a. It is said that in B-trees with realistically large minimum degrees, almost all keys are...
Homework Answers
a)
If minimum degree is large and each node have maximum number of nodes, then the B-tree will have minimum height and almost all the keys are stored in the leaf nodes.
Assume height of the B-tree is h and each node in the B-tree is full. Then the total number of keys in the tree , n= (2t)h+1-1.
The number of keys at the depth h or leaves in the B-tree= [(2t)h+1-1]-[ (2t)h-1]
The ratio between total number of keys and the number of leaves( or percentage of leaves in the total number of keys)
= [(2t)h+1-1]-[ (2t)h-1] / (2t)h+1-1 ≈ 1-1/2t= (2t-1)/2t > 99%
Therefore, almost keys are stored in the leaves.
For suppose , t=100 then (2t-1)/2t =200-1/200=199/200= 0.995 or 99.5%.
Thus, if t=100, 99.5% of keys will be stored in the leaves.
For suppose , t=200 then (2t-1)/2t =400-1/400=399/400= 0.9975 or 99.75%.
Thus, if t=200, 99.75% of keys will be stored in the leaves.
b)
The above modified B-TREE-SEARCH takes a root node and a key k to be searched as input and returns the all occurrences of k in the tree pointed to by x.
Add Answer to:
a. It is said that in B-trees with realistically large minimum
degrees, almost all keys are...
It is said that in B-trees with realistically large minimum degrees, almost all keys are stored...
It is said that in B-trees with realistically large minimum degrees, almost all keys are stored in the leaf nodes. Justify this statement mathematically. Numerically demonstrate your mathematical justification with examples of t = 100 and 200.
A student believes that Binary Search Trees possess the following property.
(a) A student believes that Binary Search Trees possess the following property. Suppose we search for a key and the matching node is a leaf node. Let L be the set of all nodes to the left of the search path, P the set of all nodes on the search path, and R be the set of all nodes to the right of the search path. The student claims that any three keys I ∈ L, p ∈ P, and...
package hw3; import java.util.LinkedList; /* *********************************************************************** * A simple BST with int keys and no values...
package hw3; import java.util.LinkedList; /* *********************************************************************** * A simple BST with int keys and no values * * Complete each function below. * Write each function as a separate recursive definition (do not use more than one helper per function). * Depth of root==0. * Height of leaf==0. * Size of empty tree==0. * Height of empty tree=-1. * * TODO: complete the functions in this file. * DO NOT change the Node class. * DO NOT change the name...
k-d tree Background One generalization of binary trees is the k-d tree, which stores k-dimensional data....
k-d tree Background One generalization of binary trees is the k-d tree, which stores k-dimensional data. Every internal node of a k-d tree indicates the dimension d and the value v in that dimension that it discriminates by. An internal node has exactly two children, containing data that is less-than-or-equal and data that is greater than v in dimension d. For example, if the node distinguishes on dimension 1, value 107, then the left child is for data with y...
Add printRang method to BST.java that, given a low key value, and high key value, print...
Add printRang method to BST.java that, given a low key value, and high key value, print all records in a sorted order whose values fall between the two given keys. (Both low key and high key do not have to be a key on the list). BST.java import java.lang.Comparable; /** Binary Search Tree implementation for Dictionary ADT */ class BST<Key extends Comparable<? super Key>, E> implements Dictionary<Key, E> { private BSTNode<Key,E> root; // Root of the BST int nodecount; //...
1) Extend the Binary Search Tree ADT to include a public method leafCount that returns the...
1) Extend the Binary Search Tree ADT to include
a public method leafCount that returns the number of leaf nodes in
the tree.
2) Extend the Binary Search Tree ADT to include a
public method singleParent-Count that returns the number of nodes
in the tree that have only one child.
3) The Binary search tree ADT is extended to
include a boolean method similarTrees that receives references to
two binary trees and determines whether the shapes of the trees are...
You will construct a Huffman tree based on the given frequencies of 26 English alphabets in...
You will construct a Huffman tree based on the given frequencies of 26 English alphabets in upper case plus the space character. An internal tree node class in HuffmanTree with necessary information is required. • You will not randomly switch left and right children when merger two trees. Instead, you will build a right-heavy tree according to the following strategies to select the right child. (1) The tree that is taller will be the right child, i.e., the height is...
Write a C++ program to validate computer user-ids and passwords. A list of valid ids and...
Write a C++ program to validate computer user-ids and passwords. A list of valid ids and passwords (unsorted) is read from a file and stored in a Binary Search Tree (BST) of UserInfo objects. When user-ids and passwords are entered during execution, this BST is searched to determine whether they are legal. Input (file): UserInfo records for valid users Input (keyboard): Ids and passwords of users logging in Output (screen): Messages indicating whether user-ids and passwords are valid, as well...
For this assignment, you will write a program to work with Huffman encoding. Huffman code is...
For this assignment, you will write a program to work with Huffman encoding. Huffman code is an optimal prefix code, which means no code is the prefix of another code. Most of the code is included. You will need to extend the code to complete three additional methods. In particular, code to actually build the Huffman tree is provided. It uses a data file containing the frequency of occurrence of characters. You will write the following three methods in the...
Create a class to represent a term in an algebraic expression. As defined here, a term...
Create a class to represent a term in an algebraic expression. As defined here, a term consists of an integer coefficient and a nonnegative integer exponent. E.g. in the term 4x2, the coefficient is 4 and the exponent 2 in -6x8, the coefficient is -6 and the exponent 8 Your class will have a constructor that creates a Term object with a coefficient and exponent passed as parameters, and accessor methods that return the coefficient and the exponent. Your class...
1) Extend the Binary Search Tree ADT to include
a public method leafCount that returns the number of leaf nodes in
the tree.
2) Extend the Binary Search Tree ADT to include a
public method singleParent-Count that returns the number of nodes
in the tree that have only one child.
3) The Binary search tree ADT is extended to
include a boolean method similarTrees that receives references to
two binary trees and determines whether the shapes of the trees are...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago