LECTURE 27:GRAPH ADT

CSC 213 – Large Scale Programming

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

Overview of Remainder of Term

What We Are Not Discussing

Graphs

Mathematically, graph is pair (V, E) where V is collection of nodes, called vertices Two nodes can be connected by an edge in

E Position implemented by Vertex & Edge

classes ORD PVD

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SFO

LAX

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Edge Types

Edge connects two vertices in the graph Image we have edge connecting u & v (u,v) is name given to this edge

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 u is origin or source v is destination

Life Death

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 u is origin or source v is destination

Undirected edge is alternative Vertices listed in any order Subway lines normally undirected

Life Death

Best Canisius

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

John

DavidPaul

brown.edu

cox.net

cs.brown.edu

att.netqwest.net

math.brown.edu

cslab1bcslab1a

Applications

Electronic circuits Transportation networks Databases Packing suitcases Finding terrorists Scheduling college’s exams Assigning classes to rooms Garbage collection Coloring countries on a map Playing minesweeper

Other Applications

Terminology

Edge incident on its endpoints U & V endpoints of a

Vertices adjacent when joined by edge U adjacent to V V adjacent to U Directedness unimportant

determining adjacency

XU

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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)

XU

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Path Terminology

Path is 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 pathXU

V

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Path Terminology

Simple path is 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 XU

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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

XU

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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’s end 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 element x

insertEdge(v,w,x): add edge (v,w) with element x

removeVertex(v): remove v (& incident edges)

removeEdge(e): remove e

Retrieval methods incidentEdges(v): get

edges incident to v

For Next Lecture

New weekly assignment available now Usual time for when it is due: 5PM on

Tuesday Consider design & develop tests for

program #2 2nd deadline is Friday, so get cracking Spend time working on this: design saves

coding Reading on implementing Graph for

Friday What are simplest implementations of

Graph? When would each be good to use is

program?