2 3 t r e e s a a t r e e s b t r e e s a n n o u n c e m
play

2 - 3 t r e e s , A A t r e e s , B - t r e e - PowerPoint PPT Presentation

Aug 28, 2022 •444 likes •990 views

2 - 3 t r e e s , A A t r e e s , B - t r e e s A n n o u n c e m e n t C o n s u l t a t i o n t i m e s 1 0 - 1 2 , r o o m E S 6 1 ! Mo n d a y 9 Ma y t h

  1. 2 - 3 t r e e s , A A t r e e s , B - t r e e s

  2. A n n o u n c e m e n t C o n s u l t a t i o n t i m e s – 1 0 - 1 2 , r o o m E S 6 1 ! ● Mo n d a y 9 Ma y t h ● Tiu r s d a y 1 2 Ma y t h ● Tiu r s d a y 1 9 Ma y t h ● Mo n d a y 2 3 Ma y r d N o p l a n – j u s t c o m e a n d a s k q u e s t i o n s P . S . d o n ' t f o r g e t t h e r e a r e e x e r c i s e s o n t h e w e b s i t e !

  3. 2 - 3 t r e e s I n a b i n a r y t r e e , e a c h n o d e h a s t w o c h i l d r e n I n a 2 - 3 t r e e , e a c h n o d e h a s e i t h e r 2 c h i l d r e n ( a ) o r 3 ( a ) 2 - n o d e 3 - n o d e A 2 - n o d e i s a n o r m a l B S T n o d e : ● O n e d a t a v a l u e x , w h i c h i s g r e a t e r t h a n a l l v a l u e s i n t h e l e f t s u b t r e e a n d l e s s t h a n a l l v a l u e s i n t h e r i g h t s u b t r e e A 3 - n o d e i s d i fg e r e n t : ● T d a t a v a l u e s a n d w o x y ● A l l t h e v a l u e s i n t h e l e f t s u b t r e e a r e l e s s t h a n x ● A l l t h e v a l u e s i n t h e m i d d l e s u b t r e e a r e b e t w e e n a n d x y ● A l l t h e v a l u e s i n t h e r i g h t s u b t r e e a r e g r e a t e r t h a n y

  4. 2 - 3 t r e e s A n e x a m p l e o f a 2 - 3 t r e e :

  5. W h y 2 - 3 t r e e s ? Wi t h a 2 - 3 t r e e w e c a n m a i n t a i n t h e i n v a r i a n t : ● Tie t r e e i s a l w a y s p e r f e c t l y b a l a n c e d ! I n v a r i a n t : a l l c h i l d r e n o f e a c h n o d e h a v e t h e s a m e h e i g h t a l w a y s ● I n p a r t i c u l a r , a n y n o n - l e a f 2 - n o d e h a s 2 c h i l d r e n ● A n y n o n - l e a f 3 - n o d e h a s 3 c h i l d r e n Tii s w a s n ' t p o s s i b l e w i t h b i n a r y s e a r c h t r e e s

  6. W h i c h o f t h e s e a r e 2 - 3 t r e e s ? 7 7 2 1 11 5 2 1 1 1 5 1 3 4 5 9 1 3 1 7 1 9 1 9 1 3 1 71 9 7 7 2 2 1 11 5 1 11 5 1 5 9 1 3 1 71 9 1 5 9 1 71 9

  7. W h i c h o f t h e s e a r e 2 - 3 t r e e s ? 7 7 2 1 11 5 2 1 1 1 5 1 3 4 5 9 1 3 1 7 1 9 1 9 1 3 1 71 9 O n l y t h i s o n e 7 7 ( w h y ? ) 2 2 1 11 5 1 11 5 1 5 9 1 3 1 71 9 1 5 9 1 71 9

  8. I n s e r t i o n i n t o a 2 - 3 t r e e T o i n s e r t a v a l u e ( e . g . 4 ) i n t o a 2 - 3 t r e e , w e s t a r t b y d o i n g a n o r m a l i n s e r t i o n . . . 7 2 1 1 1 5 1 5 9 1 3 1 7 1 9 W e b r o k e t h e b a l a n c e i n v a r i a n t ! 4

  9. I n s e r t i o n i n t o a 2 - 3 t r e e T o fj x t h e b a l a n c e i n v a r i a n t , w e a b s o r b t h e b a d n o d e i n t o i t s p a r e n t ! 7 2 1 1 1 5 1 9 1 3 1 7 1 9 4 5 4 g o t a b s o r b e d i n t o 5

