solved recursively and tested. updated iterative solution with new te…

…st. -@iamserda

neetcodeio/algostructybeginners/Lv3-Recursion/factorial_iterative.py

@@ -1,8 +1,18 @@
 def factorial(n):
+    if n < 0:
+        return
     result = 1
     for i in range(1, n + 1):
         result *= i
     return result
 
 
+# TESTING ARENA
 assert factorial(5) == 5 * 4 * 3 * 2 * 1
+assert factorial(10) == 3628800
+assert factorial(0) == 1
+assert factorial(1) == 1
+assert (
+    factorial(100)
+    == 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
+)

neetcodeio/algostructybeginners/Lv3-Recursion/factorial_recursive.py

@@ -0,0 +1,33 @@
+def factorial(num):
+    # base case, stops the recursion.
+    if num <= 1:
+        return 1
+    else:
+        # recursive case
+        return num * factorial(num - 1)
+
+
+# n! = n * (n-1)!
+# 1! = 1
+# 0! = 1
+# Space complexity is O(n) because we are stacking
+# each recursive call pending until we find a base case
+# where num is 1 or num is 0.
+
+# A never ending recursion leads to memory stack,
+# area of memory where function data are stored
+# temporarily while the function is running.
+# Too many of these recursive-calls will eventually lead to
+# a stack overflow, too much data on
+
+assert factorial(5) == 5 * 4 * 3 * 2 * 1
+assert factorial(10) == 3628800
+assert factorial(0) == 1
+assert factorial(1) == 1
+assert (
+    factorial(100)
+    == 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
+)
+
+ans = str(factorial(10))
+print(ans, len(ans))