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

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. ・ Find cut with no black crossing edges; color its min-weight edge black. ・ Repeat until V - 1 edges are colored black. 0-7 0.16 2-3 0.17 1 1-7 0.19 3 0-2 0.26 5 5-7 0.28 7 1-3 0.29 2 1-5 0.32 0 2-7 0.34 4-5 0.35 1-2 0.36 6 4 4-7 0.37 0-4 0.38 an edge-weighted graph 6-2 0.40 3-6 0.52 6-0 0.58 6-4 0.93 2

Greedy MST algorithm demo ・ 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. crossing edges crossing edge (sorted by weight) 1 3 5 in MST 0-2 0.26 1-3 0.29 7 2 2-7 0.34 1-2 0.36 0 6-0 0.58 6-4 0.93 6 4 min-weight grey vertices form crossing edge one side of cut 3

Greedy MST algorithm demo ・ 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. 1 3 5 7 2 0 6 4 MST edges 0-2 4

Greedy MST algorithm demo ・ 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. crossing edges (sorted by weight) 1 3 5 in MST 5-7 0.28 1-5 0.32 7 2 4-5 0.35 min-weight 0 crossing edge 6 4 MST edges 0-2 5

Greedy MST algorithm demo ・ 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. 1 3 5 7 2 0 6 4 MST edges 0-2 5-7 6

Greedy MST algorithm demo ・ 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. crossing edges (sorted by weight) 1 3 5 in MST 6-2 0.40 3-6 0.52 7 2 6-0 0.58 6-4 0.93 0 6 4 min-weight crossing edge MST edges 0-2 5-7 7

Greedy MST algorithm demo ・ 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. 1 3 5 7 2 0 6 4 MST edges 0-2 5-7 6-2 8

Greedy MST algorithm demo ・ 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. crossing edges (sorted by weight) 1 3 5 in MST 0-7 0.16 2-3 0.17 7 2 2-7 0.34 min-weight 4-5 0.35 0 crossing edge 1-2 0.36 4-7 0.37 6 4 3-6 0.52 MST edges 0-2 5-7 6-2 9

Greedy MST algorithm demo ・ 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. 1 3 5 7 2 0 6 4 MST edges 0-2 5-7 6-2 0-7 10

Greedy MST algorithm demo ・ 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. crossing edges min-weight (sorted by weight) crossing edge 1 3 5 in MST 2-3 0.17 1-7 0.19 7 2 1-5 0.32 1-2 0.36 0 6 4 MST edges 0-2 5-7 6-2 0-7 11

Greedy MST algorithm demo ・ 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. 1 3 5 7 2 0 6 4 MST edges 0-2 5-7 6-2 0-7 2-3 12

Greedy MST algorithm demo ・ 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. crossing edges (sorted by weight) 1 3 5 in MST 1-7 0.19 1-3 0.29 7 2 1-5 0.32 min-weight 4-5 0.35 0 crossing edge 1-2 0.36 4-7 0.37 6 4 0-4 0.38 6-4 0.93 MST edges 0-2 5-7 6-2 0-7 2-3 13

Greedy MST algorithm demo ・ 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. 1 3 5 7 2 0 6 4 MST edges 0-2 5-7 6-2 0-7 2-3 1-7 14

Greedy MST algorithm demo ・ 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. crossing edges (sorted by weight) 1 3 5 in MST 4-5 0.35 4-7 0.37 7 2 0-4 0.38 min-weight 6-4 0.93 0 crossing edge 6 4 MST edges 0-2 5-7 6-2 0-7 2-3 1-7 15

Greedy MST algorithm demo ・ 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. 1 3 5 7 2 0 6 4 MST edges 0-2 5-7 6-2 0-7 2-3 1-7 4-5 16