  10. I n s e r t i o n i n t o a 2 - 3 t r e e N o w s u p p o s e w e w a n t t o i n s e r t 3 . W e ' l l a b s o r b i t i n t o i t s p a r e n t a s b e f o r e . . . 7 2 1 1 1 5 1 4 5 9 1 3 1 7 1 9 3

  11. I n s e r t i o n i n t o a 2 - 3 t r e e W e g e t a 4 - n o d e , w h i c h i s n o t a l l o w e d ! W e fj x t h i s b y a m e t h o d c a l l e d . s p l i t t i n g 7 2 1 1 1 5 1 9 1 3 1 7 1 9 3 4 5

  12. S p l i t t i n g a 4 - n o d e T o g e t r i d o f a 4 - n o d e , w e i t i n t o s p l i t s e v e r a l 2 - n o d e s ! Tii s c r e a t e s a n e x t r a l e v e l i n t h e t r e e . W e w i l l fj x t h i s b y a b s o r b i n g y t h e r e d n o d e i n t o i t s p a r e n t . x y z x z A B C D A B C D

  13. I n s e r t i o n i n t o a 2 - 3 t r e e A f t e r s p l i t t i n g , w e a b s o r b t h e “ e x t r a l e v e l ” n o d e i n t o i t s p a r e n t . 7 A b s o r b 4 i n t o 2 . 2 1 1 1 5 1 9 1 3 1 7 1 9 4 3 5

  14. I n s e r t i o n i n t o a 2 - 3 t r e e W e r e s t o r e d t h e i n v a r i a n t ! L e t ' s t r y i n s e r t i n g 1 8 . 7 2 4 1 1 1 5 1 9 1 3 1 7 1 9 3 5

  15. I n s e r t i o n i n t o a 2 - 3 t r e e F i r s t a d d a n d a b s o r b . W e g o t a 4 - n o d e , s p l i t i t . 7 2 4 1 1 1 5 1 3 5 9 1 3 1 7 1 8 1 9

  16. I n s e r t i o n i n t o a 2 - 3 t r e e A b s o r b t h e e x t r a n o d e i n t o t h e p a r e n t . 7 2 4 1 1 1 5 1 3 5 9 1 3 1 8 1 7 1 9

  17. I n s e r t i o n i n t o a 2 - 3 t r e e W e g o t a 4 - n o d e a g a i n , s o s p l i t a n d a b s o r b . 1 5 w i l l b e a b s o r b e d 7 2 4 1 1 1 5 1 8 1 3 5 9 1 3 1 7 1 9

  18. I n s e r t i o n i n t o a 2 - 3 t r e e D o n e ! ( I f w e i n s e r t e v e n m o r e , e v e n t u a l l y t h e r o o t w i l l s p l i t , w h i c h a d d s a n e w l e v e l t o t h e t r e e . ) 7 1 5 2 4 1 1 1 8 1 3 5 9 1 3 1 7 1 9

  19. 2 - 3 i n s e r t i o n a l g o r i t h m I n s e r t t h e n e w n o d e i n t o t h e t r e e Tie n a l t e r n a t e 2 s t e p s : ● a b s o r b t h e n o d e i n t o i t s p a r e n t , m o v e u p t o t h e p a r e n t ● i f t h e n o d e i s a 4 - n o d e , i t i n t o 2 - n o d e s s p l i t S t o p o n c e y o u d o n ' t n e e d t o s p l i t

  20. 2 - 3 t r e e s , s u m m a r y 2 - 3 t r e e s d o n o t u s e r o t a t i o n , u n l i k e b a l a n c e d B S T s – i n s t e a d , t h e y k e e p t h e t r e e p e r f e c t l y b a l a n c e d ● I n v a r i a n t m a i n t a i n e d u s i n g a b s o r p t i o n ( t o r e m o v e u n w a n t e d n o d e s ) a n d ( t o e l i m i n a t e 4 - n o d e s ) s p l i t t i n g C o m p l e x i t y i s O ( l o g n ) , a s t r e e i s p e r f e c t l y b a l a n c e d C o n c e p t u a l l y m u c h s i m p l e r t h a n A V L t r e e s ! B u t i m p l e m e n t a t i o n i s r e a l l y a n n o y i n g : ( ● S e e T w o Tir e e . h s

