CS 1MD3 - Winter 2006 - Assignment #3

Generated for Student ID: 0564014

Due Date: Monday, February 27th

(You are responsible for verifying that your student number is correct!)
The following exercises involve writing very short (but tricky) functions to manipulate data structures. One of them is a recursive function which may be written in only three lines, while the rest may be written in only one line each (and are not recursive). Function signatures (the "def functionName(x,y,z):" lines) are not counted when enumerating the number of lines. So in this context, a "one-line function" actually occupies two lines: the signature on the first line, and the body on the next line.

Note: Not all students get the same number of questions because some questions are more difficult than others. We have tried to make all the assignments of roughly equal difficulty.

Question 1:

Write a recursive function to combine a list of dictionaries into one.
The function should accept a list of dictionaries [d1, d2, ..., dn].
It should return a new dictionary containing everything from d1 through dn.
If there are any keys in common among the dictionaries, the value from the last one should
be used in the new dictionary.  For example, if d3['cs1md3']=='dilatory',
d5['cs1md3']=='delightful', then the new dictionary should use the value from d5.  In other
words later dictionaries override previous dictionaries.

Question 2:

A (binary) "symmetric relation," R, is a set of ordered pairs, (x,y), such that 
if (x,y) is in R, then so is (y,x).  For example, the relation
R1 = {(1,2), (3,4), (2,1), (5,5)} is not symmetric, while the relation
R2 = {(1,2), (3,4), (2,1), (5,5), (4,3)} is symmetric.
The "symmetric closure" of a relation, R, is the smallest symmetric relation
which contains R as a subset.  In other words, it's what you get after you add
any "missing" symmetric pairs to the relation.  R2 is the symmetric closure of R1
in the examples above.
Write a one-line function which accepts a relation (a set of 2-element tuples), and
returns its symmetric closure.

Question 3:

Write a one-line function called invertDictionary that accepts a dictionary and 
returns a copy of it with the keys and values interchanged.  For example, suppose
d1 = {1: 'a', 2: 'b', 3: 'c'}.
Then the command d2 = invertDictionary(d1), would produce:
d2 = {'a': 1, 'b': 2, 'c': 3}.
You may assume that no two keys in the given dictionary map to the same value.