Quiz 09

Quiz 09



Important notes:
  1. Do not start until you are instructed to do so!
  2. You will have 20 minutes once the proctor says to start.
  3. You will have brief additional time after we stop to scan and submit your solutions.

  4. Just before the quiz...
    1. Have a fully-charged smartphone and laptop, and still plug both in if possible
    2. Log into Gradescope on your phone
    3. Change the screen timeout setting on your phone to never, so your screen doesn't go black if you don't interact with your screen for a while.
      • iPhones: Settings / Display & Brightness / Auto-Lock / Never
      • Android: Settings / Display / Screen timeout / 10 minutes (or the maximum amount of time)
    4. Turn on Do Not Disturb (or otherwise turn off all notifications).
    5. Position your webcam so we can see:
      • Your desk
      • The paper you are working on
      • Your writing utensil(s)
      • Both of your hands
      • Your phone

  5. During the quiz:
    1. You may not ask questions during the exam.
      • If you are unsure how to interpret a problem, take your best guess.
      • If you feel a question is unfair because you could not ask a question about it, please email the instructor after the quiz and describe your concern. (We are working hard to make the questions extra clear this year, but we want to know when we fail.)
    2. You may not touch your laptop or webcam.
      • This includes muting yourself at any point; the proctors may mute you though.
    3. All of these must be visible at all times:
      • Your desk
      • The paper you are working on
      • Your writing utensil(s)
      • Both of your hands
      • Your phone, with the quiz webpage
    4. For any tech fails (laptop or internet stops working, etc.):
      1. Stop taking the quiz
      2. Email the instructor (rileyrd@cmu.edu) right away
      3. We will reply soon to set up a 1-on-1 oral quiz with the course faculty

  6. After the quiz:
    1. Follow all proctor instructions on how to end the quiz.
    2. If you finish early, wait patiently until the end of the quiz. (Note: Don't use your phone...)
    3. Keep everything in view (as noted above) until the proctor calls "time".
    4. When instructed, use your phone to scan your quiz and submit the PDF to Gradescope.
    5. After submitting to Gradescope, hold your phone up to the webcam to show the receipt.
    6. Even then, remain in quiz mode until the proctor calls "all clear"

Question 1 - BST Building [6 pts]

Imagine you are constructing a binary search tree of integers, and the following integers are added in the following order:

5, 13, 57, 89, 99, 87, 32, 33

Draw the resulting binary search tree.


Question 2 - BST Traversal [4 pts]

Consider the following binary search tree:

Assuming the tree is traversed pre-order and the nodes printed, what is the resulting sequence? (Within the pre-order traversal, assume that left is followed before right.)


Question 3 - BST Free Response

Consider the following code for a binary search tree of integers. (There is nothing special here, the code is provided just in case you forgot how a binary tree is built.)


public class BinarySearchTree {
    private TreeNode root;

    private class TreeNode {
        private int data;
        private TreeNode left;
        private TreeNode right;

        private TreeNode(int data) {
            this.data = data;
        }
    }

    public BinarySearchTree() {
        root = null;
    }

    public void add(int item) {
        root = add(root, item);
    }

    private TreeNode add(TreeNode root, int item) {
        if (root == null) {
            return new TreeNode(item);
        }

        if (item < root.data) {
            root.left = add(root.left, item);
        } else {
            root.right = add(root.right, item);
        }

        return root;
    }
}

Part A [5 pts]

Write the code for a new method in this class called smallest(), which returns the value of the smallest integer in the tree. You may also write any additional helper methods that you need. Your method must be \( O(\textrm{log }N) \). If the tree is empty, return -1.

Part B [5 pts]

Write the code for a new method in this class called largestEven(), which returns the value of the largest even number in the tree. Your method must be \( O(N) \). If there are no even number in the tree, return -1.

Notes and Hints: