Common Mistakes. Quick sort. Only choosing one pivot per iteration. At each iteration, one pivot per sublist should be chosen.
|
|
- Franklin Townsend
- 5 years ago
- Views:
Transcription
1 Common Mistakes Examples of typical mistakes Correct version Quick sort Only choosing one pivot per iteration. At each iteration, one pivot per sublist should be chosen. e.g. Use a quick sort to sort the following data into ascending order. 3, 5, 7, 2, 6, 4, 1, 9, 8, First pivot is 6 3, 5, 2, 1, 4, 6 7, 9, 8 giving list 1 { 3, 5, 2, 1, 4} and list 2 {7, 9, 8} pivot for list 1 is 2 giving list 3 {1} and list 4 {3, 5, 4} and so on separating the sort into individual lists and usually dealing with all the left hand lists before moving on to the right hand lists. First pivot is 6 3, 5, 2, 1, 4, 6, 7, 9, 8 Choosing one pivot in each sublist 2 and 9 1, 2 3, 5, 4, 6, 7, 8, 9 Choosing one pivot in each sublist 1, 5 and 8 1, 2, 3, 4, 5, 6 7, 8, 9 and so on. Not selecting a pivot if the numbers in the sublist are already in the correct order. e.g. Use a quick sort to sort the following data into ascending order. 3, 4, 6, 7, 5, 9 The first pivot is 6 List is in order so stop. 3, 4, 6, 7, 5, 9 The first pivot is 6 Choosing one pivot in each sublist 4 and 9 choosing one pivot in each sublist 3, 5 and 7. All pivots chosen, the list is in order so stop. Binary search Forgetting to discard the pivot as well as half of the list. e.g. Locate the name Smith in the following list 1) Brown 2) Davies 3) Hall 1
2 1 5 First pivot is 3 2 Hall reject top of list. 3) Hall Jones reject top of list 1 5 First pivot is 3 2 Hall reject, pivot and top of list Smith, name found Smith, name found. Bin packing Forgetting to offer later items to bin 1 first then bin 2 and so on. e.g. Put the data below into bins of size 10 using the first fit algorithm. 7, 8, 2, 3 Bin 1: Bin 2: Minimum Connector (Minimum Spanning Tree) The 7 and 8 are correctly placed, but the third number, 2, should have been placed in bin 1, giving Bin 1 : Bin 2 : 8 Bin 3 : 3 Forgetting to state which arcs have been rejected when using Kruskal. e.g. Use Kruskal s algorithm to find a minimum spanning tree for the network below. Arcs: AB, DF, AC, EF, CD Arcs: AB, DF, AC, EF, reject BC, reject DE, CD. 2
3 In Prim s algorithm, only considering vertices connected to the last vertex added to the tree. e.g. Use Prim s algorithm, starting at A, to find a minimum connector for the network above. Draw your tree. AB, BC, CD, DF, FE AB, AC, CD, DF, FE. Dijsktra s algorithm When a vertex has been given its final label, all vertices directly connected to it, no matter where they are, should be given a working value. So the algorithm reaches out from one vertex to the other vertices. The error some candidates make is to not record any working values until the vertices on the left have been completed and then to look at what feeds into the next vertex. e.g. Use Dijkstra s algorithm to find the shortest route from S to B, use the diagram below to make your working clear. Shortest route is S A C B length 6. Shortest route is S A B length 7. 3
4 Route Inspection (Chinese postman) If there are four odd nodes, all possible pairings of those four nodes must be considered, not just the more likely ones. (Remember the diagram is not drawn to scale!) e.g. Use the Chinese postman algorithm to find the length of the shortest inspection route for the network below. AB + CD = = 115 AC + BD = = 101 AD + BC = = 112 So length is = 429 m So length is = 443 m Critical Path Analysis The critical activities have zero total float. They do go from double domino to double domino but this alone is not enough to pick out the critical activities. e.g. State the critical activities from the activity network below. Critical activities are A and D. 4
