The AVL Tree Rotations Tutorial


 Eugenia Gallagher
 2 years ago
 Views:
Transcription
1 The AVL Tree Rottions Tutoril By John Hrgrove Version 1.0.1, Updted Mr Astrt I wrote this doument in n effort to over wht I onsider to e drk re of the AVL Tree onept. When presented with the tsk of writing n AVL tree lss in Jv, I ws left souring the we for useful informtion on how this ll works. There ws lot of useful informtion on the wikipedi pges for AVL tree nd Tree rottion. You n find links to these pges in setion 4. The tree rottion pge on wikipedi is lking, I feel. The AVL tree pge needs work s well, ut this pge is hurting dly, nd t some point in the future, I will likely integrte most of this doument into tht pge. This doument overs oth types of rottions, nd ll 4 pplitions of them. There is lso smll setion on deiding whih rottions to use in different situtions. 1. Rottions: How they work A tree rottion n e n imtimidting onept t first. You end up in sitution where you're juggling nodes, nd these nodes hve trees tthed to them, nd it n ll eome onfusing very fst. I find it helps to lok out wht's going on with ny of the sutrees whih re tthed to the nodes you're fumling with, ut tht n e hrd. Left Rottion (LL) Imgine we hve this sitution: Figure 11 To fix this, we must perform left rottion, rooted t A. This is done in the following steps: eomes the new root. tkes ownership of 's left hild s its right hild, or in this se, null. tkes ownership of s its left hild. The tree now looks like this: Figure 12 Right Rottion (RR) A right rottion is mirror of the left rottion opertion desried ove. Imgine we hve this sitution: Figure 13
2 To fix this, we will perform single right rottion, rooted t C. This is done in the following steps: eomes the new root. tkes ownership of 's right hild, s its left hild. In this se, tht vlue is null. tkes ownership of, s it's right hild. The resulting tree: Figure 14 LeftRight Rottion (LR) or "Doule left" Sometimes single left rottion is not suffiient to lne n unlned tree. Tke this sitution: Figure 15 Perfet. It's lned. Let's insert ''. Figure 16 Our initil retion here is to do single left rottion. Let's try tht. Figure 17 Our left rottion hs ompleted, nd we're stuk in the sme sitution. If we were to do single right rottion in this sitution, we would e right k where we strted. Wht's using this? The nswer is tht this is result of the right sutree hving negtive lne. In other words, euse the right sutree ws left hevy, our rottion ws not suffiient. Wht n we do? The nswer is to perform right rottion on the right sutree. Red tht gin. We will perform right rottion on the right sutree. We re not rotting on our urrent root. We re rotting on our right hild. Think of our right sutree, isolted from our min tree, nd perform right rottion on it: Before:
3 Figure 18 After: Figure 19 After performing rottion on our right sutree, we hve prepred our root to e rotted left. Here is our tree now: Figure 110 Looks like we're redy for left rottion. Let's do tht: Figure 111 Voil. Prolem solved. RightLeft Rotition (RL) or "Doule right" A doule right rottion, or rightleft rottion, or simply RL, is rottion tht must e performed when ttempting to lne tree whih hs left sutree, tht is right hevy. This is mirror opertion of wht ws illustrted in the setion on LeftRight Rottions, or doule left rottions. Let's look t n exmple of sitution where we need to perform RightLeft rottion. Figure 112 In this sitution, we hve tree tht is unlned. The left sutree hs height of 2, nd the right sutree hs height of 0. This mkes the lne ftor of our root node,, equl to 2. Wht do we do? Some kind of right rottion is lerly neessry, ut single right rottion will not solve our prolem. Let's try it: Figure 113