  21. A A t r e e s

  22. A A t r e e s A A t r e e s i m p l e m e n t a 2 - 3 t r e e u s i n g a B S T ! A 2 - n o d e b e c o m e s a B S T n o d e A 3 - n o d e b e c o m e s t w o B S T n o d e s : x x y A y A B C W e ' l l a l w a y s t r a n s l a t e a 3 - n o d e B C i n t o a n o d e a n d i t s r i g h t c h i l d

  23. A A t r e e s , t h e p l a n A n A A t r e e i s r e a l l y a 2 - 3 t r e e , b u t w e s t o r e i t i n a b i n a r y s e a r c h t r e e ● A b i t l i k e w h a t w e d i d f o r b i n a r y h e a p s W e ' l l n e e d t o a d d e x t r a i n f o r m a t i o n t o t h e n o d e s , a n d i n v a r i a n t s , s o t h a t : ● A n y A A t r e e m u s t c o r r e s p o n d t o a 2 - 3 t r e e ● W e c a n t e l l w h e t h e r e a c h n o d e i n t h e t r e e i s a 2 - n o d e , o r p a r t o f a 3 - n o d e Tie n w e c a n a d a p t 2 - 3 i n s e r t i o n t o A A t r e e s ! ● F o r s e a r c h i n g , w e c a n j u s t u s e B S T s e a r c h

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Greenhouse Gases Greenhouse Gases EES 3310/5310 EES 3310/5310 Global Climate Change Global

Greenhouse Gases Greenhouse Gases EES 3310/5310 EES 3310/5310 Global Climate Change Global

Greenhouse Gases Greenhouse Gases EES 3310/5310 EES 3310/5310 Global Climate Change Global Climate Change Jonathan Gilligan Jonathan Gilligan Class #5: Class #5: Wednesday, January 15 Wednesday, January 15 2020 2020 Ofce Hours

730 views • 69 slides
Chapter 18 The Interstellar Medium Units of Chapter 18 18.1 Interstellar Matter 18.2 Emission

Chapter 18 The Interstellar Medium Units of Chapter 18 18.1 Interstellar Matter 18.2 Emission

Chapter 18 The Interstellar Medium Units of Chapter 18 18.1 Interstellar Matter 18.2 Emission Nebulae 18.3 Dark Dust Clouds Ultraviolet Astronomy and the Local Bubble 18.4 21-Centimeter Radiation 18.5 Interstellar Molecules 18.1

477 views • 24 slides
Modeling Biological Processes for Reading Comprehension Vivek

Modeling Biological Processes for Reading Comprehension Vivek

Modeling Biological Processes for Reading Comprehension Vivek Srikumar University of Utah (Previously, Stanford University) Jonathan Berant , Pei-Chun Chen,

730 views • 71 slides
MONTE CARLO NEUTRINO TRANSPORT IN POST-MERGER DISKS S HERWOOD R ICHERS D AN K ASEN , E VAN OC

MONTE CARLO NEUTRINO TRANSPORT IN POST-MERGER DISKS S HERWOOD R ICHERS D AN K ASEN , E VAN OC

MONTE CARLO NEUTRINO TRANSPORT IN POST-MERGER DISKS S HERWOOD R ICHERS D AN K ASEN , E VAN OC ONNOR , R ODRIGO F ERNANDEZ , C HRISTIAN O TT Daniel Perley Daniel Perley NINJA-2 Catalog Daniel Perley NINJA-2 Catalog SHORT GRB M ERGING

552 views • 31 slides
Polysemy in Verbs: Systematic Relations between Senses and Their Effect on Annotation Anna

Polysemy in Verbs: Systematic Relations between Senses and Their Effect on Annotation Anna

Polysemy in Verbs: Systematic Relations between Senses and Their Effect on Annotation Anna Rumshisky Olga Batiukova Brandeis University Annotation Task Problem: Word sense disambiguation In particular: Disambiguation of

764 views • 72 slides
Tradability and the Labor-Market Impact of Immigration: Theory and Evidence from the United States

Tradability and the Labor-Market Impact of Immigration: Theory and Evidence from the United States

Tradability and the Labor-Market Impact of Immigration: Theory and Evidence from the United States Ariel Burstein , Gordon Hanson , Lin Tian INSEAD , Jonathan Vogel UCLA UCSD UCLA November 2018 Immigration and domestic labor market outcomes

1.12k views • 74 slides
Nanoparticle-enhanced photosensors for UV light detection Steve Magill Argonne National

