lec0425-GraphImplementations-ann - Announcements: MP 7...

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Unformatted text preview: Announcements: MP 7 available. Due 512,-11:59p. Today: a _ Graphs - Weiss, Chapter 9 I n : ‘18 vech-ts Implementation in ,. . I Traversal :. U I 0 q: .‘f‘ 177.15 9199/7 i5 .sl‘mp/e and Con/flafed, how :er ego/3:5 does {2' hat? a m I 0 II V ° 48 '97 M: at has-t .... ..-,'(zt MO‘:5'4 -....3 .... -- Graphs: Toward implementation. . .(ADT) lnsertVertex(pair keyData) removeEdoe(ed9e e); removeVertex(vertex v): Data: lnctdentEdges(vertex v); Vertlces [ w‘ “3”. on a Edges + some structure that reflects the connectivity of the graph 'ffloimmf): am destinetion(edge e); Functlons: (merely a smattering...) lnsertEdge(vertex v1. vertex v2. pair keyData) .3:- is (ohm; J, areAdjaoent(vertex v1. vertex v2); .—' a I (‘0'); ( Va“) M = n \E "' M Graphs: Egge__l__ist (a first implementation) Some funcions we'l compare: insortVortoxWorux v) 1) removeVertex(vertex v) 00“) areAdjacenuvelex v. vegex u) 0 (m ) hcidentEdgeqvonox v) Graphs: Adjageimy Matrix Some funcions we'l compare: hartVortoxWortox v) "x w “5“” :mkxfig" 000 .qaerjacenuveflex v. vertex u) a I > hcidenlEdgouvortox wan) Nil Graphs: |__i§t Some funcions wo'l compare: hscrtVortax(veflox v) romoveVortox(vertox V) aroAdjaconuvortox v. vo x u) 0 min ahdmntEdgofime v) (Mam) Graphs: Asymptotic Performance - n vertioes. m edges o no parallel edges Edge Adjacency Adjacency - no self-loops List List Matrix - Bounds are big-O II + I" H + I" incidentEd o es(v) dcg( r) insertVertex(u) insertEdge(l-. w, l ) removeVertex(l-) dcg( v) removeEdge(v) - areAdjacent (v. w minldcgl r). dk‘g( w)) — Ia How do we get from here to there? Need: I. POM/nan 'v/(X4d/1ZI/(2/1l/ 2. 6/1‘9/7 I'Mo/Pmpnz‘m‘ion 3. ‘rmerfla/ q. fZ/Bnrf'f/IMS. Graphs — traversal ' Objective: - fl . \frslt every vertex and every edge. ln the graph. H U u Purpose: — «- We can search for interesting substructures lo the graph. Contrast graph traversal to BST traversal: Ordered - oObvious start - Graphs: Traversal - DFS Ariadne. Theseus. and the Minotaur Hun I a «1'1an min: : aw! J.i».‘..).i.' v‘,-.]l‘ g) 1“, IN 15:. 'MH‘ P 11;: HIJIIMM urn.” :_;.‘.H HIJ ' |'.1.‘a'.v' M‘wl t"‘| PM}: y>,1‘_\.tu‘ r I)!" .~..-mr 7\.—l"ll'll.71: Fy—N DFS: 'visits“ each vertex classifies each edge as either “discovery” or “back” Algorithm DFS(G) Algorithm DFS(G.v) Input: graph G Input: graph G and sum vertex v Output: labelng at the edges Output: lebelng of the edges of G In the of G as discovery edges and connected component of v as discovery edges beck edges and back edges For 3! u In G.vettlces() setLabel(v. VISITED) setLebeKu. UNEXPLORED) For el w In G.edjecentVerttoee(v) For 9! e in G.edges() tf getLabel(w) = UNEXPLORED setLebeKe, UNEXPLORED) eetLebel((v.w).DlSCOVERY) For 0! v h G.vertlces() DFS(G.w) If getLebel(v) = UNEXPLORED etse If getLebeI((v.w)) = UNEXPLORED OFS(G.v) setLabel(e.8ACK) A B C D E Graphs: DFS example Graphs: DFS Analysis setting/getting labels every vertex labeled twloe every edge is labeled twice querying vertices total lncldent edges TOTAL RUNNING TIME: ...
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lec0425-GraphImplementations-ann - Announcements: MP 7...

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