Trees-related questions
Beginning with an empty binary search tree, what binary search tree is formed when you add the following letters in the order given? J, N, B, A, W, E, T
Represent the following binary tree with an array
What is the result of adding 3 and 4 to the 2-3 tree shown below?
Why does a node in a red-black tree require less memory than a node in a 2-3-4 tree?
Why can’t a Red-Black Tree have a black child node with exactly one black child and no red child?
What is the maximum height of a Red-Black Tree with 14 nodes?
Homework Answers
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Beginning with an empty binary search tree, what binary search tree is formed when you add the following letters in the order given?
A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ
Data structures C++1- A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ in height by no more than 1 Out of the following choices, which is the minimum set of nodes, if removed, will make the BST balanced?2- Which of the following is true for Red-Black Trees ? Select all choices that apply! Select one or more: a. For each node in the tree, all paths from that node to any leaf nodes contain...
Recall from Assignment 2 the definition of a binary tree data structure: either an empty tree,...
Recall from Assignment 2 the definition of a binary tree data structure: either an empty tree, or a node with two children that are trees. Let T(n) denote the number of binary trees with n nodes. For example T(3) 5 because there are five binary trees with three nodes: (a) Using the recursive definition of a binary tree structure, or otherwise, derive a recurrence equation for T(n). (8 marks) A full binary tree is a non-empty binary tree where every...
Insert the following values in the given order into a Binary Search Tree and use the...
Insert the following values in the given order into a Binary Search Tree and use the resulting BST in the next 5 questions. 15 8 3 6 23 9 11 10 20 13 5 9. What is the height of the resulting Binary Search Tree? 10. What is the depth of the node that stores the value 11? 11. Is there a path from the node storing the value 15 to the node storing the value 5? If so, show...
C++ Binary Search trees Depth first traversal is the same as _____ order traversal. When we add...
C++ Binary Search trees Depth first traversal is the same as _____ order traversal. When we add a new node to an existing binary search tree, it will always become a ______. When we delete a node with 2 children from a binary search tree, we replace the node with ______.
QUESTION 9 Consider the following binary search tree: If the root node, 50, is deleted, which node will become the new root? A 15 B 24 C 37 D 62 QUESTION 10 In the...
QUESTION 9
Consider the following binary search tree:
If the root node, 50, is deleted, which node will become the new
root?
A
15
B
24
C
37
D
62
QUESTION 10
In the following trees EXCEPT______, the left and right subtrees
of any node have heights that differ by at most 1.
A
complete trees
B
perfect full trees
C
balanced binary trees
D
binary search trees
QUESTION 11
A perfect full binary tree whose height is 5 has...
Trees and Heaps 1. Show that the maximum number of nodes in a binary tree of...
Trees and Heaps 1. Show that the maximum number of nodes in a binary tree of height h is 2h+1 − 1. 2. A full node is a node with two children. Prove that the number of full nodes plus one is equal to the number of leaves in a nonempty binary tree. 3. What is the minimum number of nodes in an AVL tree of height 15? 4. Show the result of inserting 14, 12, 18, 20, 27, 16,...
Draw the tree resulting from inserting the following values into a binary search tree in order...
Draw the tree resulting from inserting the following values into a binary search tree in order without re-balancing: 40, 10, 60, 30, 20, 90, 70, 50 Null pointers can be omitted as long as it is clear whether a single child is a left or right child. THEN For every node in the tree, the values that can be in the subtree rooted at that node are constrained by ancestors to be in some range of integers. The root (the...
In this assignment, you will add several methods to the Binary Search Tree. You should have compl...
In this assignment, you will add several methods to the Binary Search Tree. You should have completed the following three methods in the lab: public void insert(Key key, Value value) public Value get(Key key) public void inorder(Node root) For this assignment, you will implement the following: public void remove(Node root, Key key) public Key getMin(Node n) public Key getMax(Node n) public int height(Node n) The main method contains the statements to check whether your implementation works. You need to change...
in python 11.1 Binary Search Tree In this assignment, you will implement a Binary Search Tree...
in python
11.1 Binary Search Tree In this assignment, you will implement a Binary Search Tree You will also need to implement a Node class. This class will not be tested, but is needed to implement the BST. Your BST must implement the following methods. You are free to implement additional helper methods. It is recommended you create your own helper methods Constructor: Creates an Empty Tree String Method: Returns the string "Empty Tree" for an empty tree. Otherwise, returns...
Data Structures and Algorithms What is the: a. maximum number of levels that a binary search...
Data Structures and Algorithms What is the: a. maximum number of levels that a binary search tree with 100 nodes can have? b. minimum number of levels that a binary search tree with 100 nodes can have? c. maximum total number of nodes in a binary tree that has N levels? (Remember that the root is level 0.) d. maximum number of nodes in the Nth level of a binary tree? e. number of ancestors of a node in the...
Recall from Assignment 2 the definition of a binary tree data structure: either an empty tree, or a node with two children that are trees. Let T(n) denote the number of binary trees with n nodes. For example T(3) 5 because there are five binary trees with three nodes: (a) Using the recursive definition of a binary tree structure, or otherwise, derive a recurrence equation for T(n). (8 marks) A full binary tree is a non-empty binary tree where every...
QUESTION 9
Consider the following binary search tree:
If the root node, 50, is deleted, which node will become the new
root?
A
15
B
24
C
37
D
62
QUESTION 10
In the following trees EXCEPT______, the left and right subtrees
of any node have heights that differ by at most 1.
A
complete trees
B
perfect full trees
C
balanced binary trees
D
binary search trees
QUESTION 11
A perfect full binary tree whose height is 5 has...
in python
11.1 Binary Search Tree In this assignment, you will implement a Binary Search Tree You will also need to implement a Node class. This class will not be tested, but is needed to implement the BST. Your BST must implement the following methods. You are free to implement additional helper methods. It is recommended you create your own helper methods Constructor: Creates an Empty Tree String Method: Returns the string "Empty Tree" for an empty tree. Otherwise, returns...
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