12

Look at the following picture. This is a representation of a street network. The blue dots represent parking meters. Make a graphical representation of this street network. Note that any sidewalks without parking meters are not represented by edges because those streets are not necessary in our network. Vertices should represent street intersections.

Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

Download PDF Report

Upload
others
View
15
Download
0

Embed Size (px)

Citation preview

Page 1: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

Lookatthefollowingpicture.Thisisarepresentationofastreetnetwork.Thebluedotsrepresentparkingmeters.Makeagraphicalrepresentationofthisstreetnetwork.Notethatanysidewalkswithoutparkingmetersarenotrepresentedbyedgesbecausethosestreetsarenotnecessaryinournetwork.Verticesshouldrepresentstreetintersections.

Page 2: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

DoesthisnetworkhaveanEulerCircuit?DoesthisnetworkhaveanEulerPath?WhywouldanEulerPathnotbeoptimalforthisspecificproblemaboutparkingmeters?

Et start*

*

End

no

yes ↳ Found.SE#ttopedD9Ffret

Don't end upback at

my ca

Page 3: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

Sowhatisthebestrouteforcollectingthemoneyfromthemeters?Canyoumakeacircuitforthisgraph?(rememberacircuitjuststartsandendsatthesameplace,itcanpassthesameedgemorethanonce)

Page 4: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

Isthereawaytoaddonlyafew(oronly1)edgetomakethisintoanEulercircuit?

¥*

)*

Page 5: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

Byaddingjustoneedge,wecanmakeanEulercircuit,butnote,theedgeisnotreallynew,itisjustreused

Page 6: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

Whatwejustdidiscalledeulerizingagraph.• Wetookagraphandaddededgesbyduplicatingexistingedgestomakeaconnectedevenvalentgraph

• WefoundanEulercircuitontheeulerizedgraph

EulerizingaGraph—addingedgesthatduplicateexistingedgestoaconnectedgraphtomakeallvalenceseven.

Goal → make m Euler Circuit

Page 7: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

EulerizingaGraphExample:1) locatetheverticeswithoddvalence

2

3z

2

Page 8: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

2) addoneendofanedgeateachoddvertex,matchupthenewedgewithanexistingedgeintheoriginalgraph

duplicated

124fdplicafd

→

•

31

$44

z.

Page 9: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

3) createanEulercircuit

Page 10: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

4) “Squeeze”theEulercircuitontotheoriginalgraph.Notethattherewillbetworeusesofedgesandeachreusecorrespondstoanaddededge

GeneralRule:Thenumberofreusesofedgesequalsthenumberofaddededgesduringeulerization

Page 11: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

Howdowefindthebesteulerization?Didwefindthemostefficientpathforthelastgraph?

Isthereawaywherewecanhaveonlyonereuseinsteadoftwo?

.

Optimal colorization

$-4

Page 12: Look at the following picture. This is a …msjacobsmath.weebly.com/uploads/2/6/2/5/26258835/dm...Look at the following picture. This is a representation of a street network. The blue

Obviouslyonereusededgeisbetterthantwo.Sothisisabettereulerization.Thereisanalgorithmtofindthebesteulerization,butitisacomplicatedalgorithmthatwearenotgoingtoexamine.

Think!. » Please look at the following picture for 3 minutes and note all of the UNSAFE aspects of the picture

Think!. » Please look at the following picture for 3 minutes and note all of the UNSAFE aspects of the picture

Documents

COLEGIUL NATIONAL B.P.Hasdeu Buzau: Proba orala de ... · SUBIECTUL 2 - Look at the following picture. Please tell us what you can see in the picture. SUBIECTUL 3 - SET 1 SET 2 SUBIECTUL

COLEGIUL NATIONAL B.P.Hasdeu Buzau: Proba orala de ... · SUBIECTUL 2 - Look at the following picture. Please tell us what you can see in the picture. SUBIECTUL 3 - SET 1 SET 2 SUBIECTUL

Documents

Bell work Look at the picture below. The first image represents the initial explosion of the big bang, and the following images represent the expansion

Bell work Look at the picture below. The first image represents the initial explosion of the big bang, and the following images represent the expansion

Documents

A LOOK AT THE BIG PICTURE PESTICIDE REFORM

A LOOK AT THE BIG PICTURE PESTICIDE REFORM

Documents

4-Port USB DVI Multi-View KVMP Switch€¦ · 2-port USB hub and providing the following display modes: Quad View, Picture in Picture (PiP), Picture by Picture (PbP), Picture on Picture

4-Port USB DVI Multi-View KVMP Switch€¦ · 2-port USB hub and providing the following display modes: Quad View, Picture in Picture (PiP), Picture by Picture (PbP), Picture on Picture

Documents

Look at the above picture. How are these customs similar?

Look at the above picture. How are these customs similar?