4 Looks like tht didn't work. Now we hve tree tht hs lne of 2. It would pper tht we did not omplish muh. Tht is true. Wht do we do? Well, let's go k to the originl tree, efore we did our pointless right rottion: Figure 114 The reson our right rottion did not work, is euse the left sutree, or '', hs positive lne ftor, nd is thus right hevy. Performing right rottion on tree tht hs left sutree tht is right hevy will result in the prolem we just witnessed. Wht do we do? The nswer is to mke our left sutree lefthevy. We do this y performing left rottion our left sutree. Doing so leves us with this sitution: Figure 115 This is tree whih n now e lned using single right rottion. We n now perform our right rottion rooted t C. The result: Figure 116 Blne t lst. 2. Rottions, When to Use Them nd Why How to deide when you need tree rottion is usully esy, ut determining whih type of rottion you need requires little thought. A tree rottion is neessry when you hve inserted or deleted node whih leves the tree in n unlned stte. An unlned stte is defined s stte in whih ny sutree hs lne ftor of greter thn 1, or less thn 1. Tht is, ny tree with differene etween the heights of its two sutrees greter thn 1, is onsidered unlned. This is lned tree: Figure 21 1
5 2 3 This is n unlned tree: Figure This tree is onsidered unlned euse the root node hs lne ftor of 2. Tht is, the right sutree of 1 hs height of 2, nd the height of 1's left sutree is 0. Rememer tht lne ftor of tree with left sutree A nd right sutree B is B  A Simple. In figure 22, we see tht the tree hs lne of 2. This mens tht the tree is onsidered "right hevy". We n orret this y performing wht is lled "left rottion". How we determine whih rottion to use follows few si rules. See psuedo ode: IF tree is right hevy IF tree's right sutree is left hevy Perform Doule Left rottion ELSE Perform Single Left rottion ELSE IF tree is left hevy IF tree's left sutree is right hevy Perform Doule Right rottion ELSE Perform Single Right rottion As you n see, there is sitution where we need to perform "doule rottion". A single rottion in the situtions desried in the pseudo ode leve the tree in n unlned stte. Follow these rules, nd you should e le to lne n AVL tree following n insert or delete every time.
6 3. Summry It s importnt to understnd tht the exmples ove were on very smll trees to keep the onepts ler. In theory, however, if you develop n pplition whih uses AVL trees, progrmming for the situtions shown ove while using the rules provided should sle just fine. If you hve omments, questions or ritiisms, feel free to emil me t 4. Further Reding  Tree rottion pge on Wikipedi,  AVL tree pge on Wikipedi,  Animted AVL Tree Jv pplet,  AVL Trees: Tutoril nd C++ Implementtion,
Chapter. Contents: A Constructing decimal numbers
Chpter 9 Deimls Contents: A Construting deiml numers B Representing deiml numers C Deiml urreny D Using numer line E Ordering deimls F Rounding deiml numers G Converting deimls to frtions H Converting
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationLecture 15  Curve Fitting Techniques
Lecture 15  Curve Fitting Techniques Topics curve fitting motivtion liner regression Curve fitting  motivtion For root finding, we used given function to identify where it crossed zero where does fx
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More information1. Definition, Basic concepts, Types 2. Addition and Subtraction of Matrices 3. Scalar Multiplication 4. Assignment and answer key 5.
. Definition, Bsi onepts, Types. Addition nd Sutrtion of Mtries. Slr Multiplition. Assignment nd nswer key. Mtrix Multiplition. Assignment nd nswer key. Determinnt x x (digonl, minors, properties) summry
More informationAppendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:
Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you
More informationWords Symbols Diagram. abcde. a + b + c + d + e
Logi Gtes nd Properties We will e using logil opertions to uild mhines tht n do rithmeti lultions. It s useful to think of these opertions s si omponents tht n e hooked together into omplex networks. To
More informationRatio and Proportion
Rtio nd Proportion Rtio: The onept of rtio ours frequently nd in wide vriety of wys For exmple: A newspper reports tht the rtio of Repulins to Demorts on ertin Congressionl ommittee is 3 to The student/fulty
More informationThe remaining two sides of the right triangle are called the legs of the right triangle.
