diff --git a/Others/Verhoeff.java b/Others/Verhoeff.java new file mode 100644 index 00000000..5dc29898 --- /dev/null +++ b/Others/Verhoeff.java @@ -0,0 +1,158 @@ +package Others; + +import java.util.Objects; + +/** + * The Verhoeff algorithm is a checksum formula for error detection developed + * by the Dutch mathematician Jacobus Verhoeff and was first published in 1969. + * It was the first decimal check digit algorithm which detects all single-digit + * errors, and all transposition errors involving two adjacent digits. + * + *

The strengths of the algorithm are that it detects all transliteration and + * transposition errors, and additionally most twin, twin jump, jump transposition + * and phonetic errors. + * The main weakness of the Verhoeff algorithm is its complexity. + * The calculations required cannot easily be expressed as a formula. + * For easy calculation three tables are required:

+ *
    + *
  1. multiplication table
  2. + *
  3. inverse table
  4. + *
  5. permutation table
  6. + *
+ * + * @see Wiki. Verhoeff algorithm + */ +public class Verhoeff { + + /** + * Table {@code d}. + * Based on multiplication in the dihedral group D5 and is simply the Cayley table of the group. + * Note that this group is not commutative, that is, for some values of {@code j} and {@code k}, + * {@code d(j,k) ≠ d(k, j)}. + * + * @see Wiki. Dihedral group + */ + private static final byte[][] MULTIPLICATION_TABLE = { + {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} + }; + + /** + * The inverse table {@code inv}. + * Represents the multiplicative inverse of a digit, that is, the value that satisfies + * {@code d(j, inv(j)) = 0}. + */ + private static final byte[] MULTIPLICATIVE_INVERSE = {0, 4, 3, 2, 1, 5, 6, 7, 8, 9}; + + /** + * The permutation table {@code p}. + * Applies a permutation to each digit based on its position in the number. + * This is actually a single permutation {@code (1 5 8 9 4 2 7 0)(3 6)} applied iteratively; + * i.e. {@code p(i+j,n) = p(i, p(j,n))}. + */ + private static final byte[][] PERMUTATION_TABLE = { + {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} + }; + + /** + * Check input digits by Verhoeff algorithm. + * + * @param digits input to check + * @return true if check was successful, false otherwise + * @throws IllegalArgumentException if input parameter contains not only digits + * @throws NullPointerException if input is null + */ + public static boolean verhoeffCheck(String digits) { + checkInput(digits); + int[] numbers = toIntArray(digits); + + // The Verhoeff algorithm + int checksum = 0; + for (int i = 0; i < numbers.length; i++) { + int index = numbers.length - i - 1; + byte b = PERMUTATION_TABLE[i % 8][numbers[index]]; + checksum = MULTIPLICATION_TABLE[checksum][b]; + } + + return checksum == 0; + } + + /** + * Calculate check digit for initial digits and add it tho the last position. + * + * @param initialDigits initial value + * @return digits with the checksum in the last position + * @throws IllegalArgumentException if input parameter contains not only digits + * @throws NullPointerException if input is null + */ + public static String addVerhoeffChecksum(String initialDigits) { + checkInput(initialDigits); + + // Add zero to end of input value + var modifiedDigits = initialDigits + "0"; + + int[] numbers = toIntArray(modifiedDigits); + + int checksum = 0; + for (int i = 0; i < numbers.length; i++) { + int index = numbers.length - i - 1; + byte b = PERMUTATION_TABLE[i % 8][numbers[index]]; + checksum = MULTIPLICATION_TABLE[checksum][b]; + } + checksum = MULTIPLICATIVE_INVERSE[checksum]; + + return initialDigits + checksum; + } + + public static void main(String[] args) { + System.out.println("Verhoeff algorithm usage examples:"); + var validInput = "2363"; + var invalidInput = "2364"; + checkAndPrint(validInput); + checkAndPrint(invalidInput); + + System.out.println("\nCheck digit generation example:"); + var input = "236"; + generateAndPrint(input); + } + + private static void checkAndPrint(String input) { + String validationResult = Verhoeff.verhoeffCheck(input) + ? "valid" + : "not valid"; + System.out.println("Input '" + input + "' is " + validationResult); + } + + private static void generateAndPrint(String input) { + String result = addVerhoeffChecksum(input); + System.out.println("Generate and add checksum to initial value '" + input + "'. Result: '" + result + "'"); + } + + private static void checkInput(String input) { + Objects.requireNonNull(input); + if (!input.matches("\\d+")) { + throw new IllegalArgumentException("Input '" + input + "' contains not only digits"); + } + } + + private static int[] toIntArray(String string) { + return string.chars() + .map(i -> Character.digit(i, 10)) + .toArray(); + } +}