5 Critical activities are A, C and D because they go from double to double. Graphical Linear Programming Straight lines must be drawn with a ruler. The lines should be labelled. Lines such as x = 2y are often drawn as y = 2x. Don t forget the non-negativity constraints. If the objective line method is used, an objective line needs to drawn on the graph. Matchings The alternating path must both start, and finish, at an unmatched vertex. The change status step must be clearly shown. 5
Decision Mathematics practice paper
Decision Mathematics practice paper 1. based on old-syllabus January 2013. 50 minutes, 50 marks. Write answers in answers book. Figure 1 Hero s algorithm for finding a square root is described by the flow
More informationDecision Mathematics D1 Advanced/Advanced Subsidiary. Friday 17 May 2013 Morning Time: 1 hour 30 minutes
Paper Reference(s) 6689/01R Edexcel GCE Decision Mathematics D1 Advanced/Advanced Subsidiary Friday 17 May 2013 Morning Time: 1 hour 30 minutes Materials required for examination Nil Items included with
More informationDecision Mathematics D1
Pearson Edexcel International Advanced Level Decision Mathematics D1 Advanced/Advanced Subsidiary Friday 16 June 2017 Afternoon Time: 1 hour 30 minutes Paper Reference WDM01/01 You must have: D1 Answer
More informationDijkstra s Algorithm (5/9/2013)
Dijkstra s Algorithm (5/9/2013) www.alevelmathsng.co.uk (Shortest Path Problem) The aim is to find the shortest path between two specified nodes. The idea with this algorithm is to attach to each node
More informationTaxicab Geometry Part II Meeting 3
Taxicab Geometry Part II Meeting 3 Preston Carroll 22 April 2018 1. Find the taxicab distance between two consecutive letters: C A B E D (a) AB= (b) BC= (c) CD= (d) DE= 1 2. Bob the taxi driver s passenger
More informationMark Scheme (Results) Summer GCE Decision D1 (6689) Paper 1
Mark Scheme (Results) Summer 2012 GCE Decision D1 (6689) Paper 1 Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning company. We provide a wide
More informationand 6.855J. Network Simplex Animations
.8 and 6.8J Network Simplex Animations Calculating A Spanning Tree Flow -6 7 6 - A tree with supplies and demands. (Assume that all other arcs have a flow of ) What is the flow in arc (,)? Calculating
More informationRegents Exam Questions by Topic Page 1 TOOLS OF GEOMETRY: Constructions NAME:
Regents Exam Questions by Topic Page 1 1. 060925ge, P.I. G.G.17 Which illustration shows the correct construction of an angle bisector? [A] 3. 060022a, P.I. G.G.17 Using only a ruler and compass, construct
More informationUNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 2: Constructing Lines, Segments, and Angles Instruction
Prerequisite Skills This lesson requires the use of the following skills: using a compass understanding the geometry terms line, segment, ray, and angle Introduction Two basic instruments used in geometry
More informationMIDTERM REVIEW INDU 421 (Fall 2013)
MIDTERM REVIEW INDU 421 (Fall 2013) Problem #1: A job shop has received on order for high-precision formed parts. The cost of producing each part is estimated to be $65,000. The customer requires that
More informationNANYANG TECHNOLOGICAL UNIVERSITY SEMESTER II EXAMINATION MH1301 DISCRETE MATHEMATICS. Time Allowed: 2 hours
NANYANG TECHNOLOGICAL UNIVERSITY SEMESTER II EXAMINATION 206-207 DISCRETE MATHEMATICS May 207 Time Allowed: 2 hours INSTRUCTIONS TO CANDIDATES. This examination paper contains FOUR (4) questions and comprises
More informationCONSTRUCTION #1: Segment Copy
CONSTRUCTION #1: Segment Copy Objective: Given a line segment, construct a line segment congruent to the given one. Procedure: After doing this Your work should look like this Start with a line segment
More information(Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions.
