EECS12 Homework #2 Due: 11:59 PM, Friday, January 21, 2005
For this assignment you are to create and submit a single Python module; that is, a file with a “.py”
extension containing nothing but Python code (which, of course, includes comments, such as the
standard six-line header). The file must include four (4) function definitions with precisely these
names (including case):
1. CollatzSequence
2. CollatzSearch
3. IsAlphabetic
4. GetTokens
Your file, which must be named “hw2.py,” may also contain other functions and global variables,
but you will be graded exclusively on the correctness and clarity of the four functions named above
(as well as those that they may call). Here is what you need to do:
1. Read chapters 7, 8, and 10 of How to Think Like a Computer Scientist. It is recommended
that you skim all the chapters up through chapter 10, but the ones cited above are particularly
important. Also, it is recommended that you read chapters 2 and 3 in Dive into Python.Be
sure you are familiar with lists and dictionaries, in particular.
2. In 1935 a mathematician name Lothar Collatz defined the following sequence of positive inte-
gers:
an+1 =
undefined if an=1
an/2ifanis even
3an+1 ifanis odd
where a0>1 is specified (i.e. set to anything you like), and the sequence terminates as soon as
the value 1 is attained (which, as far as anybody knows, will always happen eventually). For
example, starting with a0= 3, we get the following sequence: 3, 10, 5, 16, 8, 4, 2, 1. Starting
with a0= 5, we get the following sequence: 5, 16, 8, 4, 2, 1. This type of sequence has come
to be called a Collatz sequence. Note that the length of the Collatz sequence varies wildly and
is impossible to predict from the starting value.
For this part of the assignment you are to define a Python function called CollatzSequence
that takes a single argument, call it N, and returns a list containing the entire Collatz sequence
that begins with a0=N. For example, CollatzSequence( 5 ) should return the list [5,
16, 8, 4, 2, 1 ]. (Do not worry about catching erroneous input, such as non-integer values
of N. You may simply assume that Nwill always be an integer greater than 1, and that the
sequence will always terminate.)
3. Define another function called CollatzSearch, which takes two arguments, let’s call them
num examples and min length (in that order), which are both assumed to be positive integers.
The function CollatzSearch is to search for Collatz sequences whose lengths are equal to or
greater than min length, and it is to find exactly num examples such distinct sequences. The
function is to begin searching at N= 2, incrementing by one and testing each subsequent
value o f Nusing the function CollatzSequence from the previous problem. Each time it
finds a Collatz sequence that is at least as long as min length it is to add the pair (N, S)toa
dictionary,whereNis used as the “key” and Sis the data associated with the key; here Sis to
be the actual Collatz sequence generated by a0=N. When your dictionary contains exactly
num examples entries (which you can test using the len function) the function CollatzSearch
should simply return the dictionary as its function value. For example, CollatzSearch(
1