Nanoparticle-enhanced photosensors for UV light detection Steve Magill Argonne National

Nanoparticle-enhanced photosensors for UV light detection Steve Magill Argonne National Laboratory 12/9/19 1 Motivation 12/9/19 2 Quantum Confinement If the size of the nanoparticle is smaller than the electron wavelength : ->

420 views • 30 slides
s e c n e i c S n o i t a m CareerMap: Visualizing Career Trajectory r o f n I

s e c n e i c S n o i t a m CareerMap: Visualizing Career Trajectory r o f n I

s e c n e i c S n o i t a m CareerMap: Visualizing Career Trajectory r o f n I a Kan Wu, Jie Tang, Zhou Shao, Xinyi Xu, Bo Gao & Shu Zhao n i h Dept. Of Computer Science, Tsinghua University C e c n e i c S s e

309 views • 16 slides
How to make You want people to: good presentations Understand your work Giorgio Buttazzo

How to make You want people to: good presentations Understand your work Giorgio Buttazzo

13/02/2019 Why a good presentation? How to make You want people to: good presentations Understand your work Giorgio Buttazzo Be INTERESTED in your work Think you are great! g.buttazzo@sssup.it What happens if you give a bad

267 views • 8 slides
An evolving financial system : dont leave it too late, simulate Alex Brazier Bank of England

An evolving financial system : dont leave it too late, simulate Alex Brazier Bank of England

An evolving financial system : dont leave it too late, simulate Alex Brazier Bank of England 28 September 2018 Conference on non-bank financial institutions and financial stability I am grateful to David Baumslag, Pavel Chichkanov, Sinem

255 views • 25 slides
ASTR 1120 ASTR 1120 General Astronomy: General Astronomy: Stars & Galaxies Stars &

ASTR 1120 ASTR 1120 General Astronomy: General Astronomy: Stars & Galaxies Stars &

ASTR 1120 ASTR 1120 General Astronomy: General Astronomy: Stars & Galaxies Stars & Galaxies ATH REVIEW: Tonight, 5-6pm, in RAMY N1B23 OMEWORK #1 -Due THU, Sept. 10, by 5pm, on Mastering Astronomy CLASS RECORDED STARTED - INFO

424 views • 40 slides
Neighborhood Stabilization Program Target Areas and Program Income Transfer Updates September

Neighborhood Stabilization Program Target Areas and Program Income Transfer Updates September

U.S. Department of Housing and Urban Development Neighborhood Stabilization Program Target Areas and Program Income Transfer Updates September 26, 2019 Welcome me Headquarters Staff John Laswick Njeri Santana Marilee Hansen

288 views • 28 slides
Dosimetry: Fundamentals G. Hartmann EFOMP & German Cancer Research Center (DKFZ)

Dosimetry: Fundamentals G. Hartmann EFOMP & German Cancer Research Center (DKFZ)

ICTP S Chool On M Edical P Hysics For R Adiation T Herapy : D Osimetry And T Reatment P Lanning For B Asic And A Dvanced A Pplications 13 - 24 April 2015 Miramare, Trieste, Italy Dosimetry: Fundamentals G. Hartmann EFOMP & German Cancer

1.01k views • 72 slides
Chapter 2: Dosimetric Principles, Quantities and Units Set of 131 slides based on the chapter

Chapter 2: Dosimetric Principles, Quantities and Units Set of 131 slides based on the chapter

Chapter 2: Dosimetric Principles, Quantities and Units Set of 131 slides based on the chapter authored by J.P. Seuntjens, W. Strydom, and K.R. Shortt of the IAEA publication: Review of Radiation Oncology Physics: A Handbook for Teachers and

956 views • 66 slides
BARDA BIODOSIMETRY Lynne K. Wathen, PhD October 14, 2015 Resilient People. Healthy Communities.

BARDA BIODOSIMETRY Lynne K. Wathen, PhD October 14, 2015 Resilient People. Healthy Communities.

