Dijkstra Algorithm examples

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Presentation transcript:

Dijkstra Algorithm examples

Example 1

Walk-Through Initialize array F C A B D H G E K dv pv A F   B C D E 2 Initialize array 3 F 5 C K dv pv A F   B C D E G H A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Start with G F C A B D H G E K dv pv A B C D E F G T  H 2 3 5 10 7 3  H A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Update unselected nodes 2 Update unselected nodes 3 F 5 C K dv pv A B C D 2 G E F T  H 3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Select minimum distance 2 Select minimum distance 3 F 5 C K dv pv A B C D T 2 G E F  H 3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Update unselected nodes 2 Update unselected nodes 3 F 5 C K dv pv A B C D T 2 G E 27 F 20  H 3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Select minimum distance 2 Select minimum distance 3 F 5 C K dv pv A B C D T 2 G E 27 F 20  H 3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Update unselected nodes 2 Update unselected nodes 3 F 5 C K dv pv A 7 H B 12 C D T 2 G E 27 F 20  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Select minimum distance 2 Select minimum distance 3 F 5 C K dv pv A T 7 H B 12 C D 2 G E 27 F 20  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Update unselected nodes 2 Update unselected nodes 3 F 5 C K dv pv A T 7 H B 12 C D 2 G E 27 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Select minimum distance 2 Select minimum distance 3 F 5 C K dv pv A T 7 H B 12 C D 2 G E 27 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Update unselected nodes 2 Update unselected nodes 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 22 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Select minimum distance 2 Select minimum distance 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 22 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Update unselected nodes 2 Update unselected nodes 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 22 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Select minimum distance 2 Select minimum distance 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 22 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Update unselected nodes 2 Update unselected nodes 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 19 F 17  3 A 10 7 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

Select minimum distance 2 Select minimum distance 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 19 F 17  3 A 10 7 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7 Done

Example 2

Dijkstra's Shortest Path Algorithm Find shortest path from s to t. 2 24 3 9 s 18 14 2 6 6 4 30 19 11 15 5 5 6 20 16 t 7 44

Dijkstra's Shortest Path Algorithm PQ = { s, 2, 3, 4, 5, 6, 7, t }   2 24 3 9 s 18 14  2 6 6  4 30  19 11 15 5 5 6 20 16 t 7 44  distance label 

Dijkstra's Shortest Path Algorithm PQ = { s, 2, 3, 4, 5, 6, 7, t } delmin   2 24 3 9 s 18 14  2 6 6  30  4 19 11 15 5 5 6 20 16 t 7 44  distance label 

Dijkstra's Shortest Path Algorithm PQ = { 2, 3, 4, 5, 6, 7, t } decrease key   X 9 2 24 3 9 s 18 14  X 14 2 6 6  4 30  19 11 15 5 5 6 20 16 t 7 44  distance label  15 X

Dijkstra's Shortest Path Algorithm PQ = { 2, 3, 4, 5, 6, 7, t } delmin   X 9 2 24 3 9 s 18 14  X 14 2 6 6  4 30  19 11 15 5 5 6 20 16 t 7 44  distance label  15 X

Dijkstra's Shortest Path Algorithm PQ = { 3, 4, 5, 6, 7, t }   X 9 2 24 3 9 s 18 14  X 14 2 6 6  30  4 19 11 15 5 5 6 20 16 t 7 44   15 X

Dijkstra's Shortest Path Algorithm PQ = { 3, 4, 5, 6, 7, t } decrease key  X 33  X 9 2 24 3 9 s 18 14  X 14 2 6 6   4 30 19 11 15 5 5 6 20 16 t 7 44   15 X

Dijkstra's Shortest Path Algorithm PQ = { 3, 4, 5, 6, 7, t }  X 33  X 9 2 24 3 9 delmin s 18 14  X 14 2 6 6   4 30 19 11 15 5 5 6 20 16 t 7 44   15 X

Dijkstra's Shortest Path Algorithm PQ = { 3, 4, 5, 7, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 30  X 4 19 11 15 5 5 6 20 16 t 7 44   15 X

Dijkstra's Shortest Path Algorithm PQ = { 3, 4, 5, 7, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 30  X 4 19 11 15 5 5 6 20 16 t 7 44   15 delmin X

Dijkstra's Shortest Path Algorithm PQ = { 3, 4, 5, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 X 35  X 4 30 19 11 15 5 5 6 20 16 t 7 44 59   15 X X

Dijkstra's Shortest Path Algorithm PQ = { 3, 4, 5, t } delmin 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 X 35 4 30  X 19 11 15 5 5 6 20 16 t 7 44 59   15 X X

Dijkstra's Shortest Path Algorithm PQ = { 4, 5, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 X 35 X 34 4 30  X 19 11 15 5 5 6 20 16 t 7 44 51 59   15 X X X

Dijkstra's Shortest Path Algorithm PQ = { 4, 5, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 X 35 X 34 30  X 4 19 11 15 5 5 6 20 delmin 16 t 7 44 51 59   15 X X X

Dijkstra's Shortest Path Algorithm PQ = { 4, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X 30  X 4 19 11 15 5 5 6 20 16 t 7 44 50 51 X 59   15 X X X

Dijkstra's Shortest Path Algorithm PQ = { 4, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X 30  X 4 19 11 15 5 delmin 5 6 20 16 t 7 44 50 51 X 59   15 X X X

Dijkstra's Shortest Path Algorithm PQ = { t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X 30  X 4 19 11 15 5 5 6 20 16 t 7 44 50 51 X 59   15 X X X

Dijkstra's Shortest Path Algorithm PQ = { t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X 30  X 4 19 11 15 5 5 6 20 16 t 7 44 delmin 50 51 X 59   15 X X X

Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 4, 5, 6, 7, t } PQ = { } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X  X 4 30 19 11 15 5 5 6 20 16 t 7 44 50 51 X 59   15 X X X

Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 4, 5, 6, 7, t } PQ = { } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X  X 4 30 19 11 15 5 5 6 20 16 t 7 44 50 51 X 59   15 X X X