Seventh Grade Mathematics Assessments page 1 (Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions. A. TLW use tools to draw squares, rectangles, triangles and
More informationGeometry SOL G.4 Constructions Name Date Block. Constructions
Geometry SOL G.4 Constructions Mrs. Grieser Name Date Block Constructions Grab your compass and straight edge - it s time to learn about constructions!! On the following pages you will find instructions
More informationMath 152: Applicable Mathematics and Computing
Math 152: Applicable Mathematics and Computing May 8, 2017 May 8, 2017 1 / 15 Extensive Form: Overview We have been studying the strategic form of a game: we considered only a player s overall strategy,
More informationPast questions from the last 6 years of exams for programming 101 with answers.
1 Past questions from the last 6 years of exams for programming 101 with answers. 1. Describe bubble sort algorithm. How does it detect when the sequence is sorted and no further work is required? Bubble
More informationA Level Computer Science H446/02 Algorithms and programming. Practice paper - Set 1. Time allowed: 2 hours 30 minutes
A Level Computer Science H446/02 Algorithms and programming Practice paper - Set 1 Time allowed: 2 hours 30 minutes Do not use: a calculator First name Last name Centre number Candidate number INSTRUCTIONS
More informationGeometry Final Exam Review 2012 #
1 PART 1: Multiple Choice (40 x 2 points = 80%). PART 2: Open Ended (2 x 10 = 20%) 1) Find the volume and surface area of the following rectangular prisms 2) Find the surface area of the following cylinders.
More informationFoundations of Distributed Systems: Tree Algorithms
Foundations of Distributed Systems: Tree Algorithms Stefan Schmid @ T-Labs, 2011 Broadcast Why trees? E.g., efficient broadcast, aggregation, routing,... Important trees? E.g., breadth-first trees, minimal
More informationUniversal Cycles for Permutations Theory and Applications
Universal Cycles for Permutations Theory and Applications Alexander Holroyd Microsoft Research Brett Stevens Carleton University Aaron Williams Carleton University Frank Ruskey University of Victoria Combinatorial
More informationILLUSION CONFUSION! - MEASURING LINES -
ILLUSION CONFUSION! - MEASURING LINES - WHAT TO DO: 1. Look at the line drawings below. 2. Without using a ruler, which long upright or vertical line looks the longest or do they look the same length?
More information2. Here are some triangles. (a) Write down the letter of the triangle that is. right-angled, ... (ii) isosceles. ... (2)
Topic 8 Shapes 2. Here are some triangles. A B C D F E G (a) Write down the letter of the triangle that is (i) right-angled,... (ii) isosceles.... (2) Two of the triangles are congruent. (b) Write down
More informationCoding for Efficiency
Let s suppose that, over some channel, we want to transmit text containing only 4 symbols, a, b, c, and d. Further, let s suppose they have a probability of occurrence in any block of text we send as follows
More informationFinite Mathematical Structures A
AMS 01. (Spring, 010) Estie Arkin Finite Mathematical Structures A Exam : Thursday, April 8, 010 READ THESE INSTRUCTIONS CAREFULLY. Do not start the exam until told to do so. Make certain that you have
More informationEdexcel. Decision Mathematics 1
Edexcel Decision Mathematics 1 Sorts and Searches Edited by K V Kumaran kvkumaran@gmail.com Decision Maths 1 SORTS and SEARCHES Page 1 SORTS and SEARCHES BUBBLE-SORT ALGORITHM Page 03 QUICK-SORT ALGORITHM
More information7th Grade Drawing Geometric Figures
Slide 1 / 53 Slide 2 / 53 7th Grade Drawing Geometric Figures 2015-11-23 www.njctl.org Slide 3 / 53 Topics Table of Contents Determining if a Triangle is Possible Click on a topic to go to that section
More informationMath 3 Geogebra Discovery - Equidistance Decemeber 5, 2014
Math 3 Geogebra Discovery - Equidistance Decemeber 5, 2014 Today you and your partner are going to explore two theorems: The Equidistance Theorem and the Perpendicular Bisector Characterization Theorem.
