refactor: Enhance docs, code, add tests in KeithNumber (#6748)

* refactor: Enhance docs, code, add tests in `KeithNumber`

* Fix

---------

Co-authored-by: a <alexanderklmn@gmail.com>

src/main/java/com/thealgorithms/maths/KeithNumber.java

@@ -4,57 +4,98 @@ import java.util.ArrayList;
 import java.util.Collections;
 import java.util.Scanner;
 
-final class KeithNumber {
+/**
+ * A Keith number is an n-digit positive integer where the sequence formed by
+ * starting with its digits and repeatedly adding the previous n terms,
+ * eventually reaches the number itself.
+ *
+ * <p>
+ * For example:
+ * <ul>
+ * <li>14 is a Keith number: 1, 4, 5, 9, 14</li>
+ * <li>19 is a Keith number: 1, 9, 10, 19</li>
+ * <li>28 is a Keith number: 2, 8, 10, 18, 28</li>
+ * <li>197 is a Keith number: 1, 9, 7, 17, 33, 57, 107, 197</li>
+ * </ul>
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Keith_number">Keith Number -
+ *      Wikipedia</a>
+ * @see <a href="https://mathworld.wolfram.com/KeithNumber.html">Keith Number -
+ *      MathWorld</a>
+ */
+public final class KeithNumber {
     private KeithNumber() {
     }
 
-    // user-defined function that checks if the given number is Keith or not
-    static boolean isKeith(int x) {
-        // List stores all the digits of the X
-        ArrayList<Integer> terms = new ArrayList<>();
-        // n denotes the number of digits
-        int temp = x;
-        int n = 0;
-        // executes until the condition becomes false
-        while (temp > 0) {
-            // determines the last digit of the number and add it to the List
-            terms.add(temp % 10);
-            // removes the last digit
-            temp = temp / 10;
-            // increments the number of digits (n) by 1
-            n++;
+    /**
+     * Checks if a given number is a Keith number.
+     *
+     * <p>
+     * The algorithm works as follows:
+     * <ol>
+     * <li>Extract all digits of the number and store them in a list</li>
+     * <li>Generate subsequent terms by summing the last n digits</li>
+     * <li>Continue until a term equals or exceeds the original number</li>
+     * <li>If a term equals the number, it is a Keith number</li>
+     * </ol>
+     *
+     * @param number the number to check (must be positive)
+     * @return {@code true} if the number is a Keith number, {@code false} otherwise
+     * @throws IllegalArgumentException if the number is not positive
+     */
+    public static boolean isKeith(int number) {
+        if (number <= 0) {
+            throw new IllegalArgumentException("Number must be positive");
         }
-        // reverse the List
+
+        // Extract digits and store them in the list
+        ArrayList<Integer> terms = new ArrayList<>();
+        int temp = number;
+        int digitCount = 0;
+
+        while (temp > 0) {
+            terms.add(temp % 10);
+            temp = temp / 10;
+            digitCount++;
+        }
+
+        // Reverse the list to get digits in correct order
         Collections.reverse(terms);
+
+        // Generate subsequent terms in the sequence
         int nextTerm = 0;
-        int i = n;
-        // finds next term for the series
-        // loop executes until the condition returns true
-        while (nextTerm < x) {
+        int currentIndex = digitCount;
+
+        while (nextTerm < number) {
             nextTerm = 0;
-            // next term is the sum of previous n terms (it depends on number of digits the number
-            // has)
-            for (int j = 1; j <= n; j++) {
-                nextTerm = nextTerm + terms.get(i - j);
+            // Sum the last 'digitCount' terms
+            for (int j = 1; j <= digitCount; j++) {
+                nextTerm = nextTerm + terms.get(currentIndex - j);
             }
             terms.add(nextTerm);
-            i++;
+            currentIndex++;
         }
-        // when the control comes out of the while loop, there will be two conditions:
-        // either nextTerm will be equal to x or greater than x
-        // if equal, the given number is Keith, else not
-        return (nextTerm == x);
+
+        // Check if the generated term equals the original number
+        return (nextTerm == number);
     }
 
-    // driver code
+    /**
+     * Main method for demonstrating Keith number detection.
+     * Reads a number from standard input and checks if it is a Keith number.
+     *
+     * @param args command line arguments (not used)
+     */
     public static void main(String[] args) {
-        Scanner in = new Scanner(System.in);
-        int n = in.nextInt();
-        if (isKeith(n)) {
-            System.out.println("Yes, the given number is a Keith number.");
+        Scanner scanner = new Scanner(System.in);
+        System.out.print("Enter a positive integer: ");
+        int number = scanner.nextInt();
+
+        if (isKeith(number)) {
+            System.out.println("Yes, " + number + " is a Keith number.");
         } else {
-            System.out.println("No, the given number is not a Keith number.");
+            System.out.println("No, " + number + " is not a Keith number.");
         }
-        in.close();
+        scanner.close();
     }
 }