...Chapter 6: Binary Trees Objectives Looking ahead – in this chapter, we’ll consider • Trees, Binary Trees, and Binary Search Trees • Implementing Binary Trees • Searching a Binary Search Tree • Tree Traversal • Insertion • Deletion Data Structures and Algorithms in C++, Fourth Edition 2 Objectives (continued) • • • • • • Balancing a Tree Self-Adjusting Trees Heaps Treaps k-d Trees Polish Notation and Expression Trees Data Structures and Algorithms in C++, Fourth Edition 3 Trees, Binary Trees, and Binary Search Trees • While linked lists, stacks, and queues are useful data structures, they do have limitations – Linked lists are linear in form and cannot reflect hierarchically organized data – Stacks and queues are one-dimensional structures and have limited expressiveness • To overcome these limitations, we’ll consider a new data structure, the tree • Trees consist of two components, nodes and arcs (or edges) • Trees are drawn with the root at the top, and “grow” down – The leaves of the tree (also called terminal nodes) are at the bottom of the tree Data Structures and Algorithms in C++, Fourth Edition 4 Trees, Binary Trees, and Binary Search Trees (continued) • Trees can be defined recursively as follows: 1. 2. 3. A tree with no nodes or arcs (an empty structure) is an empty tree If we have a set t1… tk of disjoint trees, the tree whose root has the roots of t1… tk as its children is a tree Only structures...
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...ABSTRACT Trees are an important part of every community. Trees increase our quality of life by bringing natural elements and wildlife habitats into urban settings. Many neighborhoods are also the home of old trees that serve as historic landmarks. The tree observations goal is to help people maintain the health of their community and their state’s trees and forest. INTRODUCTION Trees have supported and sustained life throughout our existence. Different species display an endless variety of shapes and forms. In this experiment I had tested the ability to present information about factors affecting the health and measurements of trees. METHODS I used a Biltmore stick to measure the diameter (DBH) of the tree. I also had to find an area with at least twenty trees for measurements, recorded the information I obtain on a tree observation sheet. MATERIALS Biltmore stick, tree observation sheets, an area with twenty trees, pencil RESULTS The species of trees was from a neighborhood called Green Acres. Measurements taken at the site; shown that Maple/Boxelder trees in the site was identified as a more common species in the area and illustrated in good health with minor problems. For the other selected trees, no significant difference in circumference was found between all other trees because of the weather. DISCUSSION Overall the best time to measure trees is between June and September other observations can be made anytime during...
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...the number of it levels in tacked. There is a few terms that we must know, key. A key is a value of data that is searched from an index. A rid is what is call or referred to as a record ID. The nodes are broken down in to two categories; those are referred to as internal index nodes and leaf nodes. The internal index nods stores each value of keys and page identifiers. The leaf node stores the actual keys. Question 2) Explain the details of a binary tree A binary tree is a data structure that was nodes that have two nodes called child nodes. These nodes are located on the left and right side. On a binary tree the parent nodes was two children nodes and that is the max for each parent. There are different types of binary trees and some of them are called; full binary tree, rooted binary tree and complete binary tree just to name a few. Question 3) What are real world examples of tree implementations One example that I can give is 3D games. There are many games out there and on many different systems. Not only are there games on the WII or X-Box but there are becoming more popular on media sites like facebook. How does it work,...
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... Garry Jefferson hated his stay-at-home job. Day in and day out, he read and re-read essays written by illiterates hoping to scrape up a grade in his Psychology class. Fortunately, he never saw the acne pocked faces of the students he graded, and he could only imagine the facial horrors that roamed Blue River Community College’s halls. Blue River was a small town in central Colorado, inhabited by filthy rich old folk, and their grandchildren. The streets were clean, but the buildings that flanked the pavement were as dirty as could be. Inside the stone monoliths existed drug operations, brothels, cult gatherings, you name it. When the sun set is when the roles reversed, the filth being purged from their halls by police, and their hired mercenaries. This wasn’t a daily occurrence, maybe a bi-weekly one if things got heated between local gangs, but it was enough to create a tense atmosphere that lay in the air for all of time. Garry’s hand grew tired from typing at a maddening pace, correcting horrible grammatical errors, spelling errors and general un organization. He didn’t notice it at first, and when he did, panic began to set in. Sore hands slid from his keyboard as he slowly turned in his chair, and noticed the lights outside his office room were off. What he had noticed wasn’t the droning electrical sounds emitting from the lights that suddenly stopped when the fluorescent bulbs dimmed, but the slithering sound from the hallway. Then, dead silence, so quiet he could hear...