10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right
More informationTallahassee Community College. Simplifying Radicals
Tllhssee Communit College Simplifing Rdils The squre root of n positive numer is the numer tht n e squred to get the numer whose squre root we re seeking. For emple, 1 euse if we squre we get 1, whih is
More information1 Fractions from an advanced point of view
1 Frtions from n vne point of view We re going to stuy frtions from the viewpoint of moern lger, or strt lger. Our gol is to evelop eeper unerstning of wht n men. One onsequene of our eeper unerstning
More informationQuick Guide to Lisp Implementation
isp Implementtion Hndout Pge 1 o 10 Quik Guide to isp Implementtion Representtion o si dt strutures isp dt strutures re lled Sepressions. The representtion o n Sepression n e roken into two piees, the
More informationPROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * challenge questions
PROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * hllenge questions e The ll will strike the ground 1.0 s fter it is struk. Then v x = 20 m s 1 nd v y = 0 + (9.8 m s 2 )(1.0 s) = 9.8 m s 1 The speed
More informationSquare Roots Teacher Notes
Henri Picciotto Squre Roots Techer Notes This unit is intended to help students develop n understnding of squre roots from visul / geometric point of view, nd lso to develop their numer sense round this
More informationHomework 3 Solutions
CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.
More informationIntegration by Substitution
Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is
More informationThe Math Learning Center PO Box 12929, Salem, Oregon 97309 0929 Math Learning Center
Resource Overview Quntile Mesure: Skill or Concept: 1010Q Determine perimeter using concrete models, nonstndrd units, nd stndrd units. (QT M 146) Use models to develop formuls for finding res of tringles,
More informationFormal Languages and Automata Exam
Forml Lnguges nd Automt Exm Fculty of Computers & Informtion Deprtment: Computer Science Grde: Third Course code: CSC 34 Totl Mrk: 8 Dte: 23//2 Time: 3 hours Answer the following questions: ) Consider
More informationpq Theory Power Components Calculations
ISIE 23  IEEE Interntionl Symposium on Industril Eletronis Rio de Jneiro, Brsil, 911 Junho de 23, ISBN: 78379128 pq Theory Power Components Clultions João L. Afonso, Memer, IEEE, M. J. Sepúlved Freits,
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationVariable Dry Run (for Python)
Vrile Dr Run (for Pthon) Age group: Ailities ssumed: Time: Size of group: Focus Vriles Assignment Sequencing Progrmming 7 dult Ver simple progrmming, sic understnding of ssignment nd vriles 2050 minutes
More informationModule 5. Threephase AC Circuits. Version 2 EE IIT, Kharagpur
Module 5 Threehse A iruits Version EE IIT, Khrgur esson 8 Threehse Blned Suly Version EE IIT, Khrgur In the module, ontining six lessons (7), the study of iruits, onsisting of the liner elements resistne,
More informationSeeking Equilibrium: Demand and Supply
SECTION 1 Seeking Equilirium: Demnd nd Supply OBJECTIVES KEY TERMS TAKING NOTES In Setion 1, you will explore mrket equilirium nd see how it is rehed explin how demnd nd supply intert to determine equilirium
More informationScan Tool Software Applications Installation and Updates
Sn Tool Softwre Applitions Instlltion nd Updtes Use this doument to: Unlok softwre pplitions on Sn Tool Instll new softwre pplitions on Sn Tool Instll the NGIS Softwre Suite pplitions on Personl Computer
More informationAngles 2.1. Exercise 2.1... Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example
2.1 Angles Reognise lternte n orresponing ngles Key wors prllel lternte orresponing vertilly opposite Rememer, prllel lines re stright lines whih never meet or ross. The rrows show tht the lines re prllel
More information2 DIODE CLIPPING and CLAMPING CIRCUITS
2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of
More informationState the size of angle x. Sometimes the fact that the angle sum of a triangle is 180 and other angle facts are needed. b y 127
ngles 2 CHTER 2.1 Tringles Drw tringle on pper nd lel its ngles, nd. Ter off its orners. Fit ngles, nd together. They mke stright line. This shows tht the ngles in this tringle dd up to 180 ut it is not
More informationLINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More informationMaximum area of polygon
Mimum re of polygon Suppose I give you n stiks. They might e of ifferent lengths, or the sme length, or some the sme s others, et. Now there re lots of polygons you n form with those stiks. Your jo is
More informationWHAT HAPPENS WHEN YOU MIX COMPLEX NUMBERS WITH PRIME NUMBERS?
