From 5894554d41116af83152b1ea59fbf78303d87966 Mon Sep 17 00:00:00 2001
From: Jordan Rinder <jrinder42@users.noreply.github.com>
Date: Sat, 8 Oct 2022 18:28:17 -0400
Subject: [PATCH] Add Catalan number to maths (#6845)

* Add Catalan number to maths

* updating DIRECTORY.md

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 DIRECTORY.md            |  4 +++-
 maths/catalan_number.py | 51 +++++++++++++++++++++++++++++++++++++++++
 2 files changed, 54 insertions(+), 1 deletion(-)
 create mode 100644 maths/catalan_number.py

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 64e9d5333..668da4761 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -475,6 +475,7 @@
   * [Binomial Coefficient](maths/binomial_coefficient.py)
   * [Binomial Distribution](maths/binomial_distribution.py)
   * [Bisection](maths/bisection.py)
+  * [Catalan Number](maths/catalan_number.py)
   * [Ceil](maths/ceil.py)
   * [Check Polygon](maths/check_polygon.py)
   * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py)
@@ -632,8 +633,9 @@
 
 ## Physics
   * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py)
-  * [Lorenz Transformation Four Vector](physics/lorenz_transformation_four_vector.py)
+  * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py)
   * [N Body Simulation](physics/n_body_simulation.py)
+  * [Newtons Law Of Gravitation](physics/newtons_law_of_gravitation.py)
   * [Newtons Second Law Of Motion](physics/newtons_second_law_of_motion.py)
 
 ## Project Euler
diff --git a/maths/catalan_number.py b/maths/catalan_number.py
new file mode 100644
index 000000000..4a1280a45
--- /dev/null
+++ b/maths/catalan_number.py
@@ -0,0 +1,51 @@
+"""
+
+Calculate the nth Catalan number
+
+Source:
+    https://en.wikipedia.org/wiki/Catalan_number
+
+"""
+
+
+def catalan(number: int) -> int:
+    """
+    :param number: nth catalan number to calculate
+    :return: the nth catalan number
+    Note: A catalan number is only defined for positive integers
+
+    >>> catalan(5)
+    14
+    >>> catalan(0)
+    Traceback (most recent call last):
+    ...
+    ValueError: Input value of [number=0] must be > 0
+    >>> catalan(-1)
+    Traceback (most recent call last):
+    ...
+    ValueError: Input value of [number=-1] must be > 0
+    >>> catalan(5.0)
+    Traceback (most recent call last):
+    ...
+    TypeError: Input value of [number=5.0] must be an integer
+    """
+
+    if not isinstance(number, int):
+        raise TypeError(f"Input value of [number={number}] must be an integer")
+
+    if number < 1:
+        raise ValueError(f"Input value of [number={number}] must be > 0")
+
+    current_number = 1
+
+    for i in range(1, number):
+        current_number *= 4 * i - 2
+        current_number //= i + 1
+
+    return current_number
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()