More informationExamination paper for TDT4120 Algorithms and Data Structures
Department of Computer and Information Science Examination paper for TDT0 Algorithms and Data Structures Academic contact during examination Magnus Lie Hetland Phone 98 5 99 Examination date Dec 0, 08
More informationTable of Contents Problem Solving with the Coordinate Plane
GRADE 5 UNIT 6 Table of Contents Problem Solving with the Coordinate Plane Lessons Topic 1: Coordinate Systems 1-6 Lesson 1: Construct a coordinate system on a line. Lesson 2: Construct a coordinate system
More information9.3 Properties of Chords
9.3. Properties of Chords www.ck12.org 9.3 Properties of Chords Learning Objectives Find the lengths of chords in a circle. Discover properties of chords and arcs. Review Queue 1. Draw a chord in a circle.
More informationInformed search algorithms. Chapter 3 (Based on Slides by Stuart Russell, Richard Korf, Subbarao Kambhampati, and UW-AI faculty)
Informed search algorithms Chapter 3 (Based on Slides by Stuart Russell, Richard Korf, Subbarao Kambhampati, and UW-AI faculty) Intuition, like the rays of the sun, acts only in an inflexibly straight
More informationMaterials: Computer lab or set of calculators equipped with Cabri Geometry II and lab worksheet.
Constructing Perpendiculars Lesson Summary: Students will complete the basic compass and straight edge constructions commonly taught in first year high school Geometry. Key Words: perpendicular, compass,
More informationGeometry Unit 3 Note Sheets Date Name of Lesson. Slopes of Lines. Partitioning a Segment. Equations of Lines. Quiz
Date Name of Lesson Slopes of Lines Partitioning a Segment Equations of Lines Quiz Introduction to Parallel and Perpendicular Lines Slopes and Parallel Lines Slopes and Perpendicular Lines Perpendicular
More informationYear 10 Practical Assessment Skills Lesson 1 Results tables and Graph Skills
Year 10 Practical Assessment Skills Lesson 1 Results tables and Graph Skills Aim: to be able to present results and draw appropriate types of graphs Must: identify mistakes in data recording Should: be
More information1 Robot Axis and Movement
1 Robot Axis and Movement NAME: Date: Section: INTRODUCTION Jointed arm robots are useful for many different tasks because of its range of motion and degrees of freedom. In this activity you will learn
More information3. Given the similarity transformation shown below; identify the composition:
Midterm Multiple Choice Practice 1. Based on the construction below, which statement must be true? 1 1) m ABD m CBD 2 2) m ABD m CBD 3) m ABD m ABC 1 4) m CBD m ABD 2 2. Line segment AB is shown in the
More informationA Historical Example One of the most famous problems in graph theory is the bridges of Konigsberg. The Real Koningsberg
A Historical Example One of the most famous problems in graph theory is the bridges of Konigsberg The Real Koningsberg Can you cross every bridge exactly once and come back to the start? Here is an abstraction
More informationPrevious Lecture. How can computation sort data faster for you? Sorting Algorithms: Speed Comparison. Recursive Algorithms 10/31/11
CS 202: Introduction to Computation " UIVERSITY of WISCOSI-MADISO Computer Sciences Department Professor Andrea Arpaci-Dusseau How can computation sort data faster for you? Previous Lecture Two intuitive,
More informationExtra Practice 1. Name Date. Lesson 8.1: Parallel Lines. 1. Which line segments are parallel? How do you know? a) b) c) d)
Master 8.24 Extra Practice 1 Lesson 8.1: Parallel Lines 1. Which line segments are parallel? How do you know? a) b) c) d) 2. Look at the diagram below. Find as many pairs of parallel line segments as you
More informationDATE PERIOD. Lesson Reading Guide. Line and Angle Relationships
NAME DATE PERIOD Lesson Reading Guide Get Ready for the Lesson Read the introduction at the top of page 306 in your textbook. Write your answers below. 1. Suppose that the measure of angles 4 and 6 are
More information5. Suppose the points of a scatterplot lie close to the line 3x + 2y = 6. The slope of this line is: A) 3. B) 2/3. C) 3/2. D) 3/2.
