The third programming project isvolves writing a program to read in the prooder acpresentatios

of a bisory tree and determine whether it is a balansed binary search tree. Given the bieary tree

shown below:

asterisks represent null children.

The program should repeatedly prompt the user for a binary tree. It should thes display the tree

using indestation. For the above tree, is iderted representation woukd be as follows:

$2311$

$43$

It slould then casegorise the binary tree in one of three ways

Ir is not a binary search tree

: It is a balanced bisary search tree

It is a bisary searcla tree bat it bis sot balabeed

If the tree is an a balanced binary search tree, a binary search tree coetaining the same set of

values should be corstructed and displayed in the iskented format down above It is nos

values should be constructed and displayed a the bdested format bown above. It is not expesited that the existing tree be retalanced, jost that a new tree with the same set of values be

constrocted. Thes the beight of the original tree and the batased binary search tree should be

displayed.

Showas below bi a sample sessioe that involves each of the above cases:

$1141$

$20$

It

$13$ warch tree but it ia not halanced

$63$

Origlinal tree han leight Ralanced tree han belght

$53$

It in not a binazy wesch tree

In ablition, the program should verify that the tree input has valid syntac. Eack of the following

I a calition, the program shy erress slould be detected,

Incomplese Tree

Duata is Not an lnteger

Exra Characters at the End

Missing Left Parenthesis

The program should consibt of three clases. The first class slould be the class that defines the

binary tree. It should be an immatable class with the following public methods:

A coestructor that accepts a string coesaining the peconder representatice of a bieary tree

and construcs a bieary tree

A coestructor that accepts an array list of integers and constructs a balanced binary search

tree containing those values

A mestad that outpuss the biary tree in indented form

A melbod that ecturs whether the tree is a binary searcls tree.

A mellod that returs whether the tree is balanced

A melbod that returses the beiglt of the tree

A method that returas in array list of the values in the tree

Additional private methods may be added as needed.

The second claws slould be a class that defines a clocked exception that is throw: when a tree

with ivvalid syntax is isput. The thisd class is the class that coetains the main method and

accepts the user input and displays the mouls: