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refactor: Enhance docs, code, add tests in LowestBasePalindrome (#6648)

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This commit is contained in:
Hardik Pawar
2025-10-12 14:35:30 +05:30
committed by GitHub
parent c0ca70498b
commit 14a23b709a
2 changed files with 135 additions and 26 deletions
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97
src/main/java/com/thealgorithms/others/LowestBasePalindrome.java
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@@ -4,8 +4,26 @@ import java.util.ArrayList;
import java.util.List;
/**
* @brief Class for finding the lowest base in which a given integer is a palindrome.
cf. https://oeis.org/A016026
* Utility class for finding the lowest base in which a given integer is a
* palindrome.
* <p>
* A number is a palindrome in a given base if its representation in that base
* reads the same
* forwards and backwards. For example, 15 in base 2 is 1111, which is
* palindromic.
* This class provides methods to check palindromic properties and find the
* smallest base
* where a number becomes palindromic.
* </p>
* <p>
* Example: The number 15 in base 2 is represented as [1,1,1,1], which is
* palindromic.
* The number 10 in base 3 is represented as [1,0,1], which is also palindromic.
* </p>
*
* @see <a href="https://oeis.org/A016026">OEIS A016026 - Smallest base in which
* n is palindromic</a>
* @author TheAlgorithms Contributors
*/
public final class LowestBasePalindrome {
private LowestBasePalindrome() {
@@ -37,12 +55,18 @@ public final class LowestBasePalindrome {
/**
* Computes the digits of a given number in a specified base.
* <p>
* The digits are returned in reverse order (least significant digit first).
* For example, the number 13 in base 2 produces [1,0,1,1] representing 1101 in
* binary.
* </p>
*
* @param number the number to be converted
* @param base the base to be used for the conversion
* @return a list of digits representing the number in the given base, with the most
* significant digit at the end of the list
* @throws IllegalArgumentException if the number is negative or the base is less than 2
* @param number the number to be converted (must be non-negative)
* @param base the base to be used for the conversion (must be greater than 1)
* @return a list of digits representing the number in the given base, with the
* least significant digit at the beginning of the list
* @throws IllegalArgumentException if the number is negative or the base is
* less than 2
*/
public static List<Integer> computeDigitsInBase(int number, int base) {
checkNumber(number);
@@ -58,6 +82,10 @@ public final class LowestBasePalindrome {
/**
* Checks if a list of integers is palindromic.
* <p>
* A list is palindromic if it reads the same forwards and backwards.
* For example, [1,2,1] is palindromic, but [1,2,3] is not.
* </p>
*
* @param list the list of integers to be checked
* @return {@code true} if the list is a palindrome, {@code false} otherwise
@@ -73,12 +101,29 @@ public final class LowestBasePalindrome {
}
/**
* Checks if the representation of a given number in a specified base is palindromic.
* Checks if the representation of a given number in a specified base is
* palindromic.
* <p>
* This method first validates the input, then applies optimization: if the
* number
* ends with 0 in the given base (i.e., divisible by the base), it cannot be
* palindromic
* as palindromes cannot start with 0.
* </p>
* <p>
* Examples:
* - 101 in base 10 is palindromic (101)
* - 15 in base 2 is palindromic (1111)
* - 10 in base 3 is palindromic (101)
* </p>
*
* @param number the number to be checked
* @param base the base in which the number will be represented
* @return {@code true} if the number is palindromic in the specified base, {@code false} otherwise
* @throws IllegalArgumentException if the number is negative or the base is less than 2
* @param number the number to be checked (must be non-negative)
* @param base the base in which the number will be represented (must be
* greater than 1)
* @return {@code true} if the number is palindromic in the specified base,
* {@code false} otherwise
* @throws IllegalArgumentException if the number is negative or the base is
* less than 2
*/
public static boolean isPalindromicInBase(int number, int base) {
checkNumber(number);
@@ -89,7 +134,8 @@ public final class LowestBasePalindrome {
}
if (number % base == 0) {
// If the last digit of the number in the given base is 0, it can't be palindromic
// If the last digit of the number in the given base is 0, it can't be
// palindromic
return false;
}
@@ -97,10 +143,29 @@ public final class LowestBasePalindrome {
}
/**
* Finds the smallest base in which the representation of a given number is palindromic.
* Finds the smallest base in which the representation of a given number is
* palindromic.
* <p>
* This method iteratively checks bases starting from 2 until it finds one where
* the number is palindromic. For any number n ≥ 2, the number is always
* palindromic
* in base n-1 (represented as [1, 1]), so this algorithm is guaranteed to
* terminate.
* </p>
* <p>
* Time Complexity: O(n * log(n)) in the worst case, where we check each base
* and
* convert the number to that base.
* </p>
* <p>
* Examples:
* - lowestBasePalindrome(15) returns 2 (15 in base 2 is 1111)
* - lowestBasePalindrome(10) returns 3 (10 in base 3 is 101)
* - lowestBasePalindrome(11) returns 10 (11 in base 10 is 11)
* </p>
*
* @param number the number to be checked
* @return the smallest base in which the number is a palindrome
* @param number the number to be checked (must be non-negative)
* @return the smallest base in which the number is a palindrome (base ≥ 2)
* @throws IllegalArgumentException if the number is negative
*/
public static int lowestBasePalindrome(int number) {