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Lecture 28: Graph ADT

CSC 213 – Large Scale Programming. Lecture 28: Graph ADT. Today’s Goals. Discuss what is NOT meant by term “Graph” Why no bar charts, scatter plots , & pie charts mentioned How term is used for mathematical graph Review terminology of mathematical graphs

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Lecture 28: Graph ADT

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  1. CSC 213 – Large Scale Programming Lecture 28:Graph ADT

  2. Today’s Goals • Discuss what is NOT meant by term “Graph” • Why no bar charts, scatter plots, & pie charts mentioned • How term is used for mathematical graph • Review terminology of mathematical graphs • Why do we care about edges & vertices • Directed vs. undirected more than types of plays • Which 1 of these made up: incident, adjacent, feeder • Cycles & paths not related to Queen songs • Examine Graph ADT’s method & what they do

  3. Graphs • Mathematically, graph is pair (V, E) where • Vis collection of nodes, called vertices • Two nodes can be connected by an edge in E • Positionimplemented by Vertex & Edge classes PVD 849 ORD 1843 142 SFO 802 LGA 1743 337 1387 HNL 2555 1099 LAX 1233 DFW 1120 MIA

  4. Edge Types • Edge connects two vertices in the graph • Image we have edge connecting u & v • (u,v) is name given to this edge • Edges can be directed • One-way street is directed edge • uis originor source • vis destination • Undirected edge is alternative • Vertices listed in any order • Subway lines normally undirected Life Death Best Canisius

  5. Undirected Graph Applications • Electronic circuits • Transportation networks • Databases • Packing suitcases • Finding terrorists • Assigning classes to rooms • Coloring countries on a map • Playing minesweeper

  6. Directed Graph Problems • Used to solve many problems in real-world • Not always obvious: directedness used in many ways • Examples: • Diagnose cause of injury • Schedule tasks to perform • Garbage collection • Track progress of disease • Compiling a program

  7. Graph Types • Graph is directed if all edges directed • All edges in graph must be directed • Examples include trees & Java object hierarchy • Any edge allowed in undirected graphs • Can have only undirected or mix of both edges • Roadways & CSC major are examples of this

  8. Weighted Graphs • Edge’s weight is cost of using edge • Distance, cost, travel time, &c. usable as the weight • Weights below are distance in miles • Edges undirected; but directed weighted Graph legal PVD 849 ORD 1843 142 SFO 802 LGA 1743 337 1387 HNL 2555 1099 LAX 1233 DFW 1120 MIA

  9. Terminology • Edge incident on its endpoints • U & Vendpointsofa • Vertices adjacent when joined by edge • Uadjacent to V • Vadjacent to U • Directedness unimportantdetermining adjacency V b a h j U X Z d i c e W g f Y

  10. Terminology • Degree of vertex is number incident edges • X has degree of 5 • Does not matter if edges directed or not • What the edges’ other endvertices unimportant • (Self-edges only count once) V b a h j U X Z d i c e W g f Y

  11. Path Terminology • Pathis set of vertices in Graph where • All of the consecutive vertices adjacent • May or may not have edge from last to first vertices (U,W,X,Y,W,V) is path V a b U X Z h c e W g f Y

  12. Path Terminology • Simple pathis a path which: • Is named by alternating vertices & edges • 0 or 1 appearance for each vertex & edge (V,b,X,h,Z) is simple path V a b d U X Z h c e W g f Y

  13. Cycle Terminology • Cycle is path with several additional properties • Each cycle must begin & end at same vertex • No edge required from this vertex to itself • Simple cycle is special cycle • But is also simple path (V,X,Y,W,U,V) is simple cycle V a b d U X Z h c e W g f Y

  14. Graph ADT • Accessor methods • vertices(): iterable for vertices • edges(): iterable for edges • endVertices(e): array with end points of edge e • opposite(v,e): e’send point that is not v • areAdjacent(v,w): check if v and w are adjacent • replace(v,x): make x new element at vertex v • replace(e,x): make x new element at edge e • Update methods • insertVertex(x): create vertex storing elementx • insertEdge(v,w,x): add edge (v,w) with elementx • removeVertex(v): remove v(& incident edges) • removeEdge(e): remove e • Retrieval methods • incidentEdges(v): get edges incident to v

  15. For Next Lecture • No weekly assignment this week or next • Get cracking on coding up your program #2 • Due on Wednesday, so better start working on it • How were designs & test? What could you do better? • Reading on implementing Graph for Friday • What are simplest implementations of Graph? • When would each be good to use is program?

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