#### Lowest Base Palindrome

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package com.thealgorithms.others;

import java.util.ArrayList;

/**
* @brief Class for finding the lowest base in which a given integer is a palindrome.
cf. https://oeis.org/A016026
*/
public final class LowestBasePalindrome {
private LowestBasePalindrome() {
}

private static void checkBase(int base) {
if (base <= 1) {
throw new IllegalArgumentException("base must be greater than 1.");
}
}

private static void checkNumber(int number) {
if (number < 0) {
throw new IllegalArgumentException("number must be nonnegative.");
}
}

/**
* @brief computes the representation of the input number in given base
* @param number the input number
* @param base the given base
* @exception IllegalArgumentException number is negative or base is less than 2
* @return the list containing the digits of the input number in the given base, the most
*     significant digit is at the end of the array
*/
public static ArrayList<Integer> computeDigitsInBase(int number, int base) {
checkNumber(number);
checkBase(base);
var result = new ArrayList<Integer>();
while (number > 0) {
number /= base;
}
return result;
}

/**
* @brief checks if the input array is a palindrome
* @brief list the input array
* @return true, if the input array is a palindrome, false otherwise
*/
public static boolean isPalindromic(ArrayList<Integer> list) {
for (int pos = 0; pos < list.size() / 2; ++pos) {
if (list.get(pos) != list.get(list.size() - 1 - pos)) {
return false;
}
}
return true;
}

/**
* @brief checks if representation of the input number in given base is a palindrome
* @param number the input number
* @param base the given base
* @exception IllegalArgumentException number is negative or base is less than 2
* @return true, if the input number represented in the given base is a palindrome, false
*     otherwise
*/
public static boolean isPalindromicInBase(int number, int base) {
checkNumber(number);
checkBase(base);

if (number <= 1) {
return true;
}

if (number % base == 0) {
// the last digit of number written in base is 0
return false;
}

return isPalindromic(computeDigitsInBase(number, base));
}

/**
* @brief finds the smallest base for which the representation of the input number is a
* palindrome
* @param number the input number
* @exception IllegalArgumentException number is negative
* @return the smallest base for which the representation of the input number is a palindrome
*/
public static int lowestBasePalindrome(int number) {
int base = 2;
while (!isPalindromicInBase(number, base)) {
++base;
}
return base;
}
}