The TAO of Java
Summary: In this laboratory, you will have an opportunity to enhance your understanding of the dictionary ADT and of binary search trees by exploring a binary search tree implementation of dictionaries.
Code Files from Previous Lab:
New Code Files:
In this laboratory, you will use a package entitled
a. In a terminal window, type
You should see messages about files being copied to a temporary directory.
b. Start Eclipse.
c. In Eclipse, build a project named Temp from
d. In the Temp project, you should see a package named
Drag that package to your Code project.
e. Delete the Temp project.
You can now work with the new package.
a. Sketch the binary search trees that would be created by adding the following lists of indices (each list creates a separate tree, assume the elements are added in order).
b. Is there a better or worse order to put values into a binary search tree?
c. Estimate the running time of
in terms of the number of elements in the tree or the depth of the
tree (or both).
Clearly, these nodes are insufficient, by themselves, to implement
binary search trees. What we need to do is to wrap them in
a class that builds the trees and uses them to support the
a. What fields would you expect that class to have?
b. Binary search trees assume that keys are ordered. How do you plan to compare values to determine what is smaller or larger?
c. How would you expect to implement the
get method? (You
need not write code, just sketch a strategy.)
d. How would you expect to implement the
put method? (You
need not write code, just sketch a strategy.) Note that,
put modifies the tree.
to compare that implementation to your suggestions.
f. Explain the strategy used for
As you may recall,
DictTester.java, provides a a generic tester for
TestBST.java, uses that generic tester to provide a tester customized for binary search trees.
Compile and run
TestBST and confirm that it
produces the results you expect.
a. Write a new tester for binary search trees that prompts the user for a sequence of key,value pairs, inserts each pair into the tree, and then print out the tree.
For example, we might use this tester as follows.
ji NewTestBST d a b c e Please enter the key,value pairs, one per line. Enter a blank line when you are done. > d,Dog > a,Apple > b,Binary > c,Cute > e,Echo d => Dog L a => Apple L R b => Binary L R R c => Cute R e => Echo
b. Use the tester to check your answers from exercise 1.
As you may recall, the general strategy for removing a key/value pair from a binary search tree is somewhat complex.
slide upthe right subtree of that leftmost node.
a. Write a method,
BSTNode find(BSTNode top, K key), that finds the node with the designated key. (Hint: You may want to factor out the code from
b. Write a method,
BSTNode leftmost(BSTNode top), that finds the leftmost node in a subtree. (Hint: You find the leftmost node by repeatedly following the left branch until there is no left branch.)
c. Write a method,
void slideRightUp(BSTNode top), that
slides up the values from the right subtree.
d. There are a few special cases for removal. One is that there is no right subtree. Another is that there are no subtrees at all. Determine what you should do for those special cases.
e. Put it all together into a
remove(K key) method.
f. Suppose we start with a full binary tree. What do you expect to happen if we repeatedly remove the value at the root? Confirm your answer experimentally.
As you may have noted, binary search trees only work well when elements are split nearly evenly between subtrees. (Similarly, each subtree should have about the same number of elements in each of its sub-subtrees, and so on and so forth.)
Design (but do not implement) a strategy for keeping the number of elements in each subtree approximately equivalent.
Monday, 11 April 2005 [Samuel A. Rebelsky]
Tuesday, 12 April 2005 [Samuel A. Rebelsky]
Wednesday, 13 April 2005 [Samuel A. Rebelsky]
Tuesday, 11 April 2006 [Samuel A. Rebelsky]
Wednesday, 12 April 2006 [Samuel A. Rebelsky]
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