CIT 594 Assignment 3: A Tree ADT
Spring 2014, David Matuszek

Purposes

General Idea

Your assignment is to:

Use Eclipse.

Details

An ADT has a contract with its users, which is specified by its public members and described via Javadoc. It provides certain operations, and restricts access to only those operations. Your Tree class is such an ADT. In addition, any ADT is responsible for ensuring the validity of its data. In this assignment, you are to take that responsibility very, very seriously for the Tree class.

A tree is composed of nodes. Each node has a value, and may have children. The Tree class will be genericized (have a type parameter) so that you can specify the type of values in the nodes; the children will be (references to) nodes.

Your assignment is to define the following classes and methods.

public class Tree<V>

This is your ADT class. Each object in the Tree class represents a single node; however, nodes are linked together in such a way that any node may be considered as the "root" of a complete tree. In the following, the terms "node" and "Tree" are synonyms, but I tend to use "node" when I'm talking about one specific object of type Tree, and "Tree" when I'm referring to that node and all its descendents (children, children of children, etc.).

Your Tree class should have the following constructor:
public Tree(V value, Tree<V>... children)
Creates a Tree node with the given value and zero or more children.

Note: The "..." syntax means that you can call the constructor with new Tree<type>(v), or new Tree<type>(v, c1), or new Tree<type>(v, c1, c2), or new Tree<type>(v, c1, c2, c3), etc., but when you write the code inside the constructor, you write it as if it were defined as Tree(V value, Tree<V>[] children).

Your Tree class should have the following methods:

Accessors

An accessor is a method that returns some information about the data type.

public V getValue()
Returns the value in this node of the Tree.
public Tree<V> firstChild()
Returns the first child of this tree (or null if this tree is a leaf).
public Tree<V> lastChild()
Returns the last child of this tree (or null if this tree is a leaf).
public int numberOfChildren()
Returns the number of (immediate) children of this node.
public Tree<V> child(int index) throws NoSuchElementException
Returns the index-th child of this tree (counting from zero, as with arrays). Throws a NoSuchElementException if index is less than zero or greater than or equal to the number of children.
public Iterator<Tree<V>> children()
Returns an iterator for the children of this tree. The iterator should have the usual hasNext(), next(), and remove() methods, all of which should be implemented. (Hint: Java's ArrayList already provides an iterator.)
public boolean isLeaf()
Returns false if this node has children. This is a convenience routine: The user could just test node.numberOfChildren() == 0 instead.
private boolean contains(Tree<V> node)
Returns true if this tree contains the given node (not an equal node; use ==, not equals). The root of this tree is included in the recursive search.
@Override public boolean equals(Object object)
Returns true if (1) the given object is a Tree, and (2) the value fields of the two trees are equal, and (3) each child of one Tree equals the corresponding child of the other Tree.
Notes: (1) You have to be very careful of nulls; they have to be compared using ==, while non-null objects must be compared using equals(Object), and (2) this method is recursive. You will need this method in order to do unit testing on your Tree class.
@Override
public String toString()
Returns a multiline representation of this Tree. Each line contains the toString() representation of the value in that node, terminated with a newline (\n). Each child is indented two spaces under its parent. For example:
Prints as: 
one
  two
    five
  three
  four
    six
    seven
The result of calling toString() should be: 
"one\n  two\n    five\n  three\n  four\n    six\n    seven\n"

Hint: Use a private helper function that traverses the tree in preorder, and has an indentation String as one of its parameters.

