Algorithms R OBERT S EDGEWICK | K EVIN W AYNE 4.3 G REEDY MST D EMO - - PowerPoint PPT Presentation

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Algorithms R OBERT S EDGEWICK | K EVIN W AYNE 4.3 G REEDY MST D EMO Algorithms F O U R T H E D I T I O N R OBERT S EDGEWICK | K EVIN W AYNE http://algs4.cs.princeton.edu Greedy MST algorithm demo Start with all edges colored gray.

SLIDE 1

ROBERT SEDGEWICK | KEVIN WAYNE

F O U R T H E D I T I O N

Algorithms

http://algs4.cs.princeton.edu

Algorithms

ROBERT SEDGEWICK | KEVIN WAYNE

4.3 GREEDY MST DEMO

SLIDE 2

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-7 0.16 2-3 0.17 1-7 0.19 0-2 0.26 5-7 0.28 1-3 0.29 1-5 0.32 2-7 0.34 4-5 0.35 1-2 0.36 4-7 0.37 0-4 0.38 6-2 0.40 3-6 0.52 6-0 0.58 6-4 0.93 an edge-weighted graph

SLIDE 3

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 0.26 1-3 0.29 2-7 0.34 1-2 0.36 6-0 0.58 6-4 0.93

crossing edges (sorted by weight) in MST crossing edge min-weight crossing edge grey vertices form

ne side of cut

SLIDE 4

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 MST edges

SLIDE 5

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 5-7 0.28 1-5 0.32 4-5 0.35

crossing edges (sorted by weight) in MST

0-2 MST edges

min-weight crossing edge

SLIDE 6

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 5-7 MST edges

SLIDE 7

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 6-2 0.40 3-6 0.52 6-0 0.58 6-4 0.93

crossing edges (sorted by weight) in MST

0-2 5-7 MST edges

min-weight crossing edge

SLIDE 8

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 5-7 6-2 MST edges

SLIDE 9

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-7 0.16 2-3 0.17 2-7 0.34 4-5 0.35 1-2 0.36 4-7 0.37 3-6 0.52

crossing edges (sorted by weight) in MST

0-2 5-7 6-2 MST edges

min-weight crossing edge

SLIDE 10

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 5-7 6-2 0-7 MST edges

SLIDE 11

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 5-7 6-2 0-7 MST edges

min-weight crossing edge

2-3 0.17 1-7 0.19 1-5 0.32 1-2 0.36

crossing edges (sorted by weight) in MST

SLIDE 12

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 5-7 6-2 0-7 2-3 MST edges

SLIDE 13

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 5-7 6-2 0-7 2-3 MST edges

min-weight crossing edge

1-7 0.19 1-3 0.29 1-5 0.32 4-5 0.35 1-2 0.36 4-7 0.37 0-4 0.38 6-4 0.93

crossing edges (sorted by weight) in MST

SLIDE 14

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 5-7 6-2 0-7 2-3 1-7 MST edges

SLIDE 15

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 5-7 6-2 0-7 2-3 1-7 MST edges

min-weight crossing edge

4-5 0.35 4-7 0.37 0-4 0.38 6-4 0.93

crossing edges (sorted by weight) in MST

SLIDE 16

・Start with all edges colored gray. ・Find cut with no black crossing edges; color its min-weight edge black. ・Repeat until V - 1 edges are colored black.

Greedy MST algorithm demo

5 4 7 1 3 2 6 0-2 5-7 6-2 0-7 2-3 1-7 4-5 MST edges