Ian M. Davis Homework

Students/imdavis/session01/buildgrid.py

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+# a function which takes on a single argument defining the size
+# of a grid to draw
+
+def print_grid(gridsize):
+    # define the top and bottom portion of a single grid cell
+    corner = "+"
+    midtopbot = 4 * "-"
+
+    # define the center of a single grid cell
+    gridcenter = "|" + 4 * " "
+
+    # define how to draw the complete top, bottom, and middle of the 
+    # full grid in a single direction
+    topbot = gridsize * (corner + midtopbot) + corner
+    center = gridsize * gridcenter + "|"
+
+    # build the grid in one direction
+    onedirgrid = topbot + "\n"
+    onedirgrid += 4 * (center + "\n")
+
+    #build the full grid
+    grid = gridsize * onedirgrid + topbot
+
+    # now print the grid
+    print grid
+

Students/imdavis/session01/drawgrid.py

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+# draws a grid using the buildgrid function after prompting the
+# user for the size of the grid
+
+import buildgrid
+
+try:
+    size = int(raw_input("What size grid would you like to build? "))
+    buildgrid.print_grid(size)
+except ValueError:
+    print "Please enter an integer!"

Students/imdavis/session02/ack.py

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+#!/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!"
+

Students/imdavis/session02/series.py

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+#!/usr/bin/env python2.7
+# -*- coding: utf-8 -*-
+
+def fibonacci(n):
+    """Evaluation of the nth term of the Fibonnaci Series. 
+
+    The Fibonnaci Series is defined as:
+      0th term: 0
+      1st term: 1
+      nth term: sum of previous two terms in the series
+
+    Args:
+      n (int): nth term in series (must be >= 0)
+
+    Yields:
+      nth term of the Fibonnaci Series.
+
+    """
+
+    if (n < 0):
+        print "Arguments for the Fibonnaci series must be >= 0."
+        return None
+    elif (n == 0):  # zeroth term = 0
+        return 0
+    elif (n == 1):  # first term = 1
+        return 1
+    else:
+        return fibonacci(n - 1) + fibonacci(n - 2)
+
+def lucas(n):
+    """Evaluation of the nth term of the Lucas Series. 
+
+    The Lucas Series is defined as:
+      0th term: 2
+      1st term: 1
+      nth term: sum of previous two terms in the series
+
+    Args:
+      n (int): nth term in series (must be >= 0)
+
+    Yields:
+      nth term of the Lucas Series.
+
+    """
+
+    if (n < 0):
+        print "Arguments for the Lucas series must be >= 0."
+        return None
+    elif (n == 0):  # zeroth term = 0
+        return 2
+    elif (n == 1):  # first term = 1
+        return 1
+    else:
+        return lucas(n - 1) + lucas(n - 2)
+
+def sum_series(n, zerothTerm=0, firstTerm=1):
+    """Evaluation of the nth term of a series. 
+
+    This function will return the nth term in a series which is the sum
+    of the previous two consecutive terms in the series. The user can 
+    specify any zeroth and first terms to define the series, or can use 
+    the default values of 0 and 1 to give the n-th term of the
+    Fibonacci series.
+
+    Args:
+      n (int): nth term in series (must be >= 0)
+      zerothTerm (int): zeroth term in the series (default = 0)
+      firstTerm (int): first term in the series (default = 1)
+
+    Yields:
+      nth term of the series.
+
+    """
+
+    if (n < 0):
+        print "Arguments for the series must be >= 0."
+        return None
+    elif (n == 0):
+        return zerothTerm
+    elif (n == 1):
+        return firstTerm
+    else:
+        return sum_series(n - 1, zerothTerm, firstTerm) + sum_series(n - 2, zerothTerm, firstTerm)
+
+
+if __name__ == '__main__':
+    FibanocciTestsPass = True
+    LucasTestsPass = True
+    ArbitrarySeriesTestsPass = True
+
+    # Some assertions to test the Fibonacci series function against known solutions
+    try:
+        assert fibonacci(0) == 0
+        assert fibonacci(1) == 1
+        assert fibonacci(10) == 55
+        assert fibonacci(19) == 4181
+
+    except AssertionError:
+        FibanocciTestsPass = False
+        print "All Fibonacci Tests Did Not Pass!"
+
+    # Some assertions to test the Lucas series function against known solutions
+    try:
+        assert lucas(0) == 2
+        assert lucas(1) == 1
+        assert lucas(10) == 123
+        assert lucas(20) == 15127
+
+    except AssertionError:
+        LucasTestsPass = False
+        print "All Lucas Tests Did Not Pass!"
+
+    # Some assertions to test the arbitrary series function against known solutions
+    try:
+        assert sum_series(10) == 55
+        assert sum_series(10, 0, 1) == 55
+        assert sum_series(10, 2, 1) == 123
+        assert sum_series(15, 3, 3) == 2961
+        assert sum_series(20, 5, 2) == 34435
+        assert sum_series(20, 2, 5) == 42187
+
+    except AssertionError:
+        ArbitrarySeriesTestsPass = False
+        print "All aritrary series tests did not pass"
+
+    if (FibanocciTestsPass and LucasTestsPass and ArbitrarySeriesTestsPass):
+        print "All Tests Pass!"