Description
Question 1 (33 points):
In lib280-asn6 you are provided with a fully functional 2-3 tree class called TwoThreeTree280.
Recall that 2-3 trees are keyed dictionaries. As such, the TwoThreeTree280 class implements the
KeyedBasicDict280 interface. This interface adds the methods obtain(k), delete(k) and has(k),
and set(x) (replace the item whose key matches they key of x with the item x).
Presently, TwoThreeTree280 does not implement KeyedDict280 which adds additional operations
including all of the methods in KeyedLinearIterator280 which, in turn, includes all of the public operations on a cursor. Note that KeyedDict280 is the same interface that is implemented by
KeyedChainedHashTable280 so you should be somewhat familiar with it from the previous assignment.
The task for this question is to extend the TwoThreeTree280 to a class called IterableTwoThreeTree280
which allows linear iteration over the keyed data items stored in the two-three tree in ascending keyorder. We will achieve this by adding additional references to leaf nodes so that the leaf nodes form
a bi-linked list. Note that adding this feature to a 2-3 tree results in exactly a B+ tree of order 3
(see textbook Section 17.1). We aren’t going to call it a B+ tree class though, because we are implementing specifically a B+ tree of order 3, and higher-order B+ trees will not be supported. Our
IterableTwoThreeTree280 class will be exactly a B+ tree of order 3.
Figure 1 in the Appendix shows the differences between a 2-3 tree (without iteration) and a B+ tree
of order 3 containing the same elements, with the linking of the leaf nodes to support iteration. The
algorithms for insertion and deletion are the same in both kinds of tree, except that in the case of the
B+ tree, references to/from the predecessor and successor leaf nodes in key-order have to be adjusted
to maintain the bi-linked list of leaf nodes.
The full class hierarchy of IterableTwoThreeTree280 is shown in Figure 2 of the Appendix. The
hierarchy of tree node classes is shown in Figure 3 of the Appendix.
To implement the IterableTwoThreeTree280, the following tasks must be carried out:
1. Make an extension of LeafTwoThreeNode280 that adds references to its predecessor and successor
leaf nodes. This has already been done for you in the class LinkedLeafTwoThreeNode280.
2. Override the TwoThreeTree280::createNewLeafNode() method by adding a new protected method
in IterableTwoThreeTree280 that it returns a new LinkedLeafTwoThreeNode280 object instead
of a TwoThreeNode280 object. This has already been done for you.
3. In IterableTwoThreeTree280, override the insert and delete methods of TwoThreeTree280
with modified versions that correctly maintain the additional predecessor and successor references in the LinkedLeafTwoThreeNode280. Each leaf node should always point to the the leaf
node immediately to the left of it (the predecessor) and to the right of it (the successor) even if
they are not siblings. Of course, the leaf node with the smallest key has no predecessor and the
leaf node with the largest key has no successor.
In IterableTwoThreeTree280, the insert and delete methods from TwoThreeTree280 already
have been copied, and TODO comments have been inserted indicating where you need to add
additional code to maintain the additional leaf node references. The comments also provide a
few hints. You should not have to modify any of the existing code for insert or delete, just
add new code to deal with the linking and unlinking of leaf nodes from their successors and
predecessors. Maintaining these links is very similar to inserting and removing nodes from the
middle of a doubly-linked list.
4. Implement the additional methods required by KeyedDict280 (and, by extension, KeyedLinearIterator280).
Some of these have been done for you, others have not. TODO comments in IterableTwoThreeTree280
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indicate which methods you need to implement and maybe even a hint or two. In this class, the
linear iterator allows positioning of the cursor along the leaf-level of the tree.
5. In the main() function, write a regression test to test the methods required by KeyedDict280
(and, by extension, KeyedLinearIterator280). You to not need to explicitly test the insertion
and deletion methods since testing of the methods from KeyedLinearIterator280 will reveal
any problems with the new leaf node linkages, but you will need to insert and delete items to
create test cases.
You must test all of the methods listed in the interfaces that are coloured blue in Figure 2 of
the Appendix.
Use instances of the local class called Loot, which has been defined in the main method, as the
data items to insert into the tree for testing. This class implements the type of item depicted in
Figure 1 in the Appendix consisting of the name of a magic item from a fantasy game, and its
value in gold pieces. The item keys are the item names (strings).
Hint: The toStringByLevel() method you’ve been given prints not only the 2-3 tree’s structure, but also
displays current linear ordering of the nodes that results from following the successor links in the leaf nodes,
beginning with the leftmost leaf node. This may be helpful for the debugging of step 2.
