Description
The Assignment
Start by downloading the Assignment 3 Zip File, which contains a skeleton of the code you
need to write.
1. Sorted sets with access by rank
For this assignment, you will have to test your own code thoroughly. The submission server
will consume anything that you try to print to System.out or System.err so the testing done on
the server will be almost completely opaque. It will only give you a generic error of the form
“get(i)/rank(i)/find(x) returns incorrect value”, “an exception occurred”, or “test
failed after 5 seconds”. On the positive side, testing is something you can do easily because
SlowSkiplistRankedSSet is a correct implementation that you can use to test against. Be
sure to test a good mix of operations that includes and interleaves add(x), remove(x),
get(i) and rank(x).
The RankedSSet interface is an extension of the SSet interface described in the textbook
that supports two extra operations
get(i): return the value x in the set that is larger than exactly i other elements in the
set.
rank(x): return the number, , of elements in the set that are less than x (note that x is
not necessarily in the set).
Currently there are two identical implementations of the RankedSSet interface included in
the assignment called SlowSkiplistRankedSSet and FastSkiplistRankedSSet. Both
i
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of them are slow: each of them has an implementation of get(i) and rank(x) that runs in
time, in the worst case.
Modify the FastSkiplistRankedSSet implementation so that the get(i) and rank(x)
implementations each run in expected time and none of the other operations
(add(x), remove(x), find(x), etc.) have their running-time increased by more than a small
constant factor. Looked to the SkiplistList implementation discussed in class for
inspiration on how to achieve this.
Suggestion: Once you’ve decided on your representation, implement a display() method
for your FastSkiplistRankedSSet that outputs an ASCII-graphics representation of your
data structure on System.out. Here’s example output from one that I created while making
sample solutions:
*—————————————*
*—————————————*
*—————————————*
*—————————————*
*—————————————*—————*
*———————*—–*———–*—————*
*———————*—–*—–*—–*—*—–*—–*
*———————*—–*—–*-*—*—*—*-*—–*
*————-*—*—*-*—*—–*-*—*—*—*-*—–*
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
Doing this will force you to think about your representation and will also help you debug your
implementation. With the right representation, the display() method is actually easy to
implement, requiring only a pair of nested for loops.
2. Tree Traversal Tricks
For this part of the assignment, you will be working with the BinaryTree class provided in
the zip file. It contains four uncompleted functions that you are supposed to complete. For full
marks, each of these functions should run in time and should not use recursion. See the
Ω(n)
O(log n)
O(n)
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function traverse2() in BinaryTree.java that we also discussed in class for an example
of how to do tree traversal without recursion.
The BinaryTree class implements a static method called randomBST(n) that returns a
random looking binary tree. BinaryTree also implements the toString() method so you
can use System.out.println(t) to view a representation of a BinaryTree that is closely
related to question 3. You can use this for testing your functions. Again, you should test your
own code thoroughly since the testing done on the server will be mostly opaque. On the
server, your code will be tested on a Java virtual machine with a limited stack size. You can do
similar testing yourself by using the java -Xss argument (although you won’t have to worry
about this if you don’t use recursion.).
1. The method totalDepth() should return the sum of the depths of all nodes in the tree,
or -1 if the tree has no nodes at all.
2. The method totalLeafDepth() should return the sum of the depths of all the leaves in
the tree, of -1 if the tree has no leaves. (A leaf is a node that has no left child and no
right child.)
3. The method bracketSequence() should return a string that gives the dot-bracket
representation of the binary tree. The dot-bracket representation of a binary tree can be
defined as follows:
the dot-bracket representation of a tree with no nodes is the string “.”
the dot-bracket representation of a binary tree with root node r consists of an open
bracket ( followed by the dot-bracket representation of r.left followed by the
dot-bracket representation of r.right followed by a closing bracket )
Some examples:
the dot-bracket representation of the binary tree with only one node is (..)
the dot-bracket representation of a 2-node binary tree is either ((..).) or (.
(..)) depending on whether the root has no right child or no left child
the dot-bracket representation of a the height-1 binary tree with two leaves is
((..)(..))
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4. The method prettyPrint(w) prints an ASCII drawing of the binary tree on the
PrintWriter w (using w.print(s) and w.println(s), like in Assignment 1). In this
representation,
each node is represented by an asterisk *
an edge from a node to its left child is represented by a vertical bar |
an edge from a node to its right child is represented by a sequence of one or more
hyphens –
For each edge from a node u to its right child v, the number of hyphens used to
represent the edge uv should be just enough so that the drawing of the subtree
rooted at v is separated from the drawing of the subtree rooted at u.left by
exactly one column. See the example here:
