refactor: Enhance docs, code, add tests in LeonardoNumber (#6743)

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

@@ -1,25 +1,79 @@
 package com.thealgorithms.maths;
 
 /**
- * https://en.wikipedia.org/wiki/Leonardo_number
+ * Utility class for calculating Leonardo Numbers.
+ * <p>
+ * Leonardo numbers are a sequence of numbers defined by the recurrence:
+ * L(n) = L(n-1) + L(n-2) + 1, with L(0) = 1 and L(1) = 1
+ * <p>
+ * The sequence begins: 1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, ...
+ * <p>
+ * This class provides both a recursive implementation and an optimized
+ * iterative
+ * implementation for calculating Leonardo numbers.
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Leonardo_number">Leonardo Number
+ *      - Wikipedia</a>
+ * @see <a href="https://oeis.org/A001595">OEIS A001595</a>
  */
 public final class LeonardoNumber {
     private LeonardoNumber() {
     }
 
     /**
-     * Calculate nth Leonardo Number (1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, ...)
+     * Calculates the nth Leonardo Number using recursion.
+     * <p>
+     * Time Complexity: O(2^n) - exponential due to repeated calculations
+     * Space Complexity: O(n) - due to recursion stack
+     * <p>
+     * Note: This method is not recommended for large values of n due to exponential
+     * time complexity.
+     * Consider using {@link #leonardoNumberIterative(int)} for better performance.
      *
-     * @param n the index of Leonardo Number to calculate
-     * @return nth number of Leonardo sequences
+     * @param n the index of the Leonardo Number to calculate (must be non-negative)
+     * @return the nth Leonardo Number
+     * @throws IllegalArgumentException if n is negative
      */
     public static int leonardoNumber(int n) {
         if (n < 0) {
-            throw new ArithmeticException();
+            throw new IllegalArgumentException("Input must be non-negative. Received: " + n);
         }
         if (n == 0 || n == 1) {
             return 1;
         }
-        return (leonardoNumber(n - 1) + leonardoNumber(n - 2) + 1);
+        return leonardoNumber(n - 1) + leonardoNumber(n - 2) + 1;
+    }
+
+    /**
+     * Calculates the nth Leonardo Number using an iterative approach.
+     * <p>
+     * This method provides better performance than the recursive version for large
+     * values of n.
+     * <p>
+     * Time Complexity: O(n)
+     * Space Complexity: O(1)
+     *
+     * @param n the index of the Leonardo Number to calculate (must be non-negative)
+     * @return the nth Leonardo Number
+     * @throws IllegalArgumentException if n is negative
+     */
+    public static int leonardoNumberIterative(int n) {
+        if (n < 0) {
+            throw new IllegalArgumentException("Input must be non-negative. Received: " + n);
+        }
+        if (n == 0 || n == 1) {
+            return 1;
+        }
+
+        int previous = 1;
+        int current = 1;
+
+        for (int i = 2; i <= n; i++) {
+            int next = current + previous + 1;
+            previous = current;
+            current = next;
+        }
+
+        return current;
     }
 }