fix(maths): prevent intermediate integer overflow in CatalanNumbers (#7732)

Author: Bhumit267

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

@@ -1,38 +1,43 @@
 package com.thealgorithms.maths;
 
+import java.math.BigInteger;
+
 /**
  * Calculate Catalan Numbers
  */
 public final class CatalanNumbers {
+    private static final int MAX_SUPPORTED_INDEX = 35;
+
     private CatalanNumbers() {
     }
 
     /**
-     * Calculate the nth Catalan number using a recursive formula.
+     * Calculate the nth Catalan number using the factorial formula.
      *
      * @param n the index of the Catalan number to compute
      * @return the nth Catalan number
+     * @throws IllegalArgumentException if n is negative or exceeds the maximum supported index for long
      */
     public static long catalan(final int n) {
         if (n < 0) {
             throw new IllegalArgumentException("Index must be non-negative");
         }
-        return factorial(2 * n) / (factorial(n + 1) * factorial(n));
+        if (n > MAX_SUPPORTED_INDEX) {
+            throw new IllegalArgumentException("Index exceeds maximum supported value for long");
+        }
+        return factorial(2 * n).divide(factorial(n + 1).multiply(factorial(n))).longValueExact();
     }
 
     /**
-     * Calculate the factorial of a number.
+     * Calculate the factorial of a number using BigInteger to prevent integer overflow.
      *
      * @param n the number to compute the factorial for
-     * @return the factorial of n
+     * @return the factorial of n as BigInteger
      */
-    private static long factorial(final int n) {
-        if (n == 0 || n == 1) {
-            return 1;
-        }
-        long result = 1;
+    private static BigInteger factorial(final int n) {
+        BigInteger result = BigInteger.ONE;
         for (int i = 2; i <= n; i++) {
-            result *= i;
+            result = result.multiply(BigInteger.valueOf(i));
         }
         return result;
     }

src/test/java/com/thealgorithms/maths/CatalanNumbersTest.java

@@ -19,7 +19,8 @@ class CatalanNumbersTest {
      * [input number, expected Catalan number for that input]
      */
     static Stream<Object[]> catalanNumbersProvider() {
-        return Stream.of(new Object[] {0, 1}, new Object[] {1, 1}, new Object[] {2, 2}, new Object[] {3, 5}, new Object[] {4, 14}, new Object[] {5, 42}, new Object[] {6, 132}, new Object[] {7, 429}, new Object[] {8, 1430}, new Object[] {9, 4862}, new Object[] {10, 16796});
+        return Stream.of(new Object[] {0, 1L}, new Object[] {1, 1L}, new Object[] {2, 2L}, new Object[] {3, 5L}, new Object[] {4, 14L}, new Object[] {5, 42L}, new Object[] {6, 132L}, new Object[] {7, 429L}, new Object[] {8, 1430L}, new Object[] {9, 4862L}, new Object[] {10, 16796L},
+            new Object[] {11, 58786L}, new Object[] {15, 9694845L}, new Object[] {35, 3116285494907301262L});
     }
 
     /**
@@ -28,7 +29,7 @@ static Stream<Object[]> catalanNumbersProvider() {
      */
     @ParameterizedTest
     @MethodSource("catalanNumbersProvider")
-    void testCatalanNumbers(int input, int expected) {
+    void testCatalanNumbers(int input, long expected) {
         assertEquals(expected, CatalanNumbers.catalan(input), () -> String.format("Catalan number for input %d should be %d", input, expected));
     }
 
@@ -39,5 +40,6 @@ void testCatalanNumbers(int input, int expected) {
     void testIllegalInput() {
         assertThrows(IllegalArgumentException.class, () -> CatalanNumbers.catalan(-1));
         assertThrows(IllegalArgumentException.class, () -> CatalanNumbers.catalan(-5));
+        assertThrows(IllegalArgumentException.class, () -> CatalanNumbers.catalan(36));
     }
 }