From f6bc32ec9ef133453abd29c25c6d3d296fac87e0 Mon Sep 17 00:00:00 2001 From: "Ian M. Davis" Date: Sun, 12 Oct 2014 14:56:51 -0700 Subject: [PATCH 1/6] Added the Python function to evaluate the Ackermann function to the session02 directory of my student directory --- Students/imdavis/session02/ack.py | 78 +++++++++++++++++++++++++++++++ 1 file changed, 78 insertions(+) create mode 100755 Students/imdavis/session02/ack.py diff --git a/Students/imdavis/session02/ack.py b/Students/imdavis/session02/ack.py new file mode 100755 index 00000000..f428daf3 --- /dev/null +++ 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!" + From 162ed4d4d47226fea8fff3d91f5e51a1de199b19 Mon Sep 17 00:00:00 2001 From: "Ian M. Davis" Date: Sun, 12 Oct 2014 15:51:48 -0700 Subject: [PATCH 2/6] First commit of series.py function. Calculates Fibanocci series up to 20th term correctly. Contains a useful docstring and some assertions for some basic testing. --- Students/imdavis/session02/series.py | 46 ++++++++++++++++++++++++++++ 1 file changed, 46 insertions(+) create mode 100755 Students/imdavis/session02/series.py diff --git a/Students/imdavis/session02/series.py b/Students/imdavis/session02/series.py new file mode 100755 index 00000000..dfcc77ed --- /dev/null +++ b/Students/imdavis/session02/series.py @@ -0,0 +1,46 @@ +#!/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: recursive fibonacci(n-1) + fibonacci(n) + + Args: + n (int): 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) + + +if __name__ == '__main__': + FibanocciTestsPass = True + + 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!" + + if (FibanocciTestsPass): + print "All Tests Pass!" + From de1962bb8b5090500c9ff93d2b58e0294806eccf Mon Sep 17 00:00:00 2001 From: "Ian M. Davis" Date: Sun, 12 Oct 2014 16:09:55 -0700 Subject: [PATCH 3/6] Commit of series.py after adding a new function to evaluate the nth term of the lucas function. Checked that it gives the correct result up to the 20th term of the Lucas fuction. Added some basic assertion tests. --- Students/imdavis/session02/series.py | 41 ++++++++++++++++++++++++++-- 1 file changed, 39 insertions(+), 2 deletions(-) diff --git a/Students/imdavis/session02/series.py b/Students/imdavis/session02/series.py index dfcc77ed..8cf261c3 100755 --- a/Students/imdavis/session02/series.py +++ b/Students/imdavis/session02/series.py @@ -7,7 +7,7 @@ def fibonacci(n): The Fibonnaci Series is defined as: 0th term: 0 1st term: 1 - nth term: recursive fibonacci(n-1) + fibonacci(n) + nth term: sum of previous two terms in the series Args: n (int): must be >= 0 @@ -27,9 +27,36 @@ def fibonacci(n): 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): 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) + if __name__ == '__main__': FibanocciTestsPass = True + LucasTestsPass = True try: assert fibonacci(0) == 0 @@ -41,6 +68,16 @@ def fibonacci(n): FibanocciTestsPass = False print "All Fibonacci Tests Did Not Pass!" - if (FibanocciTestsPass): + 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!" + + if (FibanocciTestsPass and LucasTestsPass): print "All Tests Pass!" From 6cf06d7f50f27ad1c5938e30477f81691579587a Mon Sep 17 00:00:00 2001 From: "Ian M. Davis" Date: Sun, 12 Oct 2014 21:20:18 -0700 Subject: [PATCH 4/6] Added the sum_series function to the series.py module. Has default zeroth and first terms to give the nth term of the Fibonacci series. Will give nth term of arbitrary series given users specified zeroth and first terms to work from. Some basic assertion tests to show it computes the correct nth term in the series and a docstring giving some details on what the function does. --- Students/imdavis/session02/series.py | 56 +++++++++++++++++++++++++--- 1 file changed, 50 insertions(+), 6 deletions(-) diff --git a/Students/imdavis/session02/series.py b/Students/imdavis/session02/series.py index 8cf261c3..69b7b434 100755 --- a/Students/imdavis/session02/series.py +++ b/Students/imdavis/session02/series.py @@ -10,7 +10,7 @@ def fibonacci(n): nth term: sum of previous two terms in the series Args: - n (int): must be >= 0 + n (int): nth term in series (must be >= 0) Yields: nth term of the Fibonnaci Series. @@ -25,7 +25,7 @@ def fibonacci(n): elif (n == 1): # first term = 1 return 1 else: - return fibonacci(n-1) + fibonacci(n-2) + return fibonacci(n - 1) + fibonacci(n - 2) def lucas(n): """Evaluation of the nth term of the Lucas Series. @@ -36,7 +36,7 @@ def lucas(n): nth term: sum of previous two terms in the series Args: - n (int): must be >= 0 + n (int): nth term in series (must be >= 0) Yields: nth term of the Lucas Series. @@ -51,13 +51,44 @@ def lucas(n): elif (n == 1): # first term = 1 return 1 else: - return lucas(n-1) + lucas(n-2) + 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 @@ -68,6 +99,7 @@ def lucas(n): 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 @@ -78,6 +110,18 @@ def lucas(n): LucasTestsPass = False print "All Lucas Tests Did Not Pass!" - if (FibanocciTestsPass and LucasTestsPass): - print "All Tests 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!" From 003ca7fb4752236a84dcc3e51248fbc0d730d7b5 Mon Sep 17 00:00:00 2001 From: "Ian M. Davis" Date: Sun, 12 Oct 2014 21:30:17 -0700 Subject: [PATCH 5/6] For completeness, push up the homework assignment from the first session as well. --- Students/imdavis/session01/buildgrid.py | 26 +++++++++++++++++++++++++ Students/imdavis/session01/drawgrid.py | 10 ++++++++++ 2 files changed, 36 insertions(+) create mode 100644 Students/imdavis/session01/buildgrid.py create mode 100644 Students/imdavis/session01/drawgrid.py diff --git a/Students/imdavis/session01/buildgrid.py b/Students/imdavis/session01/buildgrid.py new file mode 100644 index 00000000..00e9c5b5 --- /dev/null +++ b/Students/imdavis/session01/buildgrid.py @@ -0,0 +1,26 @@ +# 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 + diff --git a/Students/imdavis/session01/drawgrid.py b/Students/imdavis/session01/drawgrid.py new file mode 100644 index 00000000..e66fd49e --- /dev/null +++ b/Students/imdavis/session01/drawgrid.py @@ -0,0 +1,10 @@ +# 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!" \ No newline at end of file From ab822ab94f5691312c8af2068166c40a792c2b5d Mon Sep 17 00:00:00 2001 From: "Ian M. 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