Transformers (mutative)

A transformer is one that, applied to a data structure, produces a different data structure. A mutative transformer is one that changes the data structure to which it is applied (for example, the add method of the ArrayList class). An applicative transformer is one that produces a new data structure of the same kind (for example, the toLowerCase method of the String class).

public void setValue(V value)
Sets the value in this node of the Tree.
public void addChild(Tree<V> newChild) throws IllegalArgumentException
Adds newChild as the new last child of this tree, provided that the resultant tree is valid (see below). If the operation would result in an invalid tree, the tree is unchanged and the method throws an IllegalArgumentException.
public void addChild(int index, Tree<V> newChild) throws IllegalArgumentException
Adds newChild as the new index-th child of this tree (counting from zero), provided that the resultant tree is valid (see below). The child previously at this index, and all subsequent children, are "shifted right" (their index is increased) to make room for the new child. If the index is less than zero or greater than (not greater than or equal to) the current number of children, or if the operation would result in an invalid tree, the tree is unchanged and the method throws an IllegalArgumentException.
public void addChildren(Tree<V>... children ) throws IllegalArgumentException
Adds each Tree in children as a new child of this tree node, after any existing children, provided that the resultant tree is valid (see below). If the the addition of any child node would result in an invalid tree, that node is not added, tree modification is halted, and the method throws an IllegalArgumentException.
public Tree<V> removeChild(int index) throws NoSuchElementException
Removes and returns the index-th child of this tree, or throws a NoSuchElementException if the index is illegal. (This method, and the remove() method of the above Iterator, simply remove the child from the list of children of this tree; no major tree surgery is involved. The removed subtree remains intact.)

Notes:

A tree will be considered valid if there are no loops in it. If, starting from some node in the tree and following child links you can get back to the same node, then there is a loop and the tree is invalid. You need to test for validity in the addChild methods. We will, however, allow subtrees to be shared, provided there are no loops.

Before adding a node child as a new child of node parent (each of which may be inside some tree structure), test if node parent occurs in the tree whose root is child. If it is, do not perform the operation, but instead throw an IllegalArgumentException instead. Note that (1) the tests must search for identical (==) nodes, not just equal ones, and (2) the search is inherently recursive.

You will need the contains method to implement the validity test. Since this search method will be private, you cannot test it explicitly--rather, you test it implicitly, by making sure that your addChild methods will throw an exception when asked to construct an invalid tree.

Why shared subtrees?

Shared subtrees are occasionally useful. For example, if you were to evaluate the tree equivalent of the expression (x - y) * (x - y), you might be able to do so in such a way that you evaluate (x - y) only once.

Usually, however, trees are defined in such a way that shared subtrees are not allowed. Furthermore, I do not expect to make use of shared subtrees in this course. However, while it is fairly simple to do a recursive search to disallow loops in a tree, it is much more difficult to detect (and disallow) shared subtrees. Since shared subtrees are generally harmless, it is easier to allow them than to try to prevent them.

public class TreeTest

As part of the assignment, write, use, and turn in a JUnit test class for the Tree class. Be thorough, and don't forget to test that exceptions are thrown when they should be.

When grading your program, we will use our own JUnit tests, as well as or instead of yours, so be sure to follow the above specifications exactly. Be especially careful that your toString() has the correct spaces and newlines.

Implementation

The best way to keep the children of a node is probably in an ArrayList. If a node has no children, your code will probably be simpler with an empty ArrayList than with a null value for children.

Your equals(Object) and toString() methods, and the search method you use to look for potential loops, must be recursive. You may not use a Stack, Vector, additional ArrayList, or similar data structure, to implement these methods.

You are expected to use TDD (Test-Driven Development). This means:

Write stubs for all the methods. (Methods which return a value should return the value that is most likely to be wrong.)
Use Eclipse to generate stubs for all the JUnit test methods.
while (not all methods have been written and tested) {
    while (some method is incomplete) {
                 Write (or add to) a test for that method.
                Run the tests, and make sure the new test fails.
                Add just enough code to the method to pass the test.
                Refactor to improve the code.
    }
}  

To get started, you first need to write the constructor, and you need to write the equals method. After that, it's best to build up the methods and their tests a little at a time; for example, you will probably want to write the addChild method fairly early, but you can't test whether it correctly throws an IllegalArgumentException until you have also written the contains method. Doing things a little at a time this way is almost sure to reduce the amount of time required to write and debug the program.

Due date

Turn your assignment in to Canvas before 6 a.m. Thursday, February 6. Late programs, even if only a minute late, will be penalized 10 points for the first week. Programs later than a week may or may not be accepted for grading.