CS 1MD3 - Winter 2006 - Assignment #3

Generated for Student ID: 0470107

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 non-destructive reverseList function, as a recursive function.
Input parameter: a list, L.
Output: A new list which contains the elements of L in reverse order.
Notes: Operates recursively and leaves the original list intact.

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.
Write a one-line function which accepts a relation (a set of 2-element tuples), and
returns True if R is symmetric, and False if it is not.

Question 3:

Write a one-line function that accepts a dictionary and value and returns the set of
keys associated with that value.  Use a list comprehension.