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...i SASTRA UNIVERSITY Shanmugha Arts, Science, Technology and Research Academy Thirumalaisamudram Thanjavur – 613 402 BCSCCS705 PARALLEL COMPUTING AND ALGORITHMS LAB B.TECH (COMPUTER SCIENCE AND ENGINEERING) 7TH SEMESTER ii List of Exercises: 1. Basic arithmetic operations in parallel 2. Find out factorial of a number 3. Generation of Fibonacci series, finding prime numbers in an interval. 4. Evaluate the integral of a function 5. Merging of two sorted lists 6. Parallel tree traversals 7. Matrix multiplication 8. Enumeration sort 9. Odd-Even transposition sort 10. Bitonic merge 11. Quick sort 12. Single source shortest path iii Exercise 1 Aim: Basic Arithmetic Operations in parallel To perform a set of arithmetic operations in parallel using a cluster of computers Procedure: Step 1: Identify a set of numbers over which arithmetic operations are to be done Step 2: Identify the rank in the cluster Step 3: Split the set of numbers into domains and assign each domain to their corresponding processor Step 4: Get the result from each computer in the cluster and assimilate them at the master Step 5: Verify the time taken for the completion of each task. Algorithm:function sum(+,identity,a) = if #a == 1 then [identity] else let e = even_elts(a); o = odd_elts(a); s = scan_op(op,identity,{op(e,o): e in e; o in o}) in interleave(s,{op(s,e): s in s; e in e}); iv Input:- An array of integers Output: - The sum 3,2,7,6 P1 18 0,5,4,8 P2 17 62 2,0,1,5 P3 8...
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...Hannah Muller ENVR 102 Book Report For this book report, I read Teaching the Trees by Joan Maloof. Joan Maloof studied Plant Science at the University of Delaware, Environmental Science at the University of Maryland Eastern Shore, and Ecology at the University of Maryland College Park. Maloof is a professor at Salisbury University who teaches biology and environmental studies at Salisbury University. Aside from being a professor, Maloof is a biologist. She was always very interested in forests so from very early on Maloof has been exploring forests all over the eastern United States. She puts a lot of focus on the intertwined connections between specific tree species and the specific animals and insects that need to tree to live and in turn the tree needs them as well. Maloof possesses great enthusiasm for the woods and everything that they contain and is working on developing networking old growth forests across the United States. Teaching the Trees starts out with Joan Maloof saying how we would lose the “Magical Web” of relationships between organisms and trees (Maloof xiii). She begins talking about the services that trees provide for us. She also talks about how the benefits of trees equal healthier air for us to breathe. Japanese researchers have even found that there are 120 chemical compounds in mountain forest air that are good for us (Maloof 3). Inhaling this air can even be cancer preventing. Perhaps by trying to save the forests we are actually trying to save...
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...Data Mining Algorithms for Classification BSc Thesis Artificial Intelligence Author: Patrick Ozer Radboud University Nijmegen January 2008 Supervisor: Dr. I.G. Sprinkhuizen-Kuyper Radboud University Nijmegen Abstract Data Mining is a technique used in various domains to give meaning to the available data. In classification tree modeling the data is classified to make predictions about new data. Using old data to predict new data has the danger of being too fitted on the old data. But that problem can be solved by pruning methods which degeneralizes the modeled tree. This paper describes the use of classification trees and shows two methods of pruning them. An experiment has been set up using different kinds of classification tree algorithms with different pruning methods to test the performance of the algorithms and pruning methods. This paper also analyzes data set properties to find relations between them and the classification algorithms and pruning methods. 2 1 Introduction The last few years Data Mining has become more and more popular. Together with the information age, the digital revolution made it necessary to use some heuristics to be able to analyze the large amount of data that has become available. Data Mining has especially become popular in the fields of forensic science, fraud analysis and healthcare, for it reduces costs in time and money. One of the definitions of Data Mining is; “Data Mining is a process that consists of applying data analysis and discovery...