WHAT HAPPES WHE YOU MIX COMPLEX UMBERS WITH PRIME UMBERS? There s n ol syng, you n t pples n ornges. Mthemtns hte n t; they love to throw pples n ornges nto foo proessor n see wht hppens. Sometmes they
More informationKEY SKILLS INFORMATION TECHNOLOGY Level 3. Question Paper. 29 January 9 February 2001
KEY SKILLS INFORMATION TECHNOLOGY Level 3 Question Pper 29 Jnury 9 Ferury 2001 WHAT YOU NEED This Question Pper An Answer Booklet Aess to omputer, softwre nd printer You my use ilingul ditionry Do NOT
More informationc b 5.00 10 5 N/m 2 (0.120 m 3 0.200 m 3 ), = 4.00 10 4 J. W total = W a b + W b c 2.00
Chter 19, exmle rolems: (19.06) A gs undergoes two roesses. First: onstnt volume @ 0.200 m 3, isohori. Pressure inreses from 2.00 10 5 P to 5.00 10 5 P. Seond: Constnt ressure @ 5.00 10 5 P, isori. olume
More informationOxCORT v4 Quick Guide Revision Class Reports
OxCORT v4 Quik Guie Revision Clss Reports This quik guie is suitble for the following roles: Tutor This quik guie reltes to the following menu options: Crete Revision Clss Reports pg 1 Crete Revision Clss
More informationMATH PLACEMENT REVIEW GUIDE
MATH PLACEMENT REVIEW GUIDE This guie is intene s fous for your review efore tking the plement test. The questions presente here my not e on the plement test. Although si skills lultor is provie for your
More informationUnit 6: Exponents and Radicals
Eponents nd Rdicls : The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N):  counting numers. {,,,,, } Whole Numers (W):  counting numers with 0. {0,,,,,, } Integers (I): 
More informationSOLVING EQUATIONS BY FACTORING
316 (560) Chpter 5 Exponents nd Polynomils 5.9 SOLVING EQUATIONS BY FACTORING In this setion The Zero Ftor Property Applitions helpful hint Note tht the zero ftor property is our seond exmple of getting
More information DAY 1  Website Design and Project Planning
Wesite Design nd Projet Plnning Ojetive This module provides n overview of the onepts of wesite design nd liner workflow for produing wesite. Prtiipnts will outline the sope of wesite projet, inluding
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationFactoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
More informationEnd of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below.
End of term: TEST A You will need penil nd ruler. Yer Nme Clss Dte Complete the missing numers in the sequenes elow. 8 30 3 28 2 9 25 00 75 25 2 Put irle round ll of the following shpes whih hve 3 shded.
More informationOne Minute To Learn Programming: Finite Automata
Gret Theoreticl Ides In Computer Science Steven Rudich CS 15251 Spring 2005 Lecture 9 Fe 8 2005 Crnegie Mellon University One Minute To Lern Progrmming: Finite Automt Let me tech you progrmming lnguge
More informationPractice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn
Prtie Test 2 1. A highwy urve hs rdius of 0.14 km nd is unnked. A r weighing 12 kn goes round the urve t speed of 24 m/s without slipping. Wht is the mgnitude of the horizontl fore of the rod on the r?
More information1. Area under a curve region bounded by the given function, vertical lines and the x axis.
