• We are provided you with a scaffold to build your code on, i.e. starter code. You should download the scaffold ﬁrst and then start coding. As with Assignments 1 and 2, you can ﬁnd this code either your workspace on Ed or on mycourses.
• Search for the keyword updated to ﬁnd any places where this PDF has been updated.
• T.A. ofﬁce hours will be posted on mycourses under the “Ofﬁce Hours” tab. For zoom OH, if there is a problem with the zoom link or it is missing, please email the T.A. and the instructor.
• If you would like a TA to look at your solution code outside of ofﬁce hours, you may post a private question on the discussion board.
•We have provided you with some examples to test your code. (See TestEx-posedA3.java on mycourses. The same tests are run on Ed when you submit.) If you pass all these exposed tests, you will get 59/100. Unlike with Assignments 1 and 2, the remaining tests will be private. Therefore, we strongly encourage you to come up with more creative test cases, and to share these test cases on the discussion board. There is a crucial distinction between sharing test cases and sharing solution code. We encourage the former, whereas the latter is a serious academic offense.
• Late policy: Late assignments will be accepted up to two days late and will be penalized by 10 points per day. If you submit one minute late, this is equivalent to submitting 23 hours and 59 minutes late, etc. So, make sure you are nowhere near that threshold when you submit.
Please see the submission instructions at the end of this document for more details.
Tertiary Search Tree (TST)
The purpose of this assignment is to give you some experience with recursion. Recursion is a fundamental method in programming and the sooner you learn it, the better! The topic for this assignment is trees.
You will work with a data structure that we will call a tertiary search tree or TST.1 This is like a binary search tree (BST), except that each node in a TST has three children rather than two. We can call the three children left, middle, and right. Each node stores a element whose class type implements Comparable, so you can assume access to a compareTo() method. The subtrees deﬁned by the left, middle, and right children of a node have elements that are less than, equal to, or greater than the element at that node, respectively.
Lecture 25 gave pseudocode for binary search trees (BST) methods. You will implement similar methods for your TST class. Make sure you understand the BST pseudocode before you try to implement a TST version!
You will work with three classes:
TSTNode class (25 points)
A TSTNode has four ﬁelds: an element, and three children (left, middle, right). For this class, you will write:
• a constructor TSTNode(T element) (5 points) – assigns the given element to this node; the children are automatically initialized to null.
• height() (10 points) – returns an int which is the height of the subtree, whose root is this TSTNode
• ﬁndMin() (5 points)– returns the TSTNode containing the minimum element in the tree; you can use this as a helper method.
• ﬁndMax() (5 points)– return the TSTNode containing the maximum element in the tree; you can use this as a helper method.
You may add your own helper methods to the TSTNode class. For example, you may wish to overload the constructor.
TST class (55 points)
A TST has just one ﬁeld: the root TSTNode of the tree. A TST has several methods that are provided to you:
• height() – returns an int which is the height of the tree; it depends on the height() helper method in the TSTNode class (see above)
• toString()– toString() can be used to visualize the tree structure; recall that you can ’call’ the toString() method using System.out.print(tree) where tree is of type TST;
1This is not to be confused with a “ternary search tree” which is something else. Also, others may have used the term “tertiary search tree” to mean something other than what we mean here. We will ignore these other usages of the term.
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