Happy number (new algorithm) (#10864)

* Happy number (new algorithm)

adding new algorithm

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* Update maths/special_numbers/happy_number.py

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

* Update happy_number.py

added new changes

* Update happy_number.py

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* Update happy_number.py

* Update happy_number.py

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* Update happy_number.py

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* Update happy_number.py

added ValueError part in code

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* Update happy_number.py

modified and added raise Error code

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* Update happy_number.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

Author: 3 people

maths/special_numbers/happy_number.py

@@ -0,0 +1,48 @@
+def is_happy_number(number: int) -> bool:
+    """
+    A happy number is a number which eventually reaches 1 when replaced by the sum of
+    the square of each digit.
+
+    :param number: The number to check for happiness.
+    :return: True if the number is a happy number, False otherwise.
+
+    >>> is_happy_number(19)
+    True
+    >>> is_happy_number(2)
+    False
+    >>> is_happy_number(23)
+    True
+    >>> is_happy_number(1)
+    True
+    >>> is_happy_number(0)
+    Traceback (most recent call last):
+        ...
+    ValueError: number=0 must be a positive integer
+    >>> is_happy_number(-19)
+    Traceback (most recent call last):
+        ...
+    ValueError: number=-19 must be a positive integer
+    >>> is_happy_number(19.1)
+    Traceback (most recent call last):
+        ...
+    ValueError: number=19.1 must be a positive integer
+    >>> is_happy_number("happy")
+    Traceback (most recent call last):
+        ...
+    ValueError: number='happy' must be a positive integer
+    """
+    if not isinstance(number, int) or number <= 0:
+        msg = f"{number=} must be a positive integer"
+        raise ValueError(msg)
+
+    seen = set()
+    while number != 1 and number not in seen:
+        seen.add(number)
+        number = sum(int(digit) ** 2 for digit in str(number))
+    return number == 1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()