BARDA BIODOSIMETRY Lynne K. Wathen, PhD October 14, 2015 Resilient People. Healthy Communities. A Nation Prepared. BARDA Biodosimetry Desired Throughput Medical Evaluations & Care Follow on Point of Care Screening 2 Gy Plus ( 1

271 views • 7 slides
Patient Radiation Dose Reporting (P-RDSR) Supplement is developed by DICOM Working Group 28

Patient Radiation Dose Reporting (P-RDSR) Supplement is developed by DICOM Working Group 28

Supplement 191: Patient Radiation Dose Reporting (P-RDSR) Supplement is developed by DICOM Working Group 28 (WG-28-Physics) Patient Radiation Dose SR (P-RDSR) Current Radiation Dose SR contains only information about the x-ray system or

180 views • 17 slides
Thermal Neutron Detection Louie Cueva December 8, 2015 PHYS 575 1 Neutrons 1932

Thermal Neutron Detection Louie Cueva December 8, 2015 PHYS 575 1 Neutrons 1932

Thermal Neutron Detection Louie Cueva December 8, 2015 PHYS 575 1 Neutrons 1932 Chadwick discovered the neutron No charge, No Coulomb force, No Service! Interaction with detectors Interactions with nuclei ~10

454 views • 13 slides
FRIB Radiation Studies: Damage, Component Lifetimes, Hands-on Accessibility Dali Georgobiani

FRIB Radiation Studies: Damage, Component Lifetimes, Hands-on Accessibility Dali Georgobiani

FRIB Radiation Studies: Damage, Component Lifetimes, Hands-on Accessibility Dali Georgobiani Facility for Rare Isotope Beams (FRIB) Michigan State University, East Lansing, MI 48824 USA This material is based upon work supported by the U.S.

780 views • 19 slides
Code intercomparison and benchmark for muon fluence and absorbed dose induced by an 18 GeV

Code intercomparison and benchmark for muon fluence and absorbed dose induced by an 18 GeV

Code intercomparison and benchmark for muon fluence and absorbed dose induced by an 18 GeV electron beam after massive iron shielding uller 1 , W. R. Nelson, A. Fass` o, A. Ferrari, N. V. Mokhov, S. E. M S. Roesler, T. Sanami, S. I.

898 views • 52 slides
An overview of radiological hazards related to geological external gamma radiation in outdoor

An overview of radiological hazards related to geological external gamma radiation in outdoor

An overview of radiological hazards related to geological external gamma radiation in outdoor environments Carlos Alves 1, *, Jorge Sanjurjo-Snchez 2 1 LandS/Lab2PT (FCT UID/AUR/04509/2013; FEDER COMPETE POCI-01-0145-FEDER-007528) and Earth

417 views • 30 slides
CANCER AND LOW DOSE RESPONSES IN VIVO: IMPLICATIONS FOR RADIATION PROTECTION Ron Mitchel

CANCER AND LOW DOSE RESPONSES IN VIVO: IMPLICATIONS FOR RADIATION PROTECTION Ron Mitchel

CANCER AND LOW DOSE RESPONSES IN VIVO: IMPLICATIONS FOR RADIATION PROTECTION Ron Mitchel Radiation Biology and Health Physics Branch Atomic Energy of Canada Limited, Chalk River Laboratories, Chalk River, ON, K0J 1J0 Canada The Linear

574 views • 43 slides
Chemistry 1000 Lecture 2: Nuclear reactions and radiation Marc R. Roussel September 12, 2018

Chemistry 1000 Lecture 2: Nuclear reactions and radiation Marc R. Roussel September 12, 2018

Chemistry 1000 Lecture 2: Nuclear reactions and radiation Marc R. Roussel September 12, 2018 Marc R. Roussel Nuclear reactions and radiation September 12, 2018 1 / 23 Nuclear reactions Nuclear reactions Ordinary chemical reactions do not

497 views • 23 slides
Radiological Risk from Low Dose and Low Dose-Rate Exposures: An Epidemiologic Perspective

Radiological Risk from Low Dose and Low Dose-Rate Exposures: An Epidemiologic Perspective

Radiological Risk from Low Dose and Low Dose-Rate Exposures: An Epidemiologic Perspective MELODI Conference Munich, November 2015 Roy Shore, Linda Walsh, Werner Rhm, Tamara Azizova hrshore@gmail.com (Abridged version) Disclaimer This

389 views • 19 slides
Modeling Time Allen Davis, MSPH Jeff Gift, Ph.D. Jay Zhao, Ph.D. National Center for

Modeling Time Allen Davis, MSPH Jeff Gift, Ph.D. Jay Zhao, Ph.D. National Center for

Benchmark Dose Modeling Modeling Time Allen Davis, MSPH Jeff Gift, Ph.D. Jay Zhao, Ph.D. National Center for Environmental Assessment, U.S. EPA Disclaimer The views expressed in this presentation are those of the author(s) and do not

1.27k views • 87 slides

More recommend