2006年美赛题(ABC)

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1、2006MCMA:PositioningandMovingSprinklerSystemsforIrrigation  Thereareawidevarietyoftechniquesavailableforirrigatingafield.Thetechnologiesrangefromadvanceddripsystemstoperiodicflooding.Oneofthesystemsthatisusedonsmallerranchesistheuseof“handmove”irrigationsystems.Lightweightaluminumpipeswithsprinkl

2、erheadsareputinplaceacrossfields,andtheyaremovedbyhandatperiodicintervalstoinsurethatthewholefieldreceivesanadequateamountofwater.Thistypeofirrigationsystemischeaperandeasiertomaintainthanothersystems.Itisalsoflexible,allowingforuseonawidevarietyoffieldsandcrops.Thedisadvantageisthatitrequiresagr

3、eatdealoftimeandefforttomoveandsetuptheequipmentatregularintervals.  Giventhatthistypeofirrigationsystemistobeused,howcanitbeconfiguredtominimizetheamountoftimerequiredtoirrigateafieldthatis80metersby30meters?Forthistaskyouareaskedtofindanalgorithmtodeterminehowtoirrigatetherectangularfieldthatmi

4、nimizestheamountoftimerequiredbyaranchertomaintaintheirrigationsystem.Onepipesetisusedinthefield.Youshoulddeterminethenumberofsprinklersandthespacingbetweensprinklers,andyoushouldfindascheduletomovethepipes,includingwheretomovethem.  Apipesetconsistsofanumberofpipesthatcanbeconnectedtogetherinast

5、raightline.Eachpipehasa10cminnerdiameterwithrotatingspraynozzlesthathavea0.6cminnerdiameter.Whenputtogethertheresultingpipeis20meterslong.Atthewatersource,thepressureis420Kilo-Pascal’sandhasaflowrateof150litersperminute.Nopartofthefieldshouldreceivemorethan0.75cmperhourofwater,andeachpartofthefie

6、ldshouldreceiveatleast2centimetersofwaterevery4days.Thetotalamountofwatershouldbeappliedasuniformlyaspossible.2006MCMB:WheelChairAccessatAirports  Oneofthefrustrationswithairtravelistheneedtoflythroughmultipleairports,andeachstopgenerallyrequireseachtravelertochangetoadifferentairplane.Thiscanbee

7、speciallydifficultforpeoplewhoarenotabletoeasilywalktoadifferentflight'swaitingarea.Oneofthewaysthatanairlinecanmakethetransitioneasieristoprovideawheelchairandanescorttothosepeoplewhoaskforhelp.Itisgenerallyknownwelli