$1.(40$ pts$)$ Consider the full binary search tree pictured in Figure $26-13$a$.$ Now imagine that you traverse the tree and save its data in a file. If you then read thefile and add the data to an initially empty binary search tree, what tree will you get if the traversal was:$$

$$ Preorder

$$ Inorder

$$ Level Order

$$ Postorder

$2.(60$ pts$)$ Cnsider a method for a binary search tree that decides whether the tree is height balanced as Segment $24\mathrm{.}10$ of Chapter $24$ describes. The header of the method could be as follows:

public Boolean isBalanced$()$

Write this method for the class BinarySearchTree. It should call a private recursive method of the same name..

iCollege Submission and Grading

Submit part$1$ answers in a Word file. Make sure to test your program for part $2$ completely and thoroughly. Then, upload and submit the Word file and the.java file to iCollege under Assessments$-->$Assignments$-->$Programming Lab Project. Always double check that your submission was successful on iCollege!

The lab will be graded according to the following guidelines:

$$ A score between $0$ and$100$ will be assigned.

$$ If the sourcefile$($s$)$ are not submitted before the specified deadline or if they do not compile, the Lab score will be penalized appropriately.

$$ The programs will be evaluated todetermine if they output the correct Strings.