DISCRETE MIDTERM REVIEW 1. An outlier is an individual value that: A) extends the pattern. B) deviates from the pattern. C) determines the strength of the relationship. D) outlines the general form of
More informationConstructions. Learning Intention: By If you use 1 litre of orange, you will use 4 litres of water (1:4).
Constructions Scales Scales are important in everyday life. We use scales to draw maps, to construct building plans, in housing, street construction... It is impossible to draw building plans with the
More informationDecision Mathematics D2 Advanced/Advanced Subsidiary. Thursday 6 June 2013 Morning Time: 1 hour 30 minutes
Paper Reference(s) 6690/01 Edexcel GCE Decision Mathematics D2 Advanced/Advanced Subsidiary Thursday 6 June 2013 Morning Time: 1 hour 30 minutes Materials required for examination Nil Items included with
More informationSlopes of Lines Notes What is slope?
Slopes of Lines Notes What is slope? Find the slope of each line. 1 Find the slope of each line. Find the slope of the line containing the given points. 6, 2!!"#! 3, 5 4, 2!!"#! 4, 3 Find the slope of
More informationLink State Routing. Stefano Vissicchio UCL Computer Science CS 3035/GZ01
Link State Routing Stefano Vissicchio UCL Computer Science CS 335/GZ Reminder: Intra-domain Routing Problem Shortest paths problem: What path between two vertices offers minimal sum of edge weights? Classic
More informationObjective: Use a compass and straight edge to construct congruent segments and angles.
CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Introduction to Constructions Constructions: The drawing of various shapes using only a pair of compasses
More informationPhysical Synthesis of Bus Matrix for High Bandwidth Low Power On-chip Communications
Physical Synthesis of Bus Matrix for High Bandwidth Low Power On-chip Communications Renshen Wang 1, Evangeline Young 2, Ronald Graham 1 and Chung-Kuan Cheng 1 1 University of California San Diego 2 The
More informationTOURNAMENT ROUND. Round 1
Round 1 1. Find all prime factors of 8051. 2. Simplify where x = 628,y = 233,z = 340. [log xyz (x z )][1+log x y +log x z], 3. In prokaryotes, translation of mrna messages into proteins is most often initiated
More informationCounting Things Solutions
Counting Things Solutions Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles March 7, 006 Abstract These are solutions to the Miscellaneous Problems in the Counting Things article at:
More informationTUESDAY, 8 NOVEMBER 2016 MORNING 1 hour 45 minutes
Surname Centre Number Candidate Number Other Names 0 GCSE NEW 3300U30- A6-3300U30- MATHEMATICS UNIT : NON-CALCULATOR INTERMEDIATE TIER TUESDAY, 8 NOVEMBER 206 MORNING hour 45 minutes For s use ADDITIONAL
More informationLink State Routing. Brad Karp UCL Computer Science. CS 3035/GZ01 3 rd December 2013
Link State Routing Brad Karp UCL Computer Science CS 33/GZ 3 rd December 3 Outline Link State Approach to Routing Finding Links: Hello Protocol Building a Map: Flooding Protocol Healing after Partitions:
More informationObjective: Use a compass and straight edge to construct congruent segments and angles.
CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Oct 1 8:33 AM Oct 2 7:42 AM 1 Introduction to Constructions Constructions: The drawing of various shapes
More informationTImath.com. Geometry. Perspective Drawings
Perspective Drawings ID: 9424 Time required 35 minutes Activity Overview In this activity, students draw figures in one- and two-point perspective and compare and contrast the two types of drawings. They
More informationDownloaded from
1 IX Mathematics Chapter 8: Quadrilaterals Chapter Notes Top Definitions 1. A quadrilateral is a closed figure obtained by joining four points (with no three points collinear) in an order. 2. A diagonal
More informationUMBC 671 Midterm Exam 19 October 2009
Name: 0 1 2 3 4 5 6 total 0 20 25 30 30 25 20 150 UMBC 671 Midterm Exam 19 October 2009 Write all of your answers on this exam, which is closed book and consists of six problems, summing to 160 points.
More informationLectures: Feb 27 + Mar 1 + Mar 3, 2017
CS420+500: Advanced Algorithm Design and Analysis Lectures: Feb 27 + Mar 1 + Mar 3, 2017 Prof. Will Evans Scribe: Adrian She In this lecture we: Summarized how linear programs can be used to model zero-sum
More informationUNIT 1 GEOMETRY. (revision from 1 st ESO) Unit 8 in our books
UNIT 1 GEOMETRY (revision from 1 st ESO) Unit 8 in our books WHAT'S GEOMETRY? Geometry is the study of the size, shape and position of 2 dimensional shapes and 3 dimensional figures. In geometry, one explores
More informationTechnical Drawing Paper 1 - Higher Level (Plane and Solid Geometry)
Coimisiún na Scrúduithe Stáit State Examinations Commission 2008. M81 Leaving Certificate Examination 2008 Technical Drawing Paper 1 - Higher Level (Plane and Solid Geometry) (200 Marks) Friday 13 June
More informationDesign & Communication Graphics Ordinary Level Section A (60 Marks)
M.84A ªM.844 Leaving Certificate Examination, 2009 Design & Communication Graphics Ordinary Level Section A (60 Marks) Time: 3 Hours This examination is divided into three sections: SECTION A SECTION B
More informationMohr-Mascheroni theorem
Mohr-Mascheroni theorem NOGNENG Dorian LIX October 25, 2016 Table of Contents Introduction Constructible values Projection Intersecting a circle with a line Ratio a b c Intersecting 2 lines Conclusion
More informationphysicsandmathstutor.com
ADVANCED GCE MATHEMATICS 4737 Decision Mathematics 2 Candidates answer on the answer booklet. OCR supplied materials: 8 page answer booklet (sent with general stationery) Insert for Questions 4 and 6 (inserted)
More informationThe problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in
The problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in Grade 7 or higher. Problem C Totally Unusual The dice
More informationOutline. Tracking with Unreliable Node Sequences. Abstract. Outline. Outline. Abstract 10/20/2009
Tracking with Unreliable Node Sequences Ziguo Zhong, Ting Zhu, Dan Wang and Tian He Computer Science and Engineering, University of Minnesota Infocom 2009 Presenter: Jing He Abstract This paper proposes
More informationConstructions. Unit 9 Lesson 7
Constructions Unit 9 Lesson 7 CONSTRUCTIONS Students will be able to: Understand the meanings of Constructions Key Vocabulary: Constructions Tools of Constructions Basic geometric constructions CONSTRUCTIONS
More informationGeometric Puzzle Medley
Geometric Puzzle Medley (16 August 2018) Jim Stevenson This is a collection of simple but elegant puzzles, mostly from a British high school math teacher Catriona Shearer @Cshearer41 (https://twitter.com/cshearer41),
More informationPaper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 6 8. satspapers.org
Ma KEY STAGE 3 Mathematics test TIER 6 8 Paper 1 Calculator not allowed First name Last name School 2009 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You
More informationGraphs of Tilings. Patrick Callahan, University of California Office of the President, Oakland, CA
Graphs of Tilings Patrick Callahan, University of California Office of the President, Oakland, CA Phyllis Chinn, Department of Mathematics Humboldt State University, Arcata, CA Silvia Heubach, Department
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, :15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationBy now you should be able to explain the meaning of the following:
Unit 4.7: Circles and Area Lesson: Drawing Circle Graphs Objectives: Students will review the vocabulary of circles. Students will learn to draw angles and measure angles. Students will learn to draw a
More informationSolutions of problems for grade R5
International Mathematical Olympiad Formula of Unity / The Third Millennium Year 016/017. Round Solutions of problems for grade R5 1. Paul is drawing points on a sheet of squared paper, at intersections
More informationMathematics (JUN11MD0201) General Certificate of Education Advanced Level Examination June Unit Decision TOTAL.
Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Decision 2 Monday 20 June 2011 General Certificate of Education Advanced Level
More informationHow can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr.
Common Core Standard: 8.G.6, 8.G.7 How can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 9.2.2 What Is Special
More information3.3. You wouldn t think that grasshoppers could be dangerous. But they can damage
Grasshoppers Everywhere! Area and Perimeter of Parallelograms on the Coordinate Plane. LEARNING GOALS In this lesson, you will: Determine the perimeter of parallelograms on a coordinate plane. Determine
More information3-5 Slopes of Lines. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the value of m. 1. 2. 3. 4. undefined 0 Objectives Find the slope of a line. Use slopes to identify parallel and perpendicular
More informationNetwork Layer (Routing)
Network Layer (Routing) Where we are in the ourse Moving on up to the Network Layer! Application Transport Network Link Physical SE 61 University of Washington Topics Network service models Datagrams (packets),
More informationA C E. Answers Investigation 3. Applications. 12, or or 1 4 c. Choose Spinner B, because the probability for hot dogs on Spinner A is
Answers Investigation Applications. a. Answers will vary, but should be about for red, for blue, and for yellow. b. Possible answer: I divided the large red section in half, and then I could see that the
More informationProperties of Chords
Properties of Chords Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit www.ck12.org
More information1. When sketching long, narrow objects in OBLIQUE, distortion can be lessened by placing the long dimension along:
Draft Student Name: Teacher: District: Date: Wake County Test: 9_12 T and I IC61 - Drafting I Test 2 Description: 3.03 Apply 3D sketching Form: 501 1. When sketching long, narrow objects in OBLIQUE, distortion
More informationHeuristics, and what to do if you don t know what to do. Carl Hultquist
Heuristics, and what to do if you don t know what to do Carl Hultquist What is a heuristic? Relating to or using a problem-solving technique in which the most appropriate solution of several found by alternative
More informationCS256 Applied Theory of Computation
CS256 Applied Theory of Computation Parallel Computation III John E Savage Overview Mapping normal algorithms to meshes Shuffle operations on linear arrays Shuffle operations on two-dimensional arrays
More informationUNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS
UNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS KEY IDEAS 1. A dilation is a transformation that makes a figure larger or smaller than the original figure based on a ratio given by a scale
More informationLecture 20: Combinatorial Search (1997) Steven Skiena. skiena
Lecture 20: Combinatorial Search (1997) Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.sunysb.edu/ skiena Give an O(n lg k)-time algorithm
More informationOptimisation and Operations Research
Optimisation and Operations Research Lecture : Graph Problems and Dijkstra s algorithm Matthew Roughan http://www.maths.adelaide.edu.au/matthew.roughan/ Lecture_notes/OORII/
More information17. Symmetries. Thus, the example above corresponds to the matrix: We shall now look at how permutations relate to trees.
