function luhnValid4(cardNo) { // cardNo as a string w/ digits only
var s = 0, e = false, p = cardNo.length; while (p > 0) { p--;
s += "01234567890246813579".charAt(cardNo.charAt(p)*1 + ((e=!e)?0:10)) * 1; }
return (s % 10 == 0);
}
Corollar: Strings can be looked at as lookup tables of characters... ;-)
A perfect example of a nice lookup table application is the counting of set bits in bits lists - bits set in a a (very) long 8-bit byte string in (an interpreted) high-level language (where any bit operations are quite expensive). The lookup table has 256 entries. Each entry contains the number of bits set in an unsigned 8-bit integer equal to the index of the entry. Iterating through the string and taking the unsigned 8-bit byte equal value to access the number of bits for that byte from the lookup table. Even for low-level language - such as assembler / machine code - the lookup table is the way to go... especially in an environment, where the microcode (instruction) can handle multiple bytes up to 256 or more in an (single CISC) instruction.
Some notes:
- numberString * 1 and parseInt(numberStr) do about the same.
- there are some superfluous indentations, parenthesis,etc... supporting my brain in getting the semantics quicker... but some that I wanted to leave out, are actually required... when
it comes to arithmetic operations with short-form, value-if-then-else expressions as terms.
- some formatting may look new to you; for examples, I use the continuation comma with the
continuation on the same line as the continuation, and I 'close' things - half a tab - indented to the 'opening' item.
- All formatting is all done for the human, not the computer... 'it' does care less.
algorithm datastructure luhn lookuptable creditcard validation bitlist
