## Description

You will modify your implementation of the FMap

Collaboration between students is forbidden on this assignment. You are responsible for keeping your code hidden from all other students. Turn in your work on this assignment before 11:59 pm on the due date by following instructions on the course’s main assignments web page, http://www.ccs.neu.edu/course/cs3500sp13/Assignments.html.

Your file of Java code should begin with a block comment that lists

1. Your name, as you want the instructor to write it.

2. Your email address.

3. Any remarks that you wish to make to the instructor.

Part of your grade will depend on the quality, correctness, and efficiency of your code, part will depend on your adherence to object-oriented programming style and idioms as taught in this course, part will depend on the readability of your code (comments and indentation), and part will depend on how well you follow the procedure above for submitting your work. Assignments submitted between 12:00 am and 11:59 pm the day after the due date will receive a 20 percentage point penalty on the assignment.

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Your assignment is to write the code for a single file, FMap.java, that implements the specification below as well as the specification of assignments 4, 5, 7, and 8.

You will be given two files in /course/cs3500sp13/Assignments/A9:

Visitor.java

TestFMap.java

The Visitor.java file defines the Visitor

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Specification of the FMap

The FMap

Performance requirements:

Suppose c is a comparator that runs in O(1) time, m is an FMap

m.put(k,v) should run in O(lg n) time

m.isEmpty() should run in O(1) time

m.size() should run in O(1) time

m.containsKey(k) should run in O(lg n) time

m.containsValue(k) should run in O(n) time

m.get(k) should run in O(lg n) time

m.iterator() should run in O(n) time

iter.hasNext() should run in O(1) time

iter.next() should run in O(1) time

m.accept(v) should run in O(n*lg n) time

where all of those times are for the worst case.

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Hint: The most reasonable way to achieve that worst-case efficiency is to implement (functional) red-black trees. (The assigned reading by Okasaki is a great resource for this implementation.)

Hint: Correct programs that achieve the above efficiency for the average case but not for the worst case are likely to earn substantially more partial credit than programs that try to achieve the above efficiency for the worst case but don’t actually work.

Hint: Correct programs that don’t even try to be efficient are likely to earn substantially more partial credit than programs that try to be efficient but don’t actually work.

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The specification of hashCode() from assignment 4 is strengthened as follows.

If m1 and m2 are values of the FMap ADT, and

m1.equals(m2)

then m1.hashCode() == m2.hashCode().

If m1 and m2 are values of the FMap ADT, and

! (m1.equals(m2))

then m1.hashCode() is unlikely to be equal to m2.hashCode().

Note: The word “unlikely” will be interpreted as follows. For every type K and V, if both m1 and m2 are selected at random from a set of FMap

n == m.size() is

P(n) = 1/(2^(n+1))

and for each key k such that m.containsKey(k) the probability that

h == k.hashCode() is at most 1/5

and for each value v such that v.equals(m.get(k)) the probability that

h == v.hashCode() is at most 1/5

and the three probabilities above are independent

then the probability of m1.hashCode() == m2.hashCode() when m1 and m2 are not equal is less than 2%.