NCKU Programming Contest Training Course Strong Connected - - PowerPoint PPT Presentation

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NCKU Programming Contest Training Course Strong Connected - - PowerPoint PPT Presentation

Jan 18, 2024 14 likes •1.07k views

NCKU Programming Contest Training Course Strong Connected Component(SCC) 20 18 /0 4 / 25 Syuan-Yi Lin ( petermouse ) petermouselin @gmail.com Department of Computer Science and Information Engineering National Cheng Kung University Tainan, Taiwan

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made by tommy5198 & free999 & electorn & petermouse

NCKU CSIE Programming Contest Training Course

NCKU Programming Contest Training Course Strong Connected Component(SCC) 2018/04/25

Syuan-Yi Lin(petermouse)

petermouselin@gmail.com

Department of Computer Science and Information Engineering National Cheng Kung University Tainan, Taiwan

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NCKU CSIE Programming Contest Training Course

made by tommy5198 & petermouse

Outline

  • Articulation/Bridge

(in undirected graph)

  • Strongly Connected Component(SCC)

(in directed graph)

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NCKU CSIE Programming Contest Training Course

made by tommy5198

Graph

  • connected graph/component


connected graph/component iff all pairwise vertices exist at least one path & no more vertices can be added

  • articulation(cut-vertex)


remove articulation vertex split

  • ne component to two
  • bridge(cut-edge)

same as articulation

bridge articulation component

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NCKU CSIE Programming Contest Training Course

made by tommy5198

Articulation/Bridge

  • Find Articulation in Graph

  • Graph become non-connected if remove a Articulation.


V times DFS = O(V*(V+E)) —> too slow!


  • Vertex is not Articulation if can find alternative path


—> find cycle!


  • Use DFS —> O(V+E)
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SLIDE 5

NCKU CSIE Programming Contest Training Course

made by tommy5198 & petermouse

Articulation/Bridge

  • Concept
  • DFS traversel will construct relationships in a tree
  • if vertex u’s children can’t back to u’s ancestors

—> u is Articulation

  • if vertex u is root and has at least 2 child


—> u is Articulation

  • Bridge?

  • two Articulation u, v have an edge —> (u, v) is Bridge!
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NCKU CSIE Programming Contest Training Course

made by tommy5198

Articulation/Bridge

—> no child can back to ancestor. Articulation!

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NCKU CSIE Programming Contest Training Course

made by tommy5198

Articulation/Bridge

—> no child can back to ancestor
 and has at least 2 child. Articulation!

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NCKU CSIE Programming Contest Training Course

made by tommy5198

between two articulations
 —> Bridge!

Articulation/Bridge

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NCKU CSIE Programming Contest Training Course

made by tommy5198

Articulation/Bridge

child can back to ancestor
 NOT Articulation! ＾ ｜

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NCKU CSIE Programming Contest Training Course

made by tommy5198

  • dfn[u] = DFS traversal order

  • first visit time each vertex u in DFS
  • low[u] = min(dfn[u], lowest low[v])

  • if edge (u,v) exist and v is not u’s parent

Articulation/Bridge

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SLIDE 11

NCKU CSIE Programming Contest Training Course

made by tommy5198

Articulation/Bridge

  • Articulation

  • if vertex u’s children can’t back to u’s ancestors


—> dfn[u] <= low[v], v is u’s child


  • if vertex u is root and has at least 2 child


—> count child >= 2

  • Bridge?

  • two Articulation u, v —> dfn[u] < low[v], v is u’s child

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made by petermouse

  • code

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

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made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g

Note: This is an undirected graph

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made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1

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made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1

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made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2

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Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2

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Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 3

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SLIDE 19

made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 3

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made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 3 dfn: : 4 low: w: 4

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Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 3 dfn: : 4 low: w: 2

child node’s dfn

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Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 3 dfn: : 4 low: w: 2

g i is s not cu cut vertex ex si since ce children’s low < dfn

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made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2

child node’s low

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SLIDE 24

made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2

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SLIDE 25

made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2 dfn: : 5 low: w: 5

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Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2 dfn: : 5 low: w: 5

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SLIDE 27

made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2 dfn: : 5 low: w: 5 dfn: : 6 low: w: 6

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SLIDE 28

made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2 dfn: : 5 low: w: 5 dfn: : 6 low: w: 3

!!! child node’s dfn

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made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2 dfn: : 5 low: w: 5 dfn: : 6 low: w: 3

h i is s not cu cut verte tex si since ce children’s low < dfn

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made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2 dfn: : 5 low: w: 3 dfn: : 6 low: w: 3

child node’s low d is s not cu cut vertex ex si since ce children’s low < dfn

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SLIDE 31

made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2 dfn: : 5 low: w: 3 dfn: : 6 low: w: 3

c i c is s cu cut vertex ex since not all children’s low w < dfn

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SLIDE 32

made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2 dfn: : 5 low: w: 3 dfn: : 6 low: w: 3

d is s cu cut vertex ex since not all children’s low w < dfn

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made by riljian

Cut vertex

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b c d h g dfn: : 1 low: w: 1 dfn: : 2 low: w: 2 dfn: : 3 low: w: 2 dfn: : 4 low: w: 2 dfn: : 5 low: w: 3 dfn: : 6 low: w: 3

a a is s not cu cut vert rtex ex si since ce root

  • t an

and only y ch child

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NCKU CSIE Programming Contest Training Course

made by tommy5198

Practice UVA - 315

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NCKU CSIE Programming Contest Training Course

made by tommy5198

SCC

  • connected component in directed graph

  • same definition in undirected graph
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NCKU CSIE Programming Contest Training Course