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... Garry Jefferson hated his stay-at-home job. Day in and day out, he read and re-read essays written by illiterates hoping to scrape up a grade in his Psychology class. Fortunately, he never saw the acne pocked faces of the students he graded, and he could only imagine the facial horrors that roamed Blue River Community College’s halls. Blue River was a small town in central Colorado, inhabited by filthy rich old folk, and their grandchildren. The streets were clean, but the buildings that flanked the pavement were as dirty as could be. Inside the stone monoliths existed drug operations, brothels, cult gatherings, you name it. When the sun set is when the roles reversed, the filth being purged from their halls by police, and their hired mercenaries. This wasn’t a daily occurrence, maybe a bi-weekly one if things got heated between local gangs, but it was enough to create a tense atmosphere that lay in the air for all of time. Garry’s hand grew tired from typing at a maddening pace, correcting horrible grammatical errors, spelling errors and general un organization. He didn’t notice it at first, and when he did, panic began to set in. Sore hands slid from his keyboard as he slowly turned in his chair, and noticed the lights outside his office room were off. What he had noticed wasn’t the droning electrical sounds emitting from the lights that suddenly stopped when the fluorescent bulbs dimmed, but the slithering sound from the hallway. Then, dead silence, so quiet he could hear...
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...By mid-October, I doubted much vibrant foliage would remain on the trees outside of the valley. My drive up to Piñon Mesa seemed to confirm this assumption. Dusty aspens, all completely barren, lined the dirt road leading to Turkey Flats, the trail I planned on hiking. Crows squawked overhead as they flew from pine tree to pine tree. Stepping outside at the trailhead, I looked down to see limp brown leaves and sparse tall grasses spreading across all of the ground I could see. However, as I started walking into the forest, the brown leaves on the ground gradually had a growing number yellow leaves amongst them like bold polka dots. I was shocked; the hills looked lifeless from the road that lead me there. Looking ahead among pines were aspens...
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...Chapter 1 INTRODUCTION 1.1 Background of the Study It has been said that modeling the learner is the central aspect of intelligent tutoring systems. This realization spurred the development of student modeling systems or systems that diagnose student errors. These systems proved to be effective in areas like mathematics (subtraction, highschool algebra, differentiation) and computer programming (Pascal, Lisp,C++). The essential elements in constructing a student model are the background knowledge and the student behavior. The first component which is the background knowledge is difficult to acquire automatically and to extend, and in fact one of the major bottlenecks in the development of student modeling systems. The difficulty lies in constructing the bug library, which is the collection of common errors made by the students in a particular domain (Sison,1998). This implies that the background knowledge is a critical component in student modeling construction. Indeed, few systems are able to construct and extend bug libraries. The second component, which is the student behavior can be classified as simple and complex (Sison, 1998). Simple behavior involves classification and complex behavior involves problem solving task. Traditionally, in domains wherein the student behavior is simple (subtraction), student modeling systems used multiple behaviors as the primary input. This is known as synthetic student modeling. One drawback of this is that, the modeling system might construct...
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...Data Structures & Algorithms Coursework Assignment 1 Q1. (a) Algorithm swap(x, y): Node n head While (n.getNext () != x ) do n n.getNext() Node v y.getNext () n.setNext(y) y.setNext(x) x.setNext(v) (b) Algorithm swap Doubly(x, y): DNode n x.getPrev() DNode v y.getPrev() n.setNext(y) y.setPrev(n) y.setNext(x) x.setPrev(y) x.setNext(v) v.setPrev(x) (c) The run time complexity for the singled linked algorithm is O (n) and for the doubly linked algorithm is O (1). Doubly linked list has the best time complexity. Time complexity in singly linked list take more time because we have to move from head to the node before x Q2. (b) RedBlueStack implements Stack{ protected Object A[]; Int capacity; int top = -1; RedBlueStack(int cap) { A = new Object [capacity]; capacity = cap; } int size() { return (top + 1); } void push(Object obj) throws FullStackException { if (size() == capacity) throws new FullStackException("Stack is full."); A[++top] = obj; } Object top() throws EmptyStackException { if (isEmpty()) throws new EmptyStackException("Stack is empty."); return A[top]; } Boolean isEmpty() { return (top < 0); } Object top() throws EmptyStackException { if (isEmpty()) throws new EmptyStackException("Stack is empty."); return A[top]; } Object pop() throws EmptyStackException { Object elem; if (isEmpty()) throws new EmptyStackException("Stack...