7 Symmetries 7 Permutations A permutation of a set is a reordering of its elements Another way to look at it is as a function Φ that takes as its argument a set of natural numbers of the form {, 2,, n}
More informationQuestion Score Max Cover Total 149
CS170 Final Examination 16 May 20 NAME (1 pt): TA (1 pt): Name of Neighbor to your left (1 pt): Name of Neighbor to your right (1 pt): This is a closed book, closed calculator, closed computer, closed
More informationMATHEMATICS: PAPER II
NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 2017 MATHEMATICS: PAPER II EXAMINATION NUMBER Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of
More informationCS 787: Advanced Algorithms Homework 1
CS 787: Advanced Algorithms Homework 1 Out: 02/08/13 Due: 03/01/13 Guidelines This homework consists of a few exercises followed by some problems. The exercises are meant for your practice only, and do
More informationPlanes, Tetrahedra, and Cross Sections
Planes, Tetrahedra, and Cross Sections Los Angeles Math Circle February 26, 2017 Warm Up Problems 1. Is it possible to cut a square into 7 smaller squares, not necessarily of equal size? If so, show how
More informationCELIA SCHAHCZENSKI. FE Exam Review Computers Oct. 18, 2018
CELIA SCHAHCZENSKI FE Exam Review Computers Oct. 18, 2018 TOPICS Data Storage (2 problems) Data transmission (1 problem) Pseudo code (2 problems) Spreadsheets (3 problems) Logic Circuits (2 problems) Flowcharts
More information1-2 Measuring and Constructing Segments. Holt Geometry
1-2 Measuring and Constructing Segments Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint distance bisect length segment bisector
More informationCOMP Online Algorithms. Paging and k-server Problem. Shahin Kamali. Lecture 11 - Oct. 11, 2018 University of Manitoba
COMP 7720 - Online Algorithms Paging and k-server Problem Shahin Kamali Lecture 11 - Oct. 11, 2018 University of Manitoba COMP 7720 - Online Algorithms Paging and k-server Problem 1 / 19 Review & Plan
More informationDay 26 Bellringer. 1. Given that the pair of lines intersected by the transversal are parallel, find the value of the x in the following figures.
Day 26 Bellringer 1. Given that the pair of lines intersected by the transversal are parallel, find the value of the x in the following figures. (a) 2x + 17 3x 41 (b) 9x + 18 11x (c) x + 5 91 x HighSchoolMathTeachers@2018
More informationAlgorithms and Data Structures: Network Flows. 24th & 28th Oct, 2014
Algorithms and Data Structures: Network Flows 24th & 28th Oct, 2014 ADS: lects & 11 slide 1 24th & 28th Oct, 2014 Definition 1 A flow network consists of A directed graph G = (V, E). Flow Networks A capacity
More information2010 Pascal Contest (Grade 9)
Canadian Mathematics Competition n activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario 2010 Pascal Contest (Grade 9) Thursday, February 25, 2010
More informationLesson 10: Unknown Angle Proofs Proofs with Constructions
: Unknown Angle Proofs Proofs with Constructions Student Outcome Students write unknown angle proofs involving auxiliary lines. Lesson Notes On the second day of unknown angle proofs, students incorporate
More informationthe question of whether computers can think is like the question of whether submarines can swim -- Dijkstra
the question of whether computers can think is like the question of whether submarines can swim -- Dijkstra Game AI: The set of algorithms, representations, tools, and tricks that support the creation
More informationLesson 1: Scale Drawings
Name: : Scale Drawings Learning Target I can create scale drawings of polygonal figures by the Ratio Method I can determine the distance a point moves from the center of dilation based on the scale factor
More informationp-percent Coverage in Wireless Sensor Networks
p-percent Coverage in Wireless Sensor Networks Yiwei Wu, Chunyu Ai, Shan Gao and Yingshu Li Department of Computer Science Georgia State University October 28, 2008 1 Introduction 2 p-percent Coverage
More informationThe problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in
The problems in this booklet are organized into strands. A problem often appears in multiple strands. The problems are suitable for most students in Grade 7 or higher. Problem C Retiring and Hiring A
More informationApproximation Algorithms for Conflict-Free Vehicle Routing
Approximation Algorithms for Conflict-Free Vehicle Routing Kaspar Schupbach and Rico Zenklusen Παπαηλίου Νικόλαος CFVRP Problem Undirected graph of stations and roads Vehicles(k): Source-Destination stations
More information