Algorithms R OBERT S EDGEWICK | K EVIN W AYNE K RUSKAL ' S A LGORITHM - - PowerPoint PPT Presentation

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Mar 11, 2024 169 likes •378 views

Algorithms R OBERT S EDGEWICK | K EVIN W AYNE K RUSKAL ' S A LGORITHM 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 Kruskal's algorithm demo Consider edges in ascending order of

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

KRUSKAL'S ALGORITHM DEMO

SLIDE 2

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's 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

graph edges sorted by weight

an edge-weighted graph

SLIDE 3

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

0-7 0.16 5 4 7 1 3 2 6

does not create a cycle in MST

SLIDE 4

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

0-7 0.16 2-3 0.17 5 4 7 1 3 2 6

in MST does not create a cycle

SLIDE 5

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

0-7 0.16 2-3 0.17 1-7 0.19 5 4 7 1 3 2 6

in MST does not create a cycle

SLIDE 6

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

0-7 0.16 2-3 0.17 1-7 0.19 0-2 0.26 5 4 7 1 3 2 6

in MST does not create a cycle

SLIDE 7

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

0-7 0.16 2-3 0.17 1-7 0.19 0-2 0.26 5-7 0.28 5 4 7 1 3 2 6

in MST does not create a cycle

SLIDE 8

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

0-7 0.16 2-3 0.17 1-7 0.19 0-2 0.26 5-7 0.28 1-3 0.29 5 4 7 1 3 2 6

creates a cycle not in MST

SLIDE 9

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6

creates a cycle not in MST

SLIDE 10

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6

creates a cycle not in MST

SLIDE 11

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6

in MST does not create a cycle

SLIDE 12

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6

creates a cycle not in MST

SLIDE 13

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6

creates a cycle not in MST

SLIDE 14

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6

creates a cycle not in MST

SLIDE 15

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6

in MST does not create a cycle

SLIDE 16

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6

creates a cycle not in MST

SLIDE 17

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6

creates a cycle not in MST

SLIDE 18

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6

creates a cycle not in MST

SLIDE 19

Consider edges in ascending order of weight.

・Add next edge to tree T unless doing so would create a cycle.

Kruskal's algorithm demo

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 5 4 7 1 3 2 6 a minimum spanning tree