Fixes: #3869: Optimize solution #2 for Euler's Problem #74

project_euler/problem_074/sol2.py

@@ -20,8 +20,9 @@
 """
 
 
-def factorial(a: int) -> int:
-    """Returns the factorial of the input a
+def factorial(a: int, factorial_cache: dict = {}) -> int:
+    """Returns the factorial of the input a and a cache of factorials
+    of single digits (optionals)
     >>> factorial(5)
     120
 
@@ -31,23 +32,27 @@ def factorial(a: int) -> int:
     >>> factorial(0)
     1
     """
-
     # The factorial function is not defined for negative numbers
     if a < 0:
         raise ValueError("Invalid negative input!", a)
 
     # The case of 0! is handled separately
     if a == 0:
-        return 1
+        temporary_computation = 1
     else:
         # use a temporary support variable to store the computation
         temporary_computation = 1
+        temporary_number = a
+        while temporary_number > 0:
+            temporary_computation *= temporary_number
+            temporary_number -= 1
 
-        while a > 0:
-            temporary_computation *= a
-            a -= 1
+        # save the factorial value, for future reference for the same number
+        # in factorial_sum, e.g., 6666
+    if a < 10:
+        factorial_cache[a] = temporary_computation
 
-        return temporary_computation
+    return temporary_computation, factorial_cache
 
 
 def factorial_sum(a: int) -> int:
@@ -65,8 +70,10 @@ def factorial_sum(a: int) -> int:
         convert the digit back into an int
         and add its factorial to fact_sum.
     """
+    factorial_cache = {}
     for i in str(a):
-        fact_sum += factorial(int(i))
+        factorial_value, factorial_cache = factorial(int(i), factorial_cache)
+        fact_sum += factorial_value
 
     return fact_sum