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3 Files Provided
lib280-asn6: A copy of lib280 which includes:
• solutions to assignment 5;
• TheTwoThreeTree280 class and related node and position classes in the lib280.tree package
for Question 1.
• Partially completed IterableTwoThreeTree280 class in the in lib280.tree package for Question 1.
4 What to Hand In
IterableTwoThreeTree280.java: Your completed tree for Question 1.
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Appendix
Leather
Armor
Potion of
Healing
Vampiric
Blade
+1 Mace
2000
Blue Ioun
Stone
20000
Leather
Armor
10
Plate
Armor
350
Potion of
Healing
100
Vampiric
Blade
12000
Plate Armor Blue Ioun
Stone
Leather
Armor
Potion of
Healing
Vampiric
Blade Plate Armor Blue Ioun
Stone
+1 Mace
2000
Blue Ioun
Stone
20000
Leather
Armor
10
Plate
Armor
350
Potion of
Healing
100
Vampiric
Blade
12000
Figure 1: Top: a 2-3 tree which does not support a linear iterator; Bottom: a B+ tree of order 3 containing
the same elements. Here the keys are strings (describing magical items in a fantasy game world) and
the keyed data items contain the item name and an integer (representing the value, in gold pieces, of the
object). Note that the trees are the same except for the extra linkages of the leaf nodes.
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IterableTwoThreeTree280
#smallest: LinkedLeafTwoThreeNode280<K,I>
#largest: LinkedLeafTwoThreeNode280<K,I>
#cursor: LinkedLeafTwoThreeNode280<K,I>
#prev: LinkedLeafTwoThreeNode280<K,I>
K,I
TwoThreeTree280
#rootNode: TwoThreeNode280<K,I>
+height
#createNewLeafNode
#createNewInternalNode(TwoThreeNode, K,
TwoThreeNode, K,
TwoThreeNode)
#find(K)
#giveLeft(TwoThreeNode, TwoThreeNode)
#giveRight(TwoThreeNode, TwoThreeNode)
#stealLeft(TwoThreeNode, TwoThreeNode)
#stealRight(TwoThreeNode, TwoThreeNode)
+toString
+toStringByLevel
K,I
interface
Container280
clear
isEmpty
isFull interface
KeyedBasicDict280
delete(K)
has(K)
insert(I)
obtain(K)
set(I)
K,I
interface
KeyedDict280
deleteItem
search(K)
searchCeilingOf(K)
setItem(I)
K,I
interface
KeyedLinearIterator280
K,I
interface
CursorSaving280
currentPosition
goPosition(CursorPosition280)
interface
KeyedCursor280
itemKey
keyItemPair
K,I
interface
LinearIterator280
after
before
goAfter
goBefore
goFirst
goForth
I
interface
Cursor280
item
itemExists
I
Figure 2: Class hierarchy for IterableTwoThreeNode280. For methods, only type names of parameters are shown.
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LinkedLeafTwoThreeNode280
next: LinkedLeafTwoThreeNode280
prev: LinkedLeafTwoThreeNode280
+next
+setNext(LinkedTwoThreeNode280)
+prev
+setPrev(LinkedTwoThreeNode280)
K,I
LeafTwoThreeNode280
data : I
InternalTwoThreeNode280 K,I
key1: K
key2: K
leftSubtree: TwoThreeNode280
middleSubtree: TwoThreeNode280
rightSubtree: TwoThreeNode280
K,I
TwoThreeNode280
this is an abstract class
+getData
+getKey1
+getKey2
+getLeftSubtree
+getRightSubtree
+getMiddleSubtree
+isInternal
+isRightChild
+setKey1(K)
+setKey2(K)
+setLeftSubtree(TwoThreeNode280)
+setRightSubtree(TwoThreeNode280)
+setMiddleSubtree(TwoThreeNode280)
K,I
Figure 3: UML Class Hierarchy for 2-3 Tree Nodes in lib280. Every method that might be needed for either
an internal or a leaf node is defined in the common abstract ancestor class TwoThreeTree280 (note: because
it is abstract, it cannot be instantiated). Subclasses InternalTwoThreeNode280 and LeafTwoThreeNode280
contain the data needed for the respective types of nodes, and definitions of each method appropriate to
that type of node. Inherited methods that don’t make sense for a particular type of node (e.g. getData() on
an internal node) are defined to throw exceptions. The actual type of a reference to a TwoThreeNode can
be determined by calling isInternal which is defined by internal nodes to return true and is defined by
leaf nodes to return false. The LinkedLeafTwoThreeNode280 extends the leaf node class to add predecessor
and successor references to maintain the bi-linked list of leaf nodes in the B+ tree of order 3.
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