Adding session02 homework

Students/RPerkins/session02/ack.py

@@ -0,0 +1,46 @@
+__author__ = 'Robert W. Perkins'
+
+
+def ack(m, n):
+    """Return the result of the Ackermann function on m and n"""
+    if m < 0 or n < 0:
+        return None
+    elif m == 0:
+        return n+1
+    elif m > 0 and n == 0:
+        return ack(m-1, 1)
+    elif m > 0 and n > 0:
+        return ack(m-1, ack(m, n-1))
+
+# Testing Block
+if __name__ == "__main__":
+    assert ack(-1, 2) is None
+    assert ack(2, -1) is None
+    assert ack(-1, -1) is None
+    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
+    #  max recursion depth exceeded after this point
+    #assert ack(4, 0) == 2**2**2-3
+    #assert ack(4, 1) == 2**2**2**2-3
+    #assert ack(4, 2) == (2**65536)-3
+    #assert ack(4, 3) == (2**2**65536)-3
+    #assert ack(4, 4) == (2**2**2**65536)-3
+    print 'All tests passed'

Students/RPerkins/session02/series.py

@@ -0,0 +1,93 @@
+__author__ = 'Robert W. Perkins'
+
+
+def fibonacci(n):
+    """Return the 'n'th value in the Fibonacci series"""
+
+# test for input in valid range
+    if n < 0:
+        return None
+
+# test for n == 0
+    if n == 0:
+        return 0
+
+# base case is n == 1
+    if n == 1:
+        return 1
+    else:
+        return fibonacci(n-1) + fibonacci(n-2)
+
+def lucas(n):
+    """Return the 'n'th value in the Lucas number series"""
+
+# test for input in valid range
+    if n < 0:
+        return None
+
+# test for n == 0
+    if n == 0:
+        return 2
+
+# base case is n == 1
+    if n == 1:
+        return 1
+    else:
+        return lucas(n-1) + lucas(n-2)
+
+def sum_series(n,first=0,second=1):
+    """Return the 'n'th value of a variable series"""
+
+    """The first two numbers are passed via "first" and "second"
+    and each subsequent element is the sum of the 'n-1'th and 'n-2'th element (yes, i said tooth)"""
+
+# test for input in valid range
+    if n < 0:
+        return None
+
+# test for n == 0
+    if n == 0:
+        return first
+
+# base case is n == 1
+    if n == 1:
+        return second
+    else:
+        return sum_series(n-1,first,second) + sum_series(n-2,first,second)
+
+
+# Testing Block
+if __name__ == "__main__":
+
+    # test fibonacci function for out of range, n == zero, base case, and 18th value in series
+    assert fibonacci(-3) is None
+    assert fibonacci(0) == 0
+    assert fibonacci(1) == 1
+    assert fibonacci(17) == 1597
+
+    # test lucas function for out of range, n == zero, base case, and 11th value in series
+    assert lucas(-3) is None
+    assert lucas(0) == 2
+    assert lucas(1) == 1
+    assert lucas(10) == 123
+
+    # tests sum_series function for fibonacci behavior with no optional params
+    # for out of range, n == zero, base case, and 18th value in series
+    assert sum_series(-3) is None
+    assert sum_series(0) == 0
+    assert sum_series(1) == 1
+    assert sum_series(17) == 1597
+
+	# tests sum_series function for lucas behavior with lucas series params
+	# for out of range, n == zero, base case, and 11th value in series
+    assert sum_series(-3,2,1) is None
+    assert sum_series(0,2,1) == 2
+    assert sum_series(1,2,1) == 1
+    assert sum_series(10,2,1) == 123
+
+	# tests sum_series function for valid results with optional params
+	# for out of range, n == zero, base case, and 11th value in series
+    assert sum_series(-3,4,2) is None
+    assert sum_series(0,4,2) == 4
+    assert sum_series(1,4,2) == 2
+    assert sum_series(10,4,2) == 246