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Dijkstra's Shortest Path Algorithm

Utilize Dijkstra's Algorithm to find the shortest path from S to T in a graph. Follow steps to efficiently determine the optimal route.

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Dijkstra's Shortest Path Algorithm

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

  2. Dijkstra's Shortest Path Algorithm S = { } PQ = ( s, 2, 3, 4, 5, 6, 7, t )   2 23 3 0 9 s 18  14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44  distance label 

  3. Dijkstra's Shortest Path Algorithm S = { } PQ = ( s, 2, 3, 4, 5, 6, 7, t ) PQdelmin()   2 23 3 0 9 s 18  14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44  distance label 

  4. Dijkstra's Shortest Path Algorithm S = { s } PQ = ( 2, 6, 7, 3, 4, 5, t ) decrease key   9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44  distance label  15 X

  5. Dijkstra's Shortest Path Algorithm S = { s } PQ = ( 2, 6, 7, 3, 4, 5, t ) PQdelmin()   9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44  distance label  15 X

  6. Dijkstra's Shortest Path Algorithm S = { s, 2 } PQ = ( 6, 7, 3, 4, 5, t )   9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44   15 X

  7. Dijkstra's Shortest Path Algorithm S = { s, 2 } PQ = ( 6, 7, 3, 4, 5, t ) decrease key  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44   15 X

  8. Dijkstra's Shortest Path Algorithm S = { s, 2 } PQ = ( 6, 7, 3, 4, 5, t )  32 X  9 X 2 23 3 0 9 PQdelmin() s 18  14 X 14 6 2 6  4  19 30 11 5 15 5 6 16 20 t 7 44   15 X

  9. Dijkstra's Shortest Path Algorithm S = { s, 2, 6 } PQ = ( 7, 3, 5, 4, t )  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  44 4  X 19 30 11 5 15 5 6 16 20 t 7 44   15 X

  10. Dijkstra's Shortest Path Algorithm S = { s, 2, 6 } PQ = ( 7, 3, 5, 4, t )  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  44 4  X 19 30 11 5 15 5 6 16 20 t 7 44   15 PQdelmin() X

  11. Dijkstra's Shortest Path Algorithm S = { s, 2, 6, 7 } PQ = ( 3, 5, t, 4 )  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  35 44 X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  59 X  15 X

  12. Dijkstra's Shortest Path Algorithm S = { s, 2, 6, 7 } PQ = ( 3, 5, t, 4 ) PQdelmin()  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  35 44 X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  59 X  15 X

  13. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 6, 7 } PQ = ( 5, t, 4 )  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  35 34 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  51 59 X X  15 X

  14. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 6, 7 } PQ = ( 5, t, 4 )  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  35 34 44 X X 4  X 19 30 11 5 15 5 6 16 PQdelmin() 20 t 7 44  51 59 X X  15 X

  15. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 5, 6, 7 } PQ = ( 4, t )  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  50 51 59 X X X  15 X

  16. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 5, 6, 7 } PQ = ( 4, t )  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 PQdelmin() 15 5 6 16 20 t 7 44  50 51 59 X X X  15 X

  17. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 4, 5, 6, 7 } PQ = ( t )  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  50 51 59 X X X  15 X

  18. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 4, 5, 6, 7 } PQ = ( t )  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  PQdelmin() 50 51 59 X X X  15 X

  19. Dijkstra's Shortest Path Algorithm S = { s, 2, 3, 4, 5, 6, 7, t } PQ = ( )  32 X  9 X 2 23 3 0 9 s 18  14 X 14 6 2 6  45 35 34 X 44 X X 4  X 19 30 11 5 15 5 6 16 20 t 7 44  PQdelmin() 50 51 59 X X X  15 X

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