diff --git a/Others/Verhoeff.java b/Others/Verhoeff.java
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+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:
+ *
+ * - multiplication table
+ * - inverse table
+ * - permutation table
+ *
+ *
+ * @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();
+ }
+}