Documents

BRAIN TEASERS: Look Closely! · BRAIN TEASERS: Look Closely! Can you solve the Hidden Pictures Puzzles and the Find-the-Matching-Pair Puzzles? Find the following items in the picture

BRAIN TEASERS: Look Closely! · BRAIN TEASERS: Look Closely! Can you solve the Hidden Pictures Puzzles and the Find-the-Matching-Pair Puzzles? Find the following items in the picture

Documents

Facemask: A picture tutorial.should look like this. Following the previous steps, attach the remaining accent fabric piece to the other end ... washable mask. If you post a picture

Facemask: A picture tutorial.should look like this. Following the previous steps, attach the remaining accent fabric piece to the other end ... washable mask. If you post a picture

Documents

Look at the following picture and write three questions you have about what you see

Look at the following picture and write three questions you have about what you see

Documents

Look across this picture. Does it look like its moving? It’s not

Look across this picture. Does it look like its moving? It’s not

Documents

Look at the picture on p. 210 of your text

Look at the picture on p. 210 of your text

Documents

1.Look at the pieces of the picture. 2.Can you guess what is in the picture?

1.Look at the pieces of the picture. 2.Can you guess what is in the picture?

Documents

WRITE DOWN 5 OBSERVATIONS ABOUT THE FOLLOWING PICTURE

WRITE DOWN 5 OBSERVATIONS ABOUT THE FOLLOWING PICTURE

Documents

~Sky Gerdel. Interpreting Non-Print Look at the picture on the following slide and be thinking about the following questions as you look at it : What

~Sky Gerdel. Interpreting Non-Print Look at the picture on the following slide and be thinking about the following questions as you look at it : What

Documents

Alex - Oxford University Press2 Listen to B. Look at the pictures and tick the correct picture. today 1 2 3 today 4 Alex likes going swimming. 1 Look at the picture. B’s picture

Alex - Oxford University Press2 Listen to B. Look at the pictures and tick the correct picture. today 1 2 3 today 4 Alex likes going swimming. 1 Look at the picture. B’s picture

Documents

UNIT3 Warming up and Reading Look at the following pictures. Which picture can make you laugh?

UNIT3 Warming up and Reading Look at the following pictures. Which picture can make you laugh?

Documents

Look at the picture and think about the following ... · 1) Look at the picture and think about the following questions for 5 minutes. Write down any ideas that come to your mind:

Look at the picture and think about the following ... · 1) Look at the picture and think about the following questions for 5 minutes. Write down any ideas that come to your mind:

Documents

IRTH OF CHRIST LAP BOOK - Veritas Press · Then look up the following verses: Luke 1, Luke 2, John 20, and Revelation 15. Make a list describing what angels look like or draw a picture

IRTH OF CHRIST LAP BOOK - Veritas Press · Then look up the following verses: Luke 1, Luke 2, John 20, and Revelation 15. Make a list describing what angels look like or draw a picture

Documents

“Look at the bigger picture” an analysis of Netflix’s ......“Look at the Bigger Picture”: An Analysis of Netflix’s Business Model and Strategy From CEO Reed Hastings’

“Look at the bigger picture” an analysis of Netflix’s ......“Look at the Bigger Picture”: An Analysis of Netflix’s Business Model and Strategy From CEO Reed Hastings’

Documents

The French Revolution 1789-1791 Just Do It Activity Directions: Look at the following picture. Write down which social class each person in the photograph

The French Revolution 1789-1791 Just Do It Activity Directions: Look at the following picture. Write down which social class each person in the photograph

Documents

Geography Terms January, 2012. Directions: Look at the following pictures and see if you can match the picture to the correct geography term. Answers

Geography Terms January, 2012. Directions: Look at the following pictures and see if you can match the picture to the correct geography term. Answers

Documents

Environmental Pollution UNIT€¦ · Look at the picture. Answer the following questions orally. Give short ... as, rivers, mountains, forests, animals, birds, fish and so on. But

Environmental Pollution UNIT€¦ · Look at the picture. Answer the following questions orally. Give short ... as, rivers, mountains, forests, animals, birds, fish and so on. But

Documents

Look at the picture!!!

Look at the picture!!!

Documents

Look at the following picture closely. How would you describe this photo to someone? Explain everything you see in detail (from the puddles of water near

Look at the following picture closely. How would you describe this photo to someone? Explain everything you see in detail (from the puddles of water near

Documents

Take a look at the big picture

Take a look at the big picture

Healthcare

Look at the picture below. Which of the following ... · Which of the following statements are correct? ... Fill in the blanks with the correct auxiliary ... 4 beautiful 5 stupid

Look at the picture below. Which of the following ... · Which of the following statements are correct? ... Fill in the blanks with the correct auxiliary ... 4 beautiful 5 stupid

Documents

LOOK OF THE YEAR: THE NEW SIMPLICITY PICTURE PERFECT

LOOK OF THE YEAR: THE NEW SIMPLICITY PICTURE PERFECT

Documents

You will have 3 minutes to look at the following picture. Identify as many things (in Spanish) as you can in the picture

You will have 3 minutes to look at the following picture. Identify as many things (in Spanish) as you can in the picture

Documents

Class- IV, Subject- EVS Topic- Fun and Quarrel at play ...€¦ · NAME_____ DATE_____ Q.1. Look at the picture and write the names of following games

Class- IV, Subject- EVS Topic- Fun and Quarrel at play ...€¦ · NAME_____ DATE_____ Q.1. Look at the picture and write the names of following games

Documents

1. Look at the picture. - ingilizceciyiz.com

1. Look at the picture. - ingilizceciyiz.com

Documents