Ares y Integrtion. Are uner urve region oune y the given funtion, vertil lines n the is.. Are uner urve region oune y the given funtion, horizontl lines n the y is.. Are etween urves efine y two given
More informationSOLVING QUADRATIC EQUATIONS BY FACTORING
6.6 Solving Qudrti Equtions y Ftoring (6 31) 307 In this setion The Zero Ftor Property Applitions 6.6 SOLVING QUADRATIC EQUATIONS BY FACTORING The tehniques of ftoring n e used to solve equtions involving
More informationMathematics Higher Level
Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:
More informationStudent Access to Virtual Desktops from personally owned Windows computers
Student Aess to Virtul Desktops from personlly owned Windows omputers Mdison College is plesed to nnoune the ility for students to ess nd use virtul desktops, vi Mdison College wireless, from personlly
More informationUNIVERSITY AND WORKSTUDY EMPLOYERS WEBSITE USER S GUIDE
UNIVERSITY AND WORKSTUDY EMPLOYERS WEBSITE USER S GUIDE Tble of Contents 1 Home Pge 1 2 Pge 2 3 Your Control Pnel 3 4 Add New Job (ThreeStep Form) 46 5 Mnging Job Postings (Mnge Job Pge) 78 6 Additionl
More informationMcAfee Network Security Platform
XC240 Lod Blner Appline Quik Strt Guide Revision D MAfee Network Seurity Pltform This quik strt guide explins how to quikly set up nd tivte your MAfee Network Seurity Pltform XC240 Lod Blner. The SFP+
More informationExample 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
More informationSmall Business Cloud Services
Smll Business Cloud Services Summry. We re thick in the midst of historic sechnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly
More informationAdvanced Baseline and Release Management. Ed Taekema
Advnced Bseline nd Relese Mngement Ed Tekem Introduction to Bselines Telelogic Synergy uses bselines to perform number of criticl configurtion mngement tsks. They record the stte of the evolving softwre
More informationGRADE 4. Fractions WORKSHEETS
GRADE Frtions WORKSHEETS Types of frtions equivlent frtions This frtion wll shows frtions tht re equivlent. Equivlent frtions re frtions tht re the sme mount. How mny equivlent frtions n you fin? Lel eh
More informationEquivalence Checking. Sean Weaver
Equivlene Cheking Sen Wever Equivlene Cheking Given two Boolen funtions, prove whether or not two they re funtionlly equivlent This tlk fouses speifilly on the mehnis of heking the equivlene of pirs of
More information1 GSW IPv4 Addressing
1 For s long s I ve een working with the Internet protools, people hve een sying tht IPv6 will e repling IPv4 in ouple of yers time. While this remins true, it s worth knowing out IPv4 ddresses. Even when
More informationBayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
More information6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine soclled volumes of
More informationClause Trees: a Tool for Understanding and Implementing Resolution in Automated Reasoning
Cluse Trees: Tool for Understnding nd Implementing Resolution in Automted Resoning J. D. Horton nd Brue Spener University of New Brunswik, Frederiton, New Brunswik, Cnd E3B 5A3 emil : jdh@un. nd spener@un.
More informationRegular Sets and Expressions
Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite
More informationAutoMax Auto Feed Shredders 2015
AutoMx Auto Feed Shredders 20 Revolutionizing the Wy You Shred True innovtion brings meningful chnge nd vlue to n industry. When developing our uto feed technologies the focus ws on trnsforming the shredder
More informationFinite Automata. Informatics 2A: Lecture 3. John Longley. 25 September School of Informatics University of Edinburgh
Lnguges nd Automt Finite Automt Informtics 2A: Lecture 3 John Longley School of Informtics University of Edinburgh jrl@inf.ed.c.uk 25 September 2015 1 / 30 Lnguges nd Automt 1 Lnguges nd Automt Wht is
More informationAREA OF A SURFACE OF REVOLUTION
AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.
More informationA.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324
A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................
