CS 1MD3 - Winter 2006 - Assignment #3

Generated for Student ID: 0545760

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:

Implement the sumList function (same as sum() for lists) as a recursive function--obviously
without using sum() itself.

Question 2:

The graph of a (mathematical) function is the set of all pairs (x,y) such that 
x is in the domain of f (i.e. the set of values over which f is defined), and y = f(x).
Write a one-line Python function, dom, which accepts the graph of a mathematical function 
(i.e. a set of ordered pairs) and returns its domain.

Question 3:

Write a one-line function which accepts a dictionary and returns True if no two
keys map to the same value; False otherwise.

Question 4:

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.