1 Dijkstra's Shortest Path Algorithm Find shortest path from s to t. s 3 t 2 6 7 4 5 23 18 2 9 14 15 5 30 20 44 16 11 6 19 6.

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Presentation transcript:

1 Dijkstra's Shortest Path Algorithm Find shortest path from s to t. s 3 t

2 Dijkstra's Shortest Path Algorithm s 3 t        0 distance label S = { } PQ = { s, 2, 3, 4, 5, 6, 7, t }

3 Dijkstra's Shortest Path Algorithm s 3 t        0 distance label S = { } PQ = { s, 2, 3, 4, 5, 6, 7, t } PQdelmin()

4 Dijkstra's Shortest Path Algorithm s 3 t    14  0 distance label S = { s } PQ = { 2, 3, 4, 5, 6, 7, t } decrease key  X   X X

5 Dijkstra's Shortest Path Algorithm s 3 t    14  0 distance label S = { s } PQ = { 2, 3, 4, 5, 6, 7, t }  X   X X PQdelmin()

6 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2 } PQ = { 3, 4, 5, 6, 7, t }  X   X X

7 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2 } PQ = { 3, 4, 5, 6, 7, t }  X   X X decrease key X 32

8 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2 } PQ = { 3, 4, 5, 6, 7, t }  X   X X X 32 PQdelmin()

9 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 6 } PQ = { 3, 4, 5, 7, t }  X   X X X X

10 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 6 } PQ = { 3, 4, 5, 7, t }  X   X X X X PQdelmin()

11 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 6, 7 } PQ = { 3, 4, 5, t }  X   X X X X 35 X 59 X

12 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 6, 7 } PQ = { 3, 4, 5, t }  X   X X X X 35 X 59 X PQdelmin()

13 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 3, 6, 7 } PQ = { 4, 5, t }  X   X X X X 35 X 59 XX 51 X 34

14 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 3, 6, 7 } PQ = { 4, 5, t }  X   X X X X 35 X 59 XX 51 X 34 PQdelmin()

15 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 3, 5, 6, 7 } PQ = { 4, t }  X   X X X X 35 X 59 XX 51 X 34 X 50 X 45

16 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 3, 5, 6, 7 } PQ = { 4, t }  X   X X X X 35 X 59 XX 51 X 34 X 50 X 45 PQdelmin()

17 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 3, 4, 5, 6, 7 } PQ = { t }  X   X X X X 35 X 59 XX 51 X 34 X 50 X 45

18 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 3, 4, 5, 6, 7 } PQ = { t }  X   X X X X 35 X 59 XX 51 X 34 X 50 X 45 PQdelmin()

19 Dijkstra's Shortest Path Algorithm s 3 t    14  0 S = { s, 2, 3, 4, 5, 6, 7, t } PQ = { }  X   X X X X 35 X 59 XX 51 X 34 X 50 X 45 PQdelmin()