Step by Step solution about How to resolve the algorithm Verhoeff algorithm step by step in the Julia programming language

The code snippet above implements the Verhoeff algorithm to calculate the check digit for a given integer, and validate if the check digit is correct for a given integer.

The Verhoeff algorithm is a checksum algorithm that can be used to validate numbers, such as credit card numbers or social security numbers. It assigns a single-digit checksum to an integer value. This checksum is based on the digits of the integer, and it is used to detect errors that may have occurred during data entry or transmission.

The code calculates the checksum for a given integer by iterating over the digits of the integer and applying a series of calculations to each digit. These calculations involve multiplying the digit by a precomputed value and then adding the result to a running total. The final result of the calculations is used to compute the checksum digit.

The code also includes a validation function that checks if the check digit of a given integer is correct. The validation function calculates the expected checksum digit for the integer and compares it to the actual check digit. If the two values match, then the check digit is considered to be correct and the integer is considered to be valid.

The code demonstrates the usage of the checksum and validation functions by calculating the checksum for several different integers and then validating the checksum for each integer.

Here is a detailed explanation of the code:

const multiplicationtable = [
   0  1  2  3  4  5  6  7  8  9;
   1  2  3  4  0  6  7  8  9  5;
   2  3  4  0  1  7  8  9  5  6;
   3  4  0  1  2  8  9  5  6  7;
   4  0  1  2  3  9  5  6  7  8;
   5  9  8  7  6  0  4  3  2  1;
   6  5  9  8  7  1  0  4  3  2;
   7  6  5  9  8  2  1  0  4  3;
   8  7  6  5  9  3  2  1  0  4;
   9  8  7  6  5  4  3  2  1  0]

This is a constant matrix that is used in the checksum calculations

const permutationtable = [
   0  1  2  3  4  5  6  7  8  9;
   1  5  7  6  2  8  3  0  9  4;
   5  8  0  3  7  9  6  1  4  2;
   8  9  1  6  0  4  3  5  2  7;
   9  4  5  3  1  2  6  8  7  0;
   4  2  8  6  5  7  3  9  0  1;
   2  7  9  3  8  0  6  4  1  5;
   7  0  4  6  9  1  3  2  5  8]

This is a constant matrix that is used in the checksum calculations.

const inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]

This is a constant array that is used to invert the checksum calculations.

function verhoeffchecksum(n::Integer, validate=true, terse=true, verbose=false)

This function calculates the Verhoeff checksum for a given integer n. The validate argument specifies whether to validate the checksum for the given integer, and the terse argument specifies whether to return a boolean value indicating if the checksum is correct or not. The verbose argument specifies whether to print out the intermediate steps of the checksum calculation.

   if validate
       c, dig = 0, reverse(digits(n))
   else
       c, dig = 0, reverse(digits(10 * n))
   end

This code initializes the checksum variable c to 0 and the list of digits dig to the reverse of the digits of the input integer n. If the validate argument is true, then the checksum is calculated for the original integer n, otherwise the checksum is calculated for the integer 10 * n.

   for i in length(dig):-1:1
       ni = dig[i]
       p = permutationtable[(length(dig) - i) % 8 + 1, ni + 1]
       c = multiplicationtable[c + 1, p + 1]
       verbose && println(lpad(length(dig) - i, 2), "  $ni      $p    $c")
   end

This code iterates over the digits of the input integer n from right to left. For each digit, it calculates the value of p using the permutationtable and the value of c using the multiplicationtable. The intermediate steps of the checksum calculation are printed out if the verbose argument is true.

   verbose && !validate && println("\ninv($c) = $(inv[c + 1])")
   !terse && println(validate ? "\nThe validation for '$n' is $(c == 0 ?
       "correct" : "incorrect")." : "\nThe check digit for '$n' is $(inv[c + 1]).")
   return validate ? c == 0 : inv[c + 1]
end

This code finalizes the checksum calculation. If the validate argument is true, then the function returns true if the checksum is correct and false otherwise. If the validate argument is false, then the function returns the check digit.

The code then demonstrates the usage of the verhoeffchecksum function by calculating the checksum for several different integers and then validating the checksum for each integer.

const multiplicationtable = [
    0  1  2  3  4  5  6  7  8  9;
    1  2  3  4  0  6  7  8  9  5;
    2  3  4  0  1  7  8  9  5  6;
    3  4  0  1  2  8  9  5  6  7;
    4  0  1  2  3  9  5  6  7  8;
    5  9  8  7  6  0  4  3  2  1;
    6  5  9  8  7  1  0  4  3  2;
    7  6  5  9  8  2  1  0  4  3;
    8  7  6  5  9  3  2  1  0  4;
    9  8  7  6  5  4  3  2  1  0]

const permutationtable = [
    0  1  2  3  4  5  6  7  8  9;
    1  5  7  6  2  8  3  0  9  4;
    5  8  0  3  7  9  6  1  4  2;
    8  9  1  6  0  4  3  5  2  7;
    9  4  5  3  1  2  6  8  7  0;
    4  2  8  6  5  7  3  9  0  1;
    2  7  9  3  8  0  6  4  1  5;
    7  0  4  6  9  1  3  2  5  8]

const inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]

"""
    verhoeffchecksum(n::Integer, validate=true, terse=true, verbose=false)

Calculate the Verhoeff checksum over `n`.
Terse mode or with single argument: return true if valid (last digit is a correct check digit).
If checksum mode, return the expected correct checksum digit.
If validation mode, return true if last digit checks correctly.
"""
function verhoeffchecksum(n::Integer, validate=true, terse=true, verbose=false)
    verbose && println("\n", validate ? "Validation" : "Check digit",
        " calculations for '$n':\n\n", " i  nᵢ  p[i,nᵢ]  c\n------------------")
    # transform number list
    c, dig = 0, reverse(digits(validate ? n : 10 * n))
    for i in length(dig):-1:1
        ni = dig[i]
        p = permutationtable[(length(dig) - i) % 8 + 1, ni + 1]
        c = multiplicationtable[c + 1, p + 1]
        verbose && println(lpad(length(dig) - i, 2), "  $ni      $p    $c")
    end
    verbose && !validate && println("\ninv($c) = $(inv[c + 1])")
    !terse && println(validate ? "\nThe validation for '$n' is $(c == 0 ?
        "correct" : "incorrect")." : "\nThe check digit for '$n' is $(inv[c + 1]).")
    return validate ? c == 0 : inv[c + 1]
end

for args in [(236, false, false, true), (2363, true, false, true), (2369, true, false, true),
    (12345, false, false, true), (123451, true, false, true), (123459, true, false, true),
    (123456789012, false, false), (1234567890120, true, false), (1234567890129, true, false)]
        verhoeffchecksum(args...)
end