Can someone explain me meaning of this code in luhn algorithm?

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private static bool IsValidNumber(string number)
{
    int[] DELTAS = new int[] { 0, 1, 2, 3, 4, -4, -3, -2, -1, 0 };
    int checksum = 0;
    char[] chars = number.ToCharArray();
    for (int i = chars.Length - 1; i > -1; i--)
    {
       int j = ((int)chars[i]) - 48;
       checksum += j;
       if (((i - chars.Length) % 2) == 0)
           checksum += DELTAS[j];
    }

    return ((checksum % 10) == 0);
}

Can someone tell me, why we are using

int[] DELTAS = new int[] { 0, 1, 2, 3, 4, -4, -3, -2, -1, 0 };

whats the use of above code?

In last code

checksum += DELTAS[j];

we are basically adding , credit card number with these number { 0, 1, 2, 3, 4, -4, -3, -2, -1, 0 } one by one.

This seems more like a mathematical question rather than coding question.

But, i am stuck in this part.

Thanks in advance

Posted 1-Apr-15 0:58am

ankur1163

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PIEBALDconsult 22-Apr-15 12:51pm

Looks odd to me, and "char[] chars = number.ToCharArray()" is pointless so I suspect that that code was written by an amateur and shouldn't be trusted.

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CPallini · Answer 1 · 2015-04-01T02:02:00

DELTAS is used to perfom this step (source Wikipedia[^]) :

From the rightmost digit, which is the check digit, moving left, double the value of every second digit; if the product of this doubling operation is greater than 9 (e.g., 8 × 2 = 16), then sum the digits of the products (e.g., 16: 1 + 6 = 7, 18: 1 + 8 = 9).

indeed the DELTAS array items represent the difference of the 'sum of digits of doubled number' and the number itself:

0 => 0 * 2 = 0 => DELTAS[0] = 0
1 => 1 * 2 = 2 => DELTAS[1] = 1 (because 2 - 1 = 1)
...
6 => 6 * 2 = 12 => 1 + 2 = 3 => DELTAS[6]=-3 (because 3 - 6 = -3)
...

PIEBALDconsult · Answer 2 · 2015-04-22T07:00:00

That code is definitely obfuscated; someone trying to be clever and missing.
Notice that simply making the DELTAS array static is a huge improvement.

Consider this code:

C#

public static int
Luhn
(
  string Value
)
{
  int sum = 0 ;
  int mul = 1 ;

  for ( int i = Value.Length - 1 ; i >= 0 ; i-- )
  {
    int val = (int) Value [ i ] - 48 ;

    if ( val >= 0 && val < 10 )
    {
      val *= mul ;

      sum += val / 10 + val % 10 ;

      mul ^= 3 ;
    }
  }

  return ( sum % 10 ) ;
}

Also, consider what happens with the code you posted when a number is passed in with SPACEs or HYPHENs.

Some benchmarking results:

1000000 in 00:00:00.2791342 -- What you posted
1000000 in 00:00:00.2380398 -- What you posted, without the ridiculous ToCharArray
1000000 in 00:00:00.6797738 -- What you posted, with char[] chars = number.Where ( x => x >= '0' && x <= '9' ).ToArray();
1000000 in 00:00:00.0848604 -- What you posted, with static DELTAS
1000000 in 00:00:00.0689142 -- What you posted, with static DELTAS, without the ridiculous ToCharArray
1000000 in 00:00:00.0681335 -- What you posted, with static two-dimensional DELTAS, without the ridiculous ToCharArray
1000000 in 00:00:00.0951645 -- What I posted
1000000 in 00:00:00.0818445 -- What I posted, without the test for non-digits

Can someone explain me meaning of this code in luhn algorithm?

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