Enhance readme with Palindrome Number solution details

Added a detailed explanation and implementation for the Palindrome Number problem in Java, including constraints and follow-up considerations.

Author: javadev

src/main/java/g0001_0100/s0009_palindrome_number/readme.md

@@ -32,4 +32,63 @@ Given an integer `x`, return `true` _if_ `x` _is a_ _**palindrome**__, and_ `fal
 
 *   <code>-2<sup>31</sup> <= x <= 2<sup>31</sup> - 1</code>
 
-**Follow up:** Could you solve it without converting the integer to a string?
+**Follow up:** Could you solve it without converting the integer to a string?
+
+To solve the Palindrome Number problem in Java using a `Solution` class, we'll follow these steps:
+
+1. Define a `Solution` class with a method named `isPalindrome`.
+2. Handle special cases where `x` is negative or divisible by 10 but not equal to zero, as they cannot be palindromes.
+3. Initialize variables to keep track of the reversed number (`reversed`) and the original number (`original`).
+4. Iterate through the digits of the original number `x`:
+   - Extract the least significant digit using the modulo operator and append it to the reversed number.
+   - Update `original` by removing the least significant digit using integer division.
+5. Check if the reversed number is equal to the original number. If so, return `true`; otherwise, return `false`.
+
+Here's the implementation:
+
+```java
+public class Solution {
+
+    public boolean isPalindrome(int x) {
+        // Special cases:
+        // As discussed, negative numbers are not palindromes.
+        // Also, if the last digit of the number is 0, it can't be a palindrome unless the number is 0 itself.
+        if (x < 0 || (x % 10 == 0 && x != 0)) {
+            return false;
+        }
+
+        int reversed = 0;
+        int original = x;
+
+        while (original > reversed) {
+            int digit = original % 10;
+            reversed = reversed * 10 + digit;
+            original /= 10;
+        }
+
+        // When the length is an odd number, we can get rid of the middle digit by reversed / 10
+        // For example when the input is 12321, at the end of the while loop we get x = 12, reversed = 123,
+        // since the middle digit doesn't matter in palidrome(it will always equal to itself), we can simply get rid of it.
+        return original == reversed || original == reversed / 10;
+    }
+
+    public static void main(String[] args) {
+        Solution solution = new Solution();
+
+        // Test cases
+        int x1 = 121;
+        System.out.println("Example 1 Output: " + solution.isPalindrome(x1));
+
+        int x2 = -121;
+        System.out.println("Example 2 Output: " + solution.isPalindrome(x2));
+
+        int x3 = 10;
+        System.out.println("Example 3 Output: " + solution.isPalindrome(x3));
+
+        int x4 = -101;
+        System.out.println("Example 4 Output: " + solution.isPalindrome(x4));
+    }
+}
+```
+
+This implementation provides a solution to the Palindrome Number problem in Java.