lab03-sol

3. In a B*-tree, there can be at most 4 search-key values in each node. Assume that the height of the B*-tree is 2. The height of the tree is the length of the path from the root to a leaf node. a) What is the maximum number of leaf nodes this tree can have? Answer: b) Let N1 be a node in the tree. N1 is neither a leaf nor the root. What is the minimum number of children that N1 can have? Answer:

(i) What is meant by traversal in a tree? (ii) Name the 3 types of traversals. Write the traversal order for the tree given below. 60 41 74 16 53 65 90 25 46 55 63 70 12 42 62 64

1. For the given Red Black Tree, draw the tree, when the following entries are inserted: Jade, Bob, and Dave. You must show the intermediate states (after each rotation). Eddie Веyonce George Alicia Chris Frank Jane

Please written by computer source

Refer to the tree on the picture and answer the following questions 1. What rotation/s must be performed to make the tree balanced?2. After balancing the tree, what node will be the parent of node 71?

Which ones are correct for the tree T drawn below? (Select all that applies.) look at the picture sent Group of answer choices a) A preorder traversal of the tree yields 100 , 20 , 10 , 30 , 200 , 150 , 300. b) A preorder traversal of the tree yields 100, 20, 30, 10, 200, 150, 300. c) An inorder traversal of the tree yields 10, 20, 30, 100, 150, 200, 300. d) An inorder traversal of the tree yields 10, 20, 100, 30, 150, 200, 300. e) A postorder traversal of the tree yields 10, 30, 20, 100, 150, 300, 200. f) A postorder traversal of the tree yields 10, 30, 20, 150, 300, 200, 100.

Create an AVL tree with a height of 3 where the root of the tree would be the imbalanced alpha node if another single node X is inserted into the tree. Show the creation of the tree starting with the empty tree. Show each individual step of inserting the nodes and at each step state which rotation was done (if a rotation was done). Each value in the tree must be an integer and unique. For this problem, you can use drawings and even the visualization tools. You don’t need to implement this problem.

A H P X Problem 9 a. Copy it onto a piece of paper and draw the BST that results from adding the following letters to it (in this order): E QG F b. Then, describe in words what has to happen in order to remove the value L from the tree you drew in part (a), and draw the tree after the removal.

Question 9: Code the following problem statement using python: You are given a tree that is built in a following way: initially there is single vertex 1. All the other vertices are added one by one, from vertex 2 to vertex N, by connecting it to one of those that have been added before. You are to find the diameter of the tree after adding each vertex. Let the distance between vertex u and v be the minimal number of edges you have to pass to get from u to v, then diameter is the maximum distance between any two pairs (u,v) that have already been added to the tree. Input: 2 3 1 Output: 1 2.

All of the following are true EXCEPT: An empty tree is defined to have a height of 1. The depth of a node p is the number of ancestors of p, other than p itself. The height of a tree to be equal to the maximum of the depths of its nodes (or zero, if the tree is empty). The height of a node p in a tree T: • If p is a leaf, then the height of p is 0. • Otherwise, the height of p is one more than the maximum of the heights of p's children.

Problem 4 Counting Proofs Given what you've learned from chapter 1.4 about the difference between calculation and proofs, write up a proof or explanation for the following statement: A full binary tree of depth d has 2d–1 leaves. (Recall that a full binary tree is a binary tree where every path is the same length, i.e. all the leaf nodes are at the same depth.)

Use any drawing application to show the steps of constructing a new red-black tree by performing a sequence of insertions for these numbers: 2, 1, 4, 5, 9, 3, 6, 7. As described in the last lecture, each step of insertion or fixing up the violation should be indicated on a separate tree. So you have to start with a tree of one node (root) containing the first number (2), then the second tree involves the root and the second node(1), and so on. Don't forget to show any encountered violation while constructing the tree. In other words, indicate the case number and the needed action to treat that violation.

(e) Let X be a node in a binary search tree and let node Y be the predecessor of X. Which of the following are TRUE? Choose ALL that apply. (Assume that all nodes in the BST have distinct values, i.e., no duplicate) A. X could be in the left subtree of Y B. Y must be in the left subtree of X C. Y could be the parent of X D. None of the above is true (G) Consider the following program for finding the n-th Fibonacci number. def fibonacci (n): if n <= 1: return n return fibonacci(n-1) + fibonacci(n-2) Which of the following are TRUE? Choose ALL that apply. A. This progran will never terminate. B. This program performs many redundant computations. C. This program is inefficient because it has more than one base case. D. This program has a runtime that is upper-bounded by O(n^3), 1.e.,n cubed. E. Fibonacci lived in the 11th and 12th century, computers had not been invented then, so the above code cannot be used to compute the n-th fibonacci number.

me Portal (i) Write down the rules for the 3 types of tree traversals? (ii) Write all the three traversals for the tree given below? ( (iii) Are these 3 traversals possible only on a Binary Tree? Give reason for your answer ( hark R B M K e to search

(e) Let X be a node in a binary search tree and let node Y be the predecessor of X. Which of the following are TRUE? Choose ALL that apply. (Assume that all nodes in the BST have distinct values, i.e., no duplicate) A. X could be in the left subtree of Y B. Y must be in the left subtree of X C. Y could be the parent of X D. None of the above is true

3. Draw the AVL Tree of the following. NOTE: Show the tree before and after rotations.C O M P U T I N G a.)  Using the AVL in (3), add S E A R

34. Which of the following statements is/are true? 1. Given a rooted tree that includes nodes A and D, if node D is the parent of node A, then the height of node A is lower than that of node D. A null graph is an example of a forest. I only is true C. Both I and II are true D. Neither I nor II is true II only is true II. A. B. 34

QUESTION 5 day The government has recognized most street lights are left ON even in broad light. As an electrical engineer, you are required to design a solution to turn ON and OFF the street lights automatically and should also take into account unusually dark days. (Use information to answer a and b) 3 a. Build an objective tree for this need. b. Suggest at least TWO (2) solutions c. Briefly discuss at least three stages of design process.

using Java language

5. Draw the AVL Tree of the following. NOTE: Show the tree before and after rotations.G O L D S T A R a.). Using the AVL in (5), delete S L O T

Create two game trees for Euclid's game using a range of numbers from [1, 50]. State the pair of numbers you will be using such as i.e (20, 30). Solution should be in form of a game tree, no programming involved!

a) 511 data was stored in a computer system. It was later realized the data had been havazardly stored. This makes search and retrieving from the computer system a herculean task. It was suggested that to ease the searching process, the data should be stored in a binary search tree structure. Determine the height of the tree and explain how you arrived at the answer. b) Draw the binary expression tree for the complex expression (f*m) –b*(z+p) c) All passengers who booked a flight at a particular airline were stored as a binary search tree. Unfortunately the person whose data was used as the root node called to cancel the flight. The data was deleted from the booking list. Critically explain how the structure of the booking list will remain as a binary search tree.

(i) Write down the rules for the 3 types of tree traversals? (ii) Write all the three traversals for the tree given below? ( (iii) Are these 3 traversals possible only on a Binary Tree? Give reason for your answer Q S T W R B M A K N.

(a) Give ranks to each of the nodes below: (b) What is the type of the above tree? (c) What is the radius of the tree?