CSCI 2720			Data Structures			     Spring 2004


Programming Project 4 - due *** Saturday April 17 by midnight. ***


See the General Project Instructions on the course web site for directions
which apply to all projects, including this one.


The project has two parts, I and II.

I.   Extend your templated binary search tree class from Project 2 by adding
     top-down splay tree implementations of the basic operations, which will be
     called SplayFind( ), SplayInsert( ), and SplayRemove( ).


II.  Perform data gathering and timing tests to compare the splay trees and
     splay operations with the trees and operations from Project 2.  Also build
     a large linear tree and see how many splay operations are needed to 
     achieve a reasonably balanced tree.

Part I.  Templated Binary Search Tree class with Splay Operations

Specify and implement a binary search tree class BST<Dtype,Ctype> just as for
  Project 2 except for the addition of the three splay operations and the 
  standardizations noted below.

As in Project 2, Dtype is to be the data type for the tree and Ctype contains a
  static function lt which defines the tree's inorder ordering.  However for 
  Project 4 the assumptions for lt are less strict, as follows:
  given inputs x, and y of type Dtype, the function Ctype::lt(x,y) returns an
  integer < 0 (not necessarily -1) if x should come before y in the ordering,
  an integer > 0 (not necessarily 1) if y should come before x in the ordering,
  and 0 if x and y are equal.

The other standardization is that Stats( ) should return -1 as the ordered 
  height of an empty tree.
 
Before going on to part II you should test your BST< , > class
  using  SplayFind( ), SplayInsert( ), and SplayRemove( ), as well as all of the
  functions required for Project 2.  Make sure it works for int data and the
  default comparison, and on C style strings with the strcmp for the comparison
  function (wrapped to make it accessible, but otherwize unchanged).
  For instance, starting with an empty tree of type BST<int> the splay 
  operations should give the following results:

   insert: 10 20 30 40 50 60
   output:  1  1  1  1  1  1
pre-order: 60 50 40 30 20 10

     find: 18
   output: 0
pre-order: 10 50 30 20 40 60

   remove: 40
   output: 1
pre-order: 30 10 20 50 60


REQUIRED INTERFACE AND FEATURES

Be sure to name your class BST<Dtype> and provide public member functions
  named SplayFind( ), SplayInsert( ), SplayRemove( ) in addition to those 
  required for Project 2.  These new functions must each take a const Dtype&
  input and return an int.  Each should return 1 if the operation was 
  successful, and 0 if not (i. e., return 0 if you try to insert a key already
  present in the tree, or find or delete a key which is not present).  The 
  implementations must carry out top-down splay operations as described in the 
  paper by Sleator and Tarjan (class handout).  The functions SplayFind( ),
  SplayInsert( ), and SplayRemove( ) must be carried out as described in Section
  7.3 of the Lewis and Denenberg text except that each splay operation will be
  top-down instead of bottom-up.

Your specification should be in a file called splay.h and your implementation
  should be in splay.cc.

Part II.  Tree Shape and Timing Experiments

  (a) Repeat your experiments from Project 2 with neutral, left-biased and 
      right-biased search trees but using the functions SplayFind( ), 
      SplayInsert( ), and SplayRemove( ) instead of Find( ), Insert( ) and 
      Remove( ).  In your discussion, compare the results from Projects 2 and 4.
      Explain your findings.

  (b) SplayInsert the numbers 0 ... 9999 IN ORDER (0 first, etc.) into an empty
      BST<int> tree and run TreeStats on it. Then execute SplayFind(0), 
      SplayFind(1), SplayFind(2), ...  SplayFind(12), running TreeStats after
      each find.  In your discussion point out what is happening to the internal
      path length and explain why it is happening.

  (c) Devise your own timing experiments to compare the speed of the three splay 
      operations with the speed of the original versions from Project 2, using
      random and biased trees.  In your discussion give a summary of how they
      compare for speed on the different types of trees.  

REQUIRED INTERFACE AND FEATURES

The code for the tree shape experiments should be in a file named
  "splaytree.cc", or if you find it more convenient in separate files for the
  different types of bias and for the linear tree experiment.  The code for
  the timing runs should be in a file named "splaytime.cc".  The data you
  obtain should be tabulated in proj4_data, and you should then discuss their
  significance in a separate file, proj4_discussion.