data structures, graphs

DATA STRUCTURESMPHIL - GRAPHS

Jibrael Jos : Oct 2009

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Graph OperationGraph StructureAdjacency ListCreate GraphInsert VertexInsert ArcRetrieve Vertex

Agenda

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Operations (6)

Add Vertex Delete Vertex Add Edge Delete Edge Find Vertex Traverse Graph

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Graph – Structure (2,6,2) graphHead

Count First

graphArc Dest nextArc

graphVertex nextVertex Data inDegree outDegree Processed Arc

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Adjacency List

A 1 B1 p

B 1 A3 p C E

C 2 E1 p

E 2 C1 p

Vertex List Adjacency List

4

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Create Adjacency List

ChennaiBangalore

KolkattaMumbai Nagpur

Delhi

Hyderabad

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Adjacency List

C 2 B2 p

D 2

D

1 p M

K 1 E1 p

M 2 B3 p

Vertex List

6

B 2 M2 p

N 1 D1 p

C

N

K

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createGraph

If (mem available) allocate (newPtr) newPtr->count=0 newPtr->first=null Else newPtr=null Return newPtr

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insertVertex

If (mem Not available) return -1

allocate (newPtr) Init all 6 Find Insertion Point

Empty Graph … at beginning Middle Before First Vertex

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insertArc

If (mem Not available) return -1

Locate from Locate to Insert New Arc

outDegree of from inDegree of to Allocate Set destination of new ptr to “toPtr” Set ptr of from to newPtr (explained in next page)

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insertArc

Find Insertion Point Empty List … at first arc Middle Before First Arc

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Retrieve Vertex

If Graph -> first null return -2 Else set curr to first loop till you find if found set data out return 1 else return -2

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Minimum Spanning TreeShortest Path

Agenda

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Walk Thru

Minimum Spanning Tree Prim / Dijikstra (pg 579) Kruskal

Shortest Path Algorithm

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Minimum ST

ChennaiBangalore

KolkataMumbai Nagpur

Delhi

Hyderabad

5

3

5

2

34

3

3

Delhi: 5 or 3 D,N: 5,3,or 2 D,N,H:5,3,3 D,N,H,M:4,3 D,N,H,M,B:3 D,N,H,M,B,C:5 D,N,H,M,B,C,K

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Minimum ST

ChennaiBangalore

KolkataMumbai Nagpur

Delhi

Hyderabad

5

3

5

2

34

3

3

Start With Mumbai

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Network MST– Structure (2,7,4)

graphHead Count First

graphArc Dest inTree Weight nextEdge

graphVertex nextVertex Data inDegree outDegree inTree Processed * Edge

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M S Tree (pg 579)

Set inTree flags to false and when to true

Min Edge to Infinity (When and Why)

Min Edge Ptr (Why)

Loops (In order Vertex and Edge to initialise)

Loops (to find next Vertex and Edge to find)

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Adjacency List

C 2 B2 p

D 2

D

1 p M

K 1 E1 p

M 2 B3 p

Vertex List

6

B 2 M2 p

N 1 D1 p

C

N

K

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Shortest Path

Chennai∞

Bangalore∞

Kolkata∞

Mumbai : ∞

Nagpur∞

Delhi :∞

Hyderabad∞

5

3

5

2

34

3

3

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Shortest Path

Chennai∞

Bangalore∞

Kolkata∞

Mumbai : ∞

Nagpur∞

Delhi : 0

Hyderabad∞

5

3

5

2

34

3

3

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Shortest Path

Chennai∞

Bangalore∞

Kolkata∞

Mumbai : ∞

Nagpur3

Delhi : 0

Hyderabad∞

5

3

5

2

34

3

3

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Shortest Path

Chennai∞

Bangalore∞

Kolkata∞

Mumbai : ∞

Nagpur3

Delhi : 0

Hyderabad∞

5

3

5

2

34

3

3

5

65

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Shortest Path

Chennai∞

Bangalore∞

Kolkata∞

Mumbai : 5

Nagpur3

Delhi : 0

Hyderabad∞

5

3

5

2

34

3

3

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Shortest Path

Chennai∞

Bangalore∞

Kolkata∞

Mumbai : 5

Nagpur3

Delhi : 0

Hyderabad∞

5

3

5

2

34

3

3

9

5

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Shortest Path

Chennai∞

Bangalore∞

Kolkata∞

Mumbai : 5

Nagpur3

Delhi : 0

Hyderabad5

5

3

5

2

34

3

3

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Shortest Path

Chennai∞

Bangalore∞

Kolkata∞

Mumbai : 5

Nagpur3

Delhi : 0

Hyderabad5

5

3

5

2

34

3

3

98

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Shortest Path

Chennai∞

Bangalore8

Kolkata∞

Mumbai : 5

Nagpur3

Delhi : 0

Hyderabad5

5

3

5

2

34

3

3

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Shortest Path

Chennai11

Bangalore8

Kolkata16

Mumbai : 5

Nagpur3

Delhi : 0

Hyderabad5

5

3

5

2

34

3

3

What if we start from Hyderabad?

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Network SP– Structure (2,8,4)

graphHead Count First

graphArc Dest inTree Weight nextEdge

graphVertex nextVertex Data inDegree outDegree inTree pathLength Processed * Edge

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M S Tree (pg 583)

Set inTree flags to false and when to true

Path Length to Infinity (When and Why)

Min Edge Ptr (Why)

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M S Tree (pg 583)

Loop (In order Vertex) Loop (Edge to initialise) Loop Till Tree Complete Loop (to find next Vertex) Loop (locate smallest path) Test for shortest Path Set inTree (2 places) ,

pathLength (dest)

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Reference (PS: starting vertex only) http://

en.wikipedia.org/wiki/Graph_theory http://en.wikipedia.org/wiki/

Dijkstra’s_algorithm Furzon (for those who have no earlier

graph background): Chapter 12 Action Item