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...Solution: Number Of Nodes: 1. /* 2. * C Program to Find the Number of Nodes in a Binary Tree 3. */ 4. #include <stdio.h> 5. #include <stdlib.h> 6. 7. /* 8. * Structure of node 9. */ 10. struct btnode 11. { 12. int value; 13. struct btnode *l; 14. struct btnode *r; 15. }; 16. 17. void createbinary(); 18. void preorder(node *); 19. int count(node*); 20. node* add(int); 21. 22. typedef struct btnode node; 23. node *ptr, *root = NULL; 24. 25. int main() 26. { 27. int c; 28. 29. createbinary(); 30. preorder(root); 31. c = count(root); 32. printf("\nNumber of nodes in binary tree are:%d\n", c); 33. } 34. /* 35. * constructing the following binary tree 36. * 50 37. ...
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... Garry Jefferson hated his stay-at-home job. Day in and day out, he read and re-read essays written by illiterates hoping to scrape up a grade in his Psychology class. Fortunately, he never saw the acne pocked faces of the students he graded, and he could only imagine the facial horrors that roamed Blue River Community College’s halls. Blue River was a small town in central Colorado, inhabited by filthy rich old folk, and their grandchildren. The streets were clean, but the buildings that flanked the pavement were as dirty as could be. Inside the stone monoliths existed drug operations, brothels, cult gatherings, you name it. When the sun set is when the roles reversed, the filth being purged from their halls by police, and their hired mercenaries. This wasn’t a daily occurrence, maybe a bi-weekly one if things got heated between local gangs, but it was enough to create a tense atmosphere that lay in the air for all of time. Garry’s hand grew tired from typing at a maddening pace, correcting horrible grammatical errors, spelling errors and general un organization. He didn’t notice it at first, and when he did, panic began to set in. Sore hands slid from his keyboard as he slowly turned in his chair, and noticed the lights outside his office room were off. What he had noticed wasn’t the droning electrical sounds emitting from the lights that suddenly stopped when the fluorescent bulbs dimmed, but the slithering sound from the hallway. Then, dead silence, so quiet he could hear...
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...entrepreneurial and managerial skills and technology. FDIs complement the domestic savings in financing the capital formation in the host country. FDIs contribute to the generation of output and employment. The foreign exchange inflow augments the supply of foreign exchange, which is often scarce in the developing countries. In most cases, however, the project being set up with FDI is dependent upon imported plant and machinery, and technology. The foreign exchange -inflow takes care of these import requirements, partially or fully. The direct cost of FDI to the host country comprises remittances made on account of dividends on the equity held abroad, interest on loans or suppliers' credits extended by the foreign investors, royalties and technical fees, for transfer of technology and other services provided by the foreign partner. Unlike foreign borrowings, servicing remittances, viz., dividends in the case of FDI begin after the project starts making profits. However, the servicing burden of FDI builds up very fast, and consumes considerable foreign exchange resources of the host country. Further, these remittances have the tendency to grow over time as the enterprise consolidates and prospers. Thus, the direct impact of FDIs on the host country includes both positive and negative aspects. The favourable impact is by way of generation of output and employment by complementing the domestic savings and bringing in the much-needed entrepreneurial skills and foreign exchange...
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...THE EFFECT OF SAVINGS RATE IN CANADA The impact of savings rate in an economic has become a very conflicting issue in research and among economist all over the world. This may be due to the importance of savings generally to the economic growth and development of any nation. However, the structure of every economy cannot be generalised by a particular economics’ variation because various countries have different social security and pension schemes, and different tax systems, all of which have an effect on disposable income. In addition, the age of a country’s population, the availability and ease of credit, the overall wealth, and cultural and social factors within a country all affect savings rates within a particular country. Therefore, this paper seeks to find the effect of savings in the Canadian economy. Household saving is defined as the difference between a household’s disposable incomes mainly wages received, revenue of the self-employed and net property income and its consumption (expenditures on goods and services). The household savings rate is calculated by dividing household savings by household disposable income. A negative savings rate indicates that a household spends more than it receives as regular income and finances some of the expenditure through credit (increasing debt), through gains arising from the sale of assets (financial or non-financial), or by running down cash and deposits. Since the early-to-mid-1990s, savings rates have been stable in some...
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