[Bhumit267]

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized it.
• All filenames are in PascalCase.
• All functions and variable names follow Java naming conventions.
• All new algorithms have a URL in their comments that points to Wikipedia or other similar explanations.
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Description

In CatalanNumbers.java, catalan(n) computes the $n$-th Catalan number using the factorial formula:
$$\frac{(2n)!}{(n+1)! \cdot n!}$$

Previously, factorial(int n) used standard 64-bit signed long arithmetic. Because $21!$ and higher overflow 64-bit long (where 20! is $\approx 2.43 \times 10^{18}$ and Long.MAX_VALUE is $\approx 9.22 \times 10^{18}$), computing $(2n)!$ for any $n \ge 11$ ($2n \ge 22$) caused silent integer overflow, resulting in incorrect and negative results (e.g. catalan(11) evaluated to -65 instead of 58786).

Changes

• Updated factorial(int n) to use BigInteger internally to prevent intermediate integer overflow during multiplication.
• Kept the public API signature public static long catalan(final int n) unchanged.
• Added validation for $n > 35$ (throwing IllegalArgumentException) because $C_{35} = 3,116,285,494,907,301,262$ is the maximum Catalan number representable within a signed 64-bit long ($C_{36} > \text{Long.MAX_VALUE}$).
• Updated CatalanNumbersTest.java with test cases for $n = 11$, $n = 15$, and boundary value $n = 35$, along with testing invalid inputs ($n = 36$).

Verification

• mvn test -Dtest=CatalanNumbersTest passes (15/15 tests passing).
• mvn checkstyle:check passes with 0 violations.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 82.33%. Comparing base (1e59594) to head (8d47d21).

Additional details and impacted files

@@            Coverage Diff            @@
##             master    #7732   +/-   ##
=========================================
  Coverage     82.33%   82.33%           
+ Complexity     8445     8443    -2     
=========================================
  Files           843      843           
  Lines         26154    26154           
  Branches       5108     5109    +1     
=========================================
  Hits          21535    21535           
  Misses         3830     3830           
  Partials        789      789           

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[alxkm]

Looks good. Thanks for the contribution.