More informationActive Directory Service
In order to lern whih questions hve een nswered orretly: 1. Print these pges. 2. Answer the questions. 3. Send this ssessment with the nswers vi:. FAX to (212) 9673498. Or. Mil the nswers to the following
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationWelch Allyn CardioPerfect Workstation Installation Guide
Welch Allyn CrdioPerfect Worksttion Instlltion Guide INSTALLING CARDIOPERFECT WORKSTATION SOFTWARE & ACCESSORIES ON A SINGLE PC For softwre version 1.6.5 or lter For network instlltion, plese refer to
More informationQuick Reference Guide: Onetime Account Update
Quick Reference Guide: Onetime Account Updte How to complete The Quick Reference Guide shows wht existing SingPss users need to do when logging in to the enhnced SingPss service for the first time. 1)
More informationIf two triangles are perspective from a point, then they are also perspective from a line.
Mth 487 hter 4 Prtie Prolem Solutions 1. Give the definition of eh of the following terms: () omlete qudrngle omlete qudrngle is set of four oints, no three of whih re olliner, nd the six lines inident
More information1 Numerical Solution to Quadratic Equations
cs42: introduction to numericl nlysis 09/4/0 Lecture 2: Introduction Prt II nd Solving Equtions Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mrk Cowlishw Numericl Solution to Qudrtic Equtions Recll
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationStart Here. IMPORTANT: To ensure that the software is installed correctly, do not connect the USB cable until step 17. Remove tape and cardboard
Strt Here 1 IMPORTANT: To ensure tht the softwre is instlled correctly, do not connect the USB cle until step 17. Follow the steps in order. If you hve prolems during setup, see Trouleshooting in the lst
More informationAntiSpyware Enterprise Module 8.5
AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n ddon to the VirusScn Enterprise 8.5i product tht extends its ility
More information9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes
The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is soclled becuse when the sclr product of two vectors
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationWarmup for Differential Calculus
Summer Assignment Wrmup for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSE3BB4: Software Design III Concurrent System Design. Sample Solutions to Assignment 1
SE3BB4: Softwre Design III Conurrent System Design Winter 2011 Smple Solutions to Assignment 1 Eh question is worth 10pts. Totl of this ssignment is 70pts. Eh ssignment is worth 9%. If you think your solution
More informationMA 15800 Lesson 16 Notes Summer 2016 Properties of Logarithms. Remember: A logarithm is an exponent! It behaves like an exponent!
MA 5800 Lesson 6 otes Summer 06 Rememer: A logrithm is n eponent! It ehves like n eponent! In the lst lesson, we discussed four properties of logrithms. ) log 0 ) log ) log log 4) This lesson covers more
More information, and the number of electrons is 19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.
Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge
More informationThe Cat in the Hat. by Dr. Seuss. A a. B b. A a. Rich Vocabulary. Learning Ab Rhyming
MINILESSON IN TION The t in the Ht y Dr. Seuss Rih Voulry tme dj. esy to hndle (not wild) LERNING Lerning Rhyming OUT Words I know it is wet nd the sun is not sunny. ut we n hve Lots of good fun tht is
More informationAlgebra Review. How well do you remember your algebra?
Algebr Review How well do you remember your lgebr? 1 The Order of Opertions Wht do we men when we write + 4? If we multiply we get 6 nd dding 4 gives 10. But, if we dd + 4 = 7 first, then multiply by then
More informationCalculating Principal Strains using a Rectangular Strain Gage Rosette
Clulting Prinipl Strins using Retngulr Strin Gge Rosette Strin gge rosettes re used often in engineering prtie to determine strin sttes t speifi points on struture. Figure illustrtes three ommonly used
More informationNQF Level: 2 US No: 7480
NQF Level: 2 US No: 7480 Assessment Guide Primry Agriculture Rtionl nd irrtionl numers nd numer systems Assessor:.......................................... Workplce / Compny:.................................
More information1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply?
