Added the Python function to evaluate the Ackermann function to the session02 directory of my student directory

imdavis · imdavis · commit f6bc32ec9ef1 · 2014-10-12T14:56:51.000-07:00
diff --git a/Students/imdavis/session02/ack.py b/Students/imdavis/session02/ack.py
@@ -0,0 +1,78 @@
+#!/usr/bin/env python2.7
+# -*- coding: utf-8 -*-
+
+"""Example of a recursive function with a good docstring.  
+
+For best results to view the docstring, after importing do:
+  
+  >>> print ack.__doc__
+
+Its value grows rapidly, even for small inputs. For example A(4,2) is an 
+integer of 19,729 decimal digits. May hit maximum recursion limit.  See:
+
+  sys.getrecursionlimit()
+  sys.setrecursionlimit()
+
+"""
+
+def ack(m, n):
+    """Evaluation of the Ackermann Function. 
+
+    The Ackermann Function is defined as:
+    A(m, n) =
+      n+1                 if  m = 0
+      A(m−1, 1)           if  m > 0  and  n = 0
+      A(m−1, A(m, n−1))   if  m > 0  and  n > 0
+
+    Args:
+      m (int): must be >= 0
+      n (int): must be >= 0.
+
+    Yields:
+      Evaluation of Ackermann function for A(m, n)
+
+    """
+
+    if (m < 0 or n < 0):
+        print "Arguments for the Ackermann function must be >= 0."
+        return None
+    elif (m == 0):
+        return n + 1
+    elif (n == 0):
+        return ack(m - 1, 1)
+    else:
+        return ack(m - 1, ack(m, n - 1))
+
+if __name__ == '__main__':
+    TestsPass = True
+    
+    try:
+        assert ack(0, 0) == 1
+        assert ack(0, 1) == 2
+        assert ack(0, 2) == 3
+        assert ack(0, 3) == 4
+        assert ack(0, 4) == 5
+        assert ack(1, 0) == 2
+        assert ack(1, 1) == 3
+        assert ack(1, 2) == 4
+        assert ack(1, 3) == 5
+        assert ack(1, 4) == 6
+        assert ack(2, 0) == 3
+        assert ack(2, 1) == 5
+        assert ack(2, 2) == 7
+        assert ack(2, 3) == 9
+        assert ack(2, 4) == 11
+        assert ack(3, 0) == 5
+        assert ack(3, 1) == 13
+        assert ack(3, 2) == 29
+        assert ack(3, 3) == 61
+        assert ack(3, 4) == 125
+        assert ack(4, 0) == 13
+
+    except AssertionError:
+        TestsPass = False
+        print "All Tests Did Not Pass!"
+
+    if (TestsPass):
+        print "All Tests Pass!"
+
