Question

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{ti points} Let G = (HE) he a cermected, undirected graph. [In this ceurse wefellmu the usual cenverltierl that, unless indicated UH'IEI'WiSE, an undirected graph dues net have loops er multiple edgesjﬂsusualn = |V| andm= |E|. Art urticaria-tier: paint of G is a vertex whese remeval discerlnects G. Aswesawinclass,iiyeurunDFSmG,then{hecauseGiscermected}theeuterreutinewill havetemalte enl}r one call Exp]ere{G,r} fer some vertex r, after whim all verlices will he visited. The"tree"edgesereatedinﬂiispreeessfermasparmingteeTefGreetedatr. {a} Prm'eﬂtatrisanarliculaﬁenpeintifandenlyifithasatleasttwechildrenin'l&quot;. {b} Lettraér.TheancestersefeareﬂreveﬂicesenthesimplepathinTiremeterﬁnelusive. Praperancestersextﬂudes.Thedescendantsefearethesewhidthaveuasanancester. Prm'eﬂiatuisanarlictﬂatienpeintiianderﬂyifﬂiereisachildseiein T.sud1thatne descendantefshasahackedgetnapreperancesterefu. {c} Let lew [u] = min{pre[w} : El descendant 1.: iii tr such that (u, w] is a back edge}. Shaw hm te cmnpute all lmﬂu} in time DEM}. {:1} Show haw te cempute all arliculaticrrl points in time DEM}. Runtimes in this problem are in the ward model (baelc arithmetic etc. is in unit time}.