Add new persistence algorithm (#4751)

* Created new persistence algorithm

* Update persistence.py

* Added another persistence function

maths/persistence.py

@@ -0,0 +1,82 @@
+def multiplicative_persistence(num: int) -> int:
+    """
+    Return the persistence of a given number.
+
+    https://en.wikipedia.org/wiki/Persistence_of_a_number
+
+    >>> multiplicative_persistence(217)
+    2
+    >>> multiplicative_persistence(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: multiplicative_persistence() does not accept negative values
+    >>> multiplicative_persistence("long number")
+    Traceback (most recent call last):
+        ...
+    ValueError: multiplicative_persistence() only accepts integral values
+    """
+
+    if not isinstance(num, int):
+        raise ValueError("multiplicative_persistence() only accepts integral values")
+    if num < 0:
+        raise ValueError("multiplicative_persistence() does not accept negative values")
+
+    steps = 0
+    num_string = str(num)
+
+    while len(num_string) != 1:
+        numbers = [int(i) for i in num_string]
+
+        total = 1
+        for i in range(0, len(numbers)):
+            total *= numbers[i]
+
+        num_string = str(total)
+
+        steps += 1
+    return steps
+
+
+def additive_persistence(num: int) -> int:
+    """
+    Return the persistence of a given number.
+
+    https://en.wikipedia.org/wiki/Persistence_of_a_number
+
+    >>> additive_persistence(199)
+    3
+    >>> additive_persistence(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: additive_persistence() does not accept negative values
+    >>> additive_persistence("long number")
+    Traceback (most recent call last):
+        ...
+    ValueError: additive_persistence() only accepts integral values
+    """
+
+    if not isinstance(num, int):
+        raise ValueError("additive_persistence() only accepts integral values")
+    if num < 0:
+        raise ValueError("additive_persistence() does not accept negative values")
+
+    steps = 0
+    num_string = str(num)
+
+    while len(num_string) != 1:
+        numbers = [int(i) for i in num_string]
+
+        total = 0
+        for i in range(0, len(numbers)):
+            total += numbers[i]
+
+        num_string = str(total)
+
+        steps += 1
+    return steps
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()