Assignment 3: Bohr s model nd lser fundmentls 1. In the Bohr model, compre the mgnitudes of the electron s kinetic nd potentil energies in orit. Wht does this imply? When n electron moves in n orit, the
More informationCOMPLEX FRACTIONS. section. Simplifying Complex Fractions
58 (66) Chpter 6 Rtionl Epressions undles tht they cn ttch while working together for 0 hours. 00 600 6 FIGURE FOR EXERCISE 9 95. Selling. George sells one gzine suscription every 0 inutes, wheres Theres
More information1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator
AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.
More informationSCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Basic Algebra
SCHOOL OF ENGINEERING & BUILT ENVIRONMENT Mthemtics Bsic Alger. Opertions nd Epressions. Common Mistkes. Division of Algeric Epressions. Eponentil Functions nd Logrithms. Opertions nd their Inverses. Mnipulting
More informationHow fast can we sort? Sorting. Decisiontree model. Decisiontree for insertion sort Sort a 1, a 2, a 3. CS 3343  Spring 2009
CS 4  Spring 2009 Sorting Crol Wenk Slides courtesy of Chrles Leiserson with smll chnges by Crol Wenk CS 4 Anlysis of Algorithms 1 How fst cn we sort? All the sorting lgorithms we hve seen so fr re comprison
More informationData Security 1. 1 What is the function of the Jump instruction? 2 What are the main parts of the virus code? 3 What is the last act of the virus?
UNIT 18 Dt Seurity 1 STARTER Wht stories do you think followed these hedlines? Compre nswers within your group. 1 Love ug retes worldwide hos. 2 Hkers rk Mirosoft softwre odes. 3 We phone sm. Wht other
More informationORGANIZER QUICK REFERENCE GUIDE
NOTES ON ORGANIZING AND SCHEDULING MEETINGS Individul GoToMeeting orgnizers my hold meetings for up to 15 ttendees. GoToMeeting Corporte orgnizers my hold meetings for up to 25 ttendees. GoToMeeting orgnizers
More informationStrong acids and bases
Monoprotic AcidBse Equiliri (CH ) ϒ Chpter monoprotic cids A monoprotic cid cn donte one proton. This chpter includes uffers; wy to fi the ph. ϒ Chpter 11 polyprotic cids A polyprotic cid cn donte multiple
More informationSmall Business Networking
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationIFTA 23rd Annual Conference. Friday, October 8, 2010. Yukitoshi Higashino, MFTA
IFTA 23rd Annul Conference Fridy, Octoer 8, 2010 Border Line Pttern for the Ichimoku Kinko Hyo (Cndlestick Chrt)  Positioning with Bse Lines nd Timing for TimeBsed Loss Cutting 1 Yukitoshi Higshino,
More informationSection 54 Trigonometric Functions
5 Trigonometric Functions Section 5 Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationOr more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
More informationChapter. Fractions. Contents: A Representing fractions
Chpter Frtions Contents: A Representing rtions B Frtions o regulr shpes C Equl rtions D Simpliying rtions E Frtions o quntities F Compring rtion sizes G Improper rtions nd mixed numers 08 FRACTIONS (Chpter
More informationBoğaziçi University Department of Economics Spring 2016 EC 102 PRINCIPLES of MACROECONOMICS Problem Set 5 Answer Key
Boğziçi University Deprtment of Eonomis Spring 2016 EC 102 PRINCIPLES of MACROECONOMICS Prolem Set 5 Answer Key 1. One yer ountry hs negtive net exports. The next yer it still hs negtive net exports n
More informationLecture 3: orientation. Computer Animation
Leture 3: orienttion Computer Animtion Mop tutoril sessions Next Thursdy (Feb ) Tem distribution: :  :3  Tems 7, 8, 9 :3  :  Tems nd :  :3  Tems 5 nd 6 :3  :  Tems 3 nd 4 Pper ssignments Pper ssignment
More informationORGANIZER QUICK REFERENCE GUIDE
NOTES ON ORGANIZING AND SCHEDULING MEETINGS Individul GoToMeeting orgnizers my hold meetings for up to 15 ttendees. GoToMeeting Corporte orgnizers my hold meetings for up to 25 ttendees. GoToMeeting orgnizers
More information