Advanced Programming, Jan-Apr 2015
                  Assignment 1, due 18 Jan 2015

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Instructions:

1. For each question, write a separate Python program with the
   filename indicated in the question.

   Zip your solutions into a single archive.  Use your CMI
   username to name the zip file (e.g. "madhavan.zip") and submit
   the zip file via moodle.

   If you don't name your zip file or the enclosed Python file
   correctly, you risk losing marks.

2. If the question asks for a function, you *must* write a
   function in Python (i.e., def f(x): ... )  Ensure that the
   function you define has the name indicated in the question.
   Also ensure that your function returns the value asked for,
   rather than printing it.

   If you add code to your file to test your function, make sure
   you *remove* this code when you submit your solution.  The
   Python file you submit should have *only* the function
   definition.

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1. Filename: primes.py

   Write a Python function "primes" such that primes(n) returns
   the list of primes less than or equal to n, in ascending order.

2. Filename: nthprime.py

   Write a Python function "nthprime" such that nthprime(k)
   computes the k-th prime in the sequence {2,3,5,7,11,...},
   starting with index 0.

   For instance  nthprime(1) should return 3, nthprime(5) should
   return 13 etc. 

3. Filename: sqroot.py

   Write a function to compute (positive) square roots upto a
   given accuracy using binary search.  Given x, not necessarily
   an integer, and a tolerance delta, the initial interval for
   the square root of x is [0..1] if x < 1 and [0..x] if x >= 1.  
   Start with an estimate e = x/2 for the square root of x.
   Repeatedly halve the interval, as appropriate, until
   |x - e**2| <= delta.  You may assume that x > 0 and delta > 0.

   Your function should be called "sqroot" and should take two
   parameters, x and delta, in that order.

4, Filename: overlap.py

   Write a function "overlap" that takes two lists of integers
   and returns the number of distinct values that occur in both
   lists.  For instance;

   - overlap([1,3,4,7],[9,13,7,5,1,2]) should return 2 ("1" and
       "7" are common)

   - overlap([2,3,2,1],[4,2,5,2]) should return 1 (the value "2"
       is common, ignoring multiplicites)

   Hint: Python has a built-in sort function for lists.
     
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