Implementation for Trimorphic Number (#14229)

* Add implementation for Trimorphic Number

An algorithm that checks if a number is trimorphic, which is a number whose cube ends with the same digits as the number itself

* Add doctests for is_trimorphic function

Added doctests for the is_trimorphic function to validate its behavior with various inputs, including edge cases.

* Enhance docstring for is_trimorphic function

Added parameter and return type documentation to is_trimorphic function.

* Rename trimorphic_number.py to maths/special_numbers/trimorphic_number.py

* updating DIRECTORY.md

---------

Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: Diogenis15

DIRECTORY.md

@@ -695,6 +695,7 @@
   * Forecasting
     * [Run](machine_learning/forecasting/run.py)
   * [Frequent Pattern Growth](machine_learning/frequent_pattern_growth.py)
+  * [Gaussian Mixture Model](machine_learning/gaussian_mixture_model.py)
   * [Gaussian Naive Bayes](machine_learning/gaussian_naive_bayes.py)
   * [Gradient Boosting Classifier](machine_learning/gradient_boosting_classifier.py)
   * [Gradient Boosting Regressor](machine_learning/gradient_boosting_regressor.py)
@@ -742,6 +743,7 @@
   * [Bailey Borwein Plouffe](maths/bailey_borwein_plouffe.py)
   * [Base Neg2 Conversion](maths/base_neg2_conversion.py)
   * [Basic Maths](maths/basic_maths.py)
+  * [Bearing](maths/bearing.py)
   * [Binary Exponentiation](maths/binary_exponentiation.py)
   * [Binary Multiplication](maths/binary_multiplication.py)
   * [Binomial Coefficient](maths/binomial_coefficient.py)
@@ -878,6 +880,7 @@
     * [Hexagonal Numbers](maths/series/hexagonal_numbers.py)
     * [Logarithmic Series](maths/series/logarithmic_series.py)
     * [P Series](maths/series/p_series.py)
+  * [Shoelace Area](maths/shoelace_area.py)
   * [Sieve Of Atkin](maths/sieve_of_atkin.py)
   * [Sieve Of Eratosthenes](maths/sieve_of_eratosthenes.py)
   * [Sigmoid](maths/sigmoid.py)
@@ -909,6 +912,7 @@
     * [Pronic Number](maths/special_numbers/pronic_number.py)
     * [Proth Number](maths/special_numbers/proth_number.py)
     * [Triangular Numbers](maths/special_numbers/triangular_numbers.py)
+    * [Trimorphic Number](maths/special_numbers/trimorphic_number.py)
     * [Ugly Numbers](maths/special_numbers/ugly_numbers.py)
     * [Weird Number](maths/special_numbers/weird_number.py)
   * [Sum Of Arithmetic Series](maths/sum_of_arithmetic_series.py)

maths/special_numbers/trimorphic_number.py

@@ -0,0 +1,53 @@
+"""
+A Trimorphic Number is a number whose cube ends in the same digits as the number itself.
+For example, 4^3 = 64, which ends in 4.
+
+Reference: https://en.wikipedia.org/wiki/Automorphic_number#Trimorphic_numbers
+"""
+
+
+def is_trimorphic(number: int) -> bool:
+    """
+    Checks if a number is a Trimorphic number.
+
+    :param number: The number to check
+    :return: True if the number is trimorphic, False otherwise
+    :raises ValueError: If the input number is negative
+
+    >>> is_trimorphic(0)
+    True
+    >>> is_trimorphic(1)
+    True
+    >>> is_trimorphic(4)
+    True
+    >>> is_trimorphic(5)
+    True
+    >>> is_trimorphic(24)
+    True
+    >>> is_trimorphic(249)
+    True
+    >>> is_trimorphic(2)
+    False
+    >>> is_trimorphic(7)
+    False
+    >>> is_trimorphic(10)
+    False
+    >>> is_trimorphic(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input must be a non-negative integer
+    """
+    if number < 0:
+        raise ValueError("Input must be a non-negative integer")
+
+    if number == 0:
+        return True
+
+    cube = number**3
+    return str(cube).endswith(str(number))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()