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Add catalan number #13252

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DivyanshRajSoni
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Describe your change:

  • Add an algorithm?
  • Fix a bug or typo in an existing algorithm?
  • Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
  • Documentation change?

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All function parameters and return values are annotated with Python type hints.
  • All functions have doctests that pass the automated testing.
  • All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
  • If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing
    keyword    : "Fixes #ISSUE-NUMBER".

Implementation: Added maths/catalan_number.py with three different approaches:

  • Dynamic programming (O(n²))
  • Recursive with memoization (O(n²))
  • Binomial coefficient formula (O(n))

Testing: 18 passing doctests covering valid inputs and error cases

Reference: https://en.wikipedia.org/wiki/Catalan_number

DivyanshRajSoni and others added 5 commits October 5, 2025 08:24
@DivyanshRajSoni
Update README.md
52ac662 
Enhanced README.md file
@DivyanshRajSoni
Update README.md
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@DivyanshRajSoni
Merge pull request #1 from DivyanshRajSoni/DivyanshRajSoni-patch-11
81496db 
Update README.md
@DivyanshRajSoni
Add Catalan number algorithm with three implementations
3a6c6f6 
Implements Catalan number calculation using:
- Dynamic programming approach
- Recursive with memoization
- Binomial coefficient formula

Includes 18 passing doctests, type hints, and comprehensive documentation.
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@DivyanshRajSoni
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Please Sir , Merge it ...

@Tarannum9623
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Hi! Can you help me by telling why my build test is failing, I want to contribute search_in_a_rotated_sorted_array in search directory and my build test failed.
PR: Search in rotated sorted array #13245

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@DivyanshRajSoni @Tarannum9623