added new solution

Author: SanjarH

ackerman_function.py

@@ -0,0 +1,48 @@
+from __future__ import  division
+# Learn Python together
+""" Write a function that evaluetes the Ackermann funtion"""
+
+# Solution 1 with limited input numbers
+def ackermann(m, n):
+    if m == 0: 
+        return n + 1
+    elif m > 0 and n == 0: 
+        return ackermann(m - 1, 1)  
+    elif m > 0 and n > 0:
+        return ackermann(m - 1, ackermann(m, n - 1))
+    else:
+        return 0
+
+print(ackermann(3,4)) 
+# Output -> 125
+print(ackermann(3,7)) 
+# Output -> RecursionError: maximum recursion depth exceeded in comparison
+
+# Solution 2 using memoization
+
+cache = {} # empty dictionary for storing results
+
+def ackermann_memo(m, n):
+    if m == 0:
+        return n+1
+    
+    if n == 0:
+        # return recursively function with (m-1,1)
+        return ackermann_memo(m-1, 1)
+    # If the result of this function call has been previously calculated
+    if (m, n) in cache: 
+        # return the stored result from the dictionary
+        return cache[m, n]  
+    else:
+        # otherwise return current recusive function result in the dictionary
+        cache[m, n] = ackermann_memo(m-1, ackermann_memo(m, n-1))
+        return cache[m, n]
+
+# check
+print(ackermann_memo(3, 7))
+# output-> 1021
+print(ackermann_memo(3, 8))
+# output-> 2045
+print(ackermann_memo(4, 8))
+# output-> RecursionError: maximum recursion depth exceeded in comparison
+# Do you know why ?