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SCC

1 2 3 4 6 5

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NCKU CSIE Programming Contest Training Course

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SCC

1 2 3 4 6 5

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NCKU CSIE Programming Contest Training Course

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find all SCCs, contract all cycles —> DAG (directed acyclic graph)

  • Kosaraju's Algorithm

  • Tarjan's Algorithm


SCC

1 2 3 4 6 5

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NCKU CSIE Programming Contest Training Course

made by tommy5198

SCC

  • Kosaraju’s algorithm

twice DFS —> total complexity: O(V+E)

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made by free999 & electron

  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g

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  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g

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  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g

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made by free999 & electron

  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g

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made by free999 & electron

  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g

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  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g

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  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h <— h finish!

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  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d <— d finish!

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made by free999 & electron

  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d

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  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d

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  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f ^ f finish!

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made by free999 & electron

  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g ^ g finish!

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made by free999 & electron

  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c c finish!

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made by free999 & electron

  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c

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made by free999 & electron

  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e ^ e finish!

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made by free999 & electron

  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b b finish!

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  • Algorithm

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a a finish!

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  • Algorithm

– Reverse the graph

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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made by free999 & electron

  • Algorithm

– Reverse the graph

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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made by free999 & electron

  • Algorithm

– Reverse the graph – Re-search by the ending time

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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made by free999 & electron

  • Algorithm

– Reverse the graph – Re-search by the ending time

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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made by free999 & electron

  • Algorithm

– Reverse the graph – Re-search by the ending time

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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made by free999 & electron

  • Algorithm

– Reverse the graph – Re-search by the ending time

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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SLIDE 63

made by free999 & electron

  • Algorithm

– Reverse the graph – Re-search by the ending time

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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SLIDE 64

made by free999 & electron

  • Algorithm

– Reverse the graph – Re-search by the ending time

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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made by free999 & electron

  • Algorithm

– Reverse the graph – Re-search by the ending time

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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SLIDE 66

made by free999 & electron

  • Algorithm

– Reverse the graph – Re-search by the ending time

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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SLIDE 67

made by free999 & electron

  • Algorithm

– Reverse the graph – Re-search by the ending time

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a

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made by free999 & electron

  • Algorithm

– Reverse the graph – Re-search by the ending time

SCC

NCKU CSIE Programming Contest Training Course

a b f e c d h g h d f g c e b a 4 components

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g a dfn:1 :1 low:1 w:1

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g a dfn:1 :1 low:1 w:1

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g f g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:5 w:5

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g f g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low: w:4

In stack ack

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g f g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g f g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g h f g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g h f g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6

dfn fn == == low

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made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g f g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g f g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6

dfn fn == == low

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g d c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:7 w:7

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g d c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:7 w:7

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g d c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low: w:3

In stack ack

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  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g d c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3

slide-93
SLIDE 93

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g d c b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3

dfn fn == == low

slide-94
SLIDE 94

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3

slide-95
SLIDE 95

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3

slide-96
SLIDE 96

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g e b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3 dfn:8 :8 low:8 w:8

slide-97
SLIDE 97

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g e b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3 dfn:8 :8 low:8 w:8

slide-98
SLIDE 98

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g e b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3 dfn:8 :8 low: w:1

In stack ack

slide-99
SLIDE 99

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g e b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:2 w:2 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3 dfn:8 :8 low:1 w:1

slide-100
SLIDE 100

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g e b a dfn:1 :1 low:1 w:1 dfn:2 :2 low: w:1 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3 dfn:8 :8 low:1 w:1

children’s low < low

slide-101
SLIDE 101

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g e b a dfn:1 :1 low:1 w:1 dfn:2 :2 low:1 w:1 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3 dfn:8 :8 low:1 w:1

dfn fn == == low

slide-102
SLIDE 102

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g dfn:1 :1 low:1 w:1 dfn:2 :2 low:1 w:1 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3 dfn:8 :8 low:1 w:1

slide-103
SLIDE 103

made by riljian

  • Tarjan

SCC

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

a b f e c d h g dfn:1 :1 low:1 w:1 dfn:2 :2 low:1 w:1 dfn:3 :3 low:3 w:3 dfn:4 :4 low:4 w:4 dfn:5 :5 low:4 w:4 dfn:6 :6 low:6 w:6 dfn:7 :7 low:3 w:3 dfn:8 :8 low:1 w:1

4 st strong

  • ngly

ly co connecte cted co componen ponents

slide-104
SLIDE 104

NCKU CSIE Programming Contest Training Course

made by petermouse

Practice Uva - 11838

slide-105
SLIDE 105

made by riljian

Practice

NCKU KU CSIE IE Programm mming ng Conte test t Training ning Course se

UV UVa 11504 a 11504