fix(dynamicprogramming): handle n=0 and negative inputs safely in CatalanNumber (#7731)

Author: Bhumit267

src/main/java/com/thealgorithms/dynamicprogramming/CatalanNumber.java

@@ -21,8 +21,16 @@ private CatalanNumber() {
      * n > 50, BigInteger class should be used instead long
      *
      * @return catalanArray[n] the nth Catalan number
+     * @throws IllegalArgumentException if n is negative
      */
     static long findNthCatalan(int n) {
+        if (n < 0) {
+            throw new IllegalArgumentException("n must be non-negative");
+        }
+        if (n <= 1) {
+            return 1;
+        }
+
         // Array to store the results of subproblems i.e Catalan numbers from [1...n-1]
         long[] catalanArray = new long[n + 1];
 

src/test/java/com/thealgorithms/dynamicprogramming/CatalanNumberTest.java

@@ -1,14 +1,22 @@
 package com.thealgorithms.dynamicprogramming;
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
 
 import org.junit.jupiter.api.Test;
 
 public class CatalanNumberTest {
 
     @Test
     public void testCatalanNumber() {
+        assertEquals(1, CatalanNumber.findNthCatalan(0));
+        assertEquals(1, CatalanNumber.findNthCatalan(1));
         assertEquals(42, CatalanNumber.findNthCatalan(5));
         assertEquals(16796, CatalanNumber.findNthCatalan(10));
     }
+
+    @Test
+    public void testNegativeInput() {
+        assertThrows(IllegalArgumentException.class, () -> CatalanNumber.findNthCatalan(-1));
+    }
 }