sum of factorial (#34)

* sum of factorial

* Formatted with psf/black

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

Author: realDuYuanChao

maths/sum_of_factorial.py

@@ -0,0 +1,69 @@
+def sum_of_factorial(number: int) -> int:
+    """
+    >>> sum_of_factorial(0)
+    0
+    >>> sum_of_factorial(1)
+    1
+    >>> sum_of_factorial(2)
+    3
+    >>> sum_of_factorial(5)
+    153
+    """
+    sum_factorial = 0
+    factorial = 1
+    for i in range(1, number + 1):
+        factorial *= i
+        sum_factorial = sum_factorial + factorial
+
+    return sum_factorial
+
+
+def sum_of_factorial_circle_plus_recursion(number: int) -> int:
+    """
+    >>> sum_of_factorial_circle_plus_recursion(0)
+    0
+    >>> sum_of_factorial_circle_plus_recursion(1)
+    1
+    >>> sum_of_factorial_circle_plus_recursion(2)
+    3
+    >>> sum_of_factorial_circle_plus_recursion(5)
+    153
+    """
+    sum_factorial = 0
+    from math import factorial
+
+    for i in range(1, number + 1):
+        sum_factorial += factorial(i)
+    return sum_factorial
+
+
+def sum_of_factorial_pure_recursion(number: int) -> int:
+    """
+    >>> sum_of_factorial_pure_recursion(0)
+    0
+    >>> sum_of_factorial_pure_recursion(1)
+    1
+    >>> sum_of_factorial_pure_recursion(2)
+    3
+    >>> sum_of_factorial_pure_recursion(5)
+    153
+    """
+    if number == 1 or number == 0:
+        return number  # 1! or 0!
+    elif number == 2:
+        return 3  # 1! + 2!
+    else:
+        return (
+            sum_of_factorial_pure_recursion(number - 1)
+            + (
+                sum_of_factorial_pure_recursion(number - 1)
+                - sum_of_factorial_pure_recursion(number - 2)
+            )
+            * number
+        )
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()