DZYlovesPhysics,andheenjoyscalculatingdensity.Almosteverythinghasdensity,evenagraph.Wedefinethedensityofanon-directedgraph(nodesandedgesofthegraphhavesomevalues)asfollows:where v isthesumofthevaluesofthenodes, e isthesumofthevaluesoftheedges.OnceDZYgotagraph G,nowhewantstofindaconnectedinducedsubgraph G' ofthegraph,suchthatthedensityof G' isaslargeaspossible.Aninducedsubgrap...
Artemhasanarrayof n positiveintegers.Artemdecidedtoplaywithit.Thegameconsistsof n moves.Eachmovegoeslikethis.Artemchoosessomeelementofthearrayandremovesit.Forthat,hegetsmin(a, b) points,where a and b arenumbersthatwereadjacentwiththeremovednumber.Ifthenumberdoesn'thaveanadjacentnumbertotheleftorright,Artemdoesn'tgetanypoints.Aftertheelementisremoved,thetwopartsofthearraygluetoge...
Atthechildren'sday,thechildcametoPicks'shouse,andmessedhishouseup.Pickswasangryathim.Alotofimportantthingswerelost,inparticularthefavoritesetofPicks.Fortunately,Picksrememberssomethingabouthisset S:itselementsweredistinctintegersfrom 1 to limit;thevalueof wasequalto sum;here lowbit(x) equals 2k where k isthepositionofthefirstoneinthebinaryrepresentationof x.Forexample, low...
OnChildren'sDay,thechildgotatoyfromDelayyyasapresent.However,thechildissonaughtythathecan'twaittodestroythetoy.Thetoyconsistsof n partsand m ropes.Eachropelinkstwoparts,buteverypairofpartsislinkedbyatmostonerope.Tosplitthetoy,thechildmustremoveallitsparts.Thechildcanremoveasinglepartatatime,andeachremoveconsumeanenergy.Let'sdefineanenergyvalueofpart i as vi.Thechildspend vf1 + ...
Pashahasapositiveinteger a withoutleadingzeroes.Todayhedecidedthatthenumberistoosmallandheshouldmakeitlarger.Unfortunately,theonlyoperationPashacandoistoswaptwoadjacentdecimaldigitsoftheinteger.HelpPashacountthemaximumnumberhecangetifhehasthetimetomakeatmost k swaps.InputThesinglelinecontainstwointegers a and k (1 ≤ a ≤ 1018; 0 ≤ k ≤ 100).OutputPrintthemaximumnumbert...
DescriptionFarmerJohnwenttocutsomewoodandleftN(2<=N<=100,000)cowseatingthegrass,asusual.Whenhereturned,hefoundtohishorrorthatthecowswereinhisgardeneatinghisbeautifulflowers.Wantingtominimizethesubsequentdamage,FJdecidedtotakeimmediateactionandtransportthecowsbacktotheirbarn.EachcowiisatalocationthatisTiminutes(1<=Ti<=2,000,000)awayfromthebarn.Furthermore,whilewaitingfortra...
DescriptionFarmerJohn'sN(1<=N<=50,000)cows(numbered1..N)areplanningtorunawayandjointhecircus.Theirhoofedfeetpreventthemfromtightropewalkingandswingingfromthetrapeze(andtheirlastattemptatfiringacowoutofacannonmetwithadismalfailure).Thus,theyhavedecidedtopracticeperformingacrobaticstunts.Thecowsaren'tterriblycreativeandhaveonlycomeupwithoneacrobaticstunt:standingontopofeachothertoform...
Youhaveanarray a[1], a[2], ..., a[n],containingdistinctintegersfrom 1 to n.Yourtaskistosortthisarrayinincreasingorderwiththefollowingoperation(youmayneedtoapplyitmultipletimes):choosetwoindexes, i and j (1 ≤ i < j ≤ n; (j - i + 1) isaprimenumber);swaptheelementsonpositions i and j;inotherwords,youareallowedtoapplythefollowingsequenceofassignments: tmp = a[i], a...
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