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For the programming exercise (Part II) you are to turn in:

· a single file named assignment1.java containing all your Java source code

· a single text file named readme1.txt containing your name and any relevant information about your program (known bugs, compilation or operating anomalies, or instructions, etc).

· a single file containing the outputs of several test runs of the program demonstrating that the program works in all reasonable cases.

Part I: written exercises.

1. Begin with the following binary search tree, draw the BST that results after the operation or sequence of operations is performed. (All questions are independent and each question starts from the BST as following)

a. Insert 7

b. Insert 7, 1, 55, 29, and 19

c. Delete 8

d. Delete 8, 37, and 62

e. Insert 7, delete 8, insert 59, delete 60, insert 92, delete 50.

f. Display the output produced by an inorder traversal

g. Display the output produced by a preorder traversal

h. Display the output produced by a postorder traversal.

2. For the arithmetic expressions below, draw a binary tree that represents the expression, and then use tree traversals to find the equivalent prefix and postfix expressions.

a. (A-B)-C

b. A/ (B-(C-(D-(E-F))))

c. ((A*(B+C))/(D-(E+F)))*(G/(H/(I*J)))

3. Construct the Huffman code for the Java keyword and weights given in the following table.

Words	Weight
int	0.30
main	0.30
while	0.05
if	0.20
for	0.15

Part II: programming exercise

Start with the tree.java program (Listing 8.1) and modify it to create a binary

tree from a string of letters (like A, B, and so on) entered by the user. Each

letter will be displayed in its own node. Construct the tree so that all the nodes

that contain letters are leaves. Parent nodes can contain some non-letter

symbol like +. Make sure that every parent node has exactly two children.

Don’t worry if the tree is unbalanced. Note that this will not be a search tree;

there’s no quick way to find a given node. You may end up with something

like this:

+ E

+ D - -

+ C - - - - - -

A B - - - - - - - - - - - - - -

One way to begin is by making an array of trees. (A group of unconnected trees

is called a forest.) Take each letter typed by the user and put it in a node. Take

each of these nodes and put it in a tree, where it will be the root. Now put all

these one-node trees in the array. Start by making a new tree with + at the root

and two of the one-node trees as its children. Then keep adding one-node trees

from the array to this larger tree. Don’t worry if it’s an unbalanced tree. You

can actually store this intermediate tree in the array by writing over a cell

whose contents have already been added to the tree.

The routines find(), insert(), and delete(), which apply only to search trees,

can be deleted. Keep the displayTree() method and the traversals because they

will work on any binary tree

Hint: How to construct the Binary Tree, there are many ways to do it? We could select the easiest way. What it is? Note that all the letters are the leaves no the parents. So for the first two letters, we group them together and add a ‘+’ as its parent. Then we use this ‘+’ and we add the third letter as another child, we construct another level with a parent ‘+’, and so on, until we use all the letters.

This approach is not a balanced tree, actually it has n levels (here n is the number of nodes). Each level has exactly one letter except the root that is a ‘+’ and the bottom level, which has two characters.