refactor: Enhance docs, code, add tests in LucasSeries (#6749)

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

@@ -1,38 +1,69 @@
 package com.thealgorithms.maths;
 
 /**
- * https://en.wikipedia.org/wiki/Lucas_number
+ * Utility class for calculating Lucas numbers.
+ * The Lucas sequence is similar to the Fibonacci sequence but starts with 2 and
+ * 1.
+ * The sequence follows: L(n) = L(n-1) + L(n-2)
+ * Starting values: L(1) = 2, L(2) = 1
+ * Sequence: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ...
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Lucas_number">Lucas Number</a>
+ * @author TheAlgorithms Contributors
  */
 public final class LucasSeries {
     private LucasSeries() {
     }
 
     /**
-     * Calculate nth number of Lucas Series(2, 1, 3, 4, 7, 11, 18, 29, 47, 76,
-     * 123, ....) using recursion
+     * Calculate the nth Lucas number using recursion.
+     * Time Complexity: O(2^n) - exponential due to recursive calls
+     * Space Complexity: O(n) - recursion depth
      *
-     * @param n nth
-     * @return nth number of Lucas Series
+     * @param n the position in the Lucas sequence (1-indexed, must be positive)
+     * @return the nth Lucas number
+     * @throws IllegalArgumentException if n is less than 1
      */
     public static int lucasSeries(int n) {
-        return n == 1 ? 2 : n == 2 ? 1 : lucasSeries(n - 1) + lucasSeries(n - 2);
+        if (n < 1) {
+            throw new IllegalArgumentException("Input must be a positive integer. Provided: " + n);
+        }
+        if (n == 1) {
+            return 2;
+        }
+        if (n == 2) {
+            return 1;
+        }
+        return lucasSeries(n - 1) + lucasSeries(n - 2);
     }
 
     /**
-     * Calculate nth number of Lucas Series(2, 1, 3, 4, 7, 11, 18, 29, 47, 76,
-     * 123, ....) using iteration
+     * Calculate the nth Lucas number using iteration.
+     * Time Complexity: O(n) - single loop through n iterations
+     * Space Complexity: O(1) - constant space usage
      *
-     * @param n nth
-     * @return nth number of lucas series
+     * @param n the position in the Lucas sequence (1-indexed, must be positive)
+     * @return the nth Lucas number
+     * @throws IllegalArgumentException if n is less than 1
      */
     public static int lucasSeriesIteration(int n) {
+        if (n < 1) {
+            throw new IllegalArgumentException("Input must be a positive integer. Provided: " + n);
+        }
+        if (n == 1) {
+            return 2;
+        }
+        if (n == 2) {
+            return 1;
+        }
+
         int previous = 2;
         int current = 1;
-        for (int i = 1; i < n; i++) {
+        for (int i = 2; i < n; i++) {
             int next = previous + current;
             previous = current;
             current = next;
         }
-        return previous;
+        return current;
     }
 }