Dijkstra's Shortest Path Algorithm

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A demonstration of Dijkstra's Shortest Path Algorithm by example

A demonstration of Dijkstra's Shortest Path Algorithm by example

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  • 1. Dijkstra's Shortest Path Algorithm
    • Find shortest path from s to t.
    s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6
  • 2. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6        0 distance label S = { } PQ = { s, 2, 3, 4, 5, 6, 7, t }
  • 3. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6        0 distance label S = { } PQ = { s, 2, 3, 4, 5, 6, 7, t } delmin
  • 4. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9    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 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9    14  0 distance label S = { s } PQ = { 2, 3, 4, 5, 6, 7, t }  X   X X delmin
  • 6. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9    14  0 S = { s, 2 } PQ = { 3, 4, 5, 6, 7, t }  X   X X
  • 7. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9    14  0 S = { s, 2 } PQ = { 3, 4, 5, 6, 7, t }  X   X X decrease key X 33
  • 8. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9    14  0 S = { s, 2 } PQ = { 3, 4, 5, 6, 7, t }  X   X X X 33 delmin
  • 9. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9    14  0 S = { s, 2, 6 } PQ = { 3, 4, 5, 7, t }  X   X X X 33 44 X X 32
  • 10. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 6 } PQ = { 3, 4, 5, 7, t }  X   X X 44 X delmin  X 33 X 32
  • 11. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 6, 7 } PQ = { 3, 4, 5, t }  X   X X 44 X 35 X 59 X 24  X 33 X 32
  • 12. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 6, 7 } PQ = { 3, 4, 5, t }  X   X X 44 X 35 X 59 X delmin  X 33 X 32
  • 13. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 3, 6, 7 } PQ = { 4, 5, t }  X   X X 44 X 35 X 59 X X 51 X 34  X 33 X 32
  • 14. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 3, 6, 7 } PQ = { 4, 5, t }  X   X X 44 X 35 X 59 X X 51 X 34 delmin  X 33 X 32 24
  • 15. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 3, 5, 6, 7 } PQ = { 4, t }  X   X X 44 X 35 X 59 X X 51 X 34 24 X 50 X 45  X 33 X 32
  • 16. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 3, 5, 6, 7 } PQ = { 4, t }  X   X X 44 X 35 X 59 X X 51 X 34 24 X 50 X 45 delmin  X 33 X 32
  • 17. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 3, 4, 5, 6, 7 } PQ = { t }  X   X X 44 X 35 X 59 X X 51 X 34 24 X 50 X 45  X 33 X 32
  • 18. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 3, 4, 5, 6, 7 } PQ = { t }  X   X X 44 X 35 X 59 X X 51 X 34 X 50 X 45 delmin  X 33 X 32 24
  • 19. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 3, 4, 5, 6, 7, t } PQ = { }  X   X X 44 X 35 X 59 X X 51 X 34 X 50 X 45  X 33 X 32
  • 20. Dijkstra's Shortest Path Algorithm s 3 t 2 6 7 4 5 24 18 2 9 14 15 5 30 20 44 16 11 6 19 6 15 9   14  0 S = { s, 2, 3, 4, 5, 6, 7, t } PQ = { }  X   X X 44 X 35 X 59 X X 51 X 34 X 50 X 45  X 33 X 32