#### Verhoeff

d
```package com.thealgorithms.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.
*
* <p>
* 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:</p>
* <ol>
* <li>multiplication table</li>
* <li>inverse table</li>
* <li>permutation table</li>
* </ol>
*
* @see <a href="https://en.wikipedia.org/wiki/Verhoeff_algorithm">Wiki.
* Verhoeff algorithm</a>
*/
public final class Verhoeff {
private 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 <a href="https://en.wikipedia.org/wiki/Dihedral_group">Wiki.
* Dihedral group</a>
*/
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) {
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();
}
}
```