1. Dijkstra’s Algorithm We are given a directed weighted graph
There are no negative weights.
We need to solve the single source shortest path problem.
The source is given to be 1.

2. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
Processed nodes will be shown in red.
Partially processed nodes will be shown in green.
The partially processed nodes will be kept in a heap, where the key is value.
Unprocessed nodes will be shown in black.
Search tree pointers will be shown in red.
The back pointers are the reverse of the search tree pointers.

3. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap 1
value
back *

4. The value of a node is the weight of the shortest path found so far.29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
11:1
9:2
20:27
value
back *
17:34
The value of a node is the weight of the shortest path found so far.

5. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
9:2
14:4
20:27
value
back *
17:34
6:32

6. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
14:4
10:4
20:27
value
back *
17:34
6:32

7. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
10:4
12:6
20:27
value
back *
17:34
6:32

8. A better path to 20 is found; its value and backpointer are updated.29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
12:6
6:32
20:8
value
back *
17:34
A better path to 20 is found; its value and backpointer are updated.

9. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
20:8
5:10
17:34
value
back *
6:32

10. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
5:10
3:15
19:28
value
back *
6:32
15:30
17:34

11. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
3:14
15:30
2:18
value
back *
6:32
17:34
19:28

12. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
2:18
15:30
8:22
value
back *
6:32
17:34
19:28

13. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
8:18
15:30
7:25
value
back *
6:32
17:34
19:28

14. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
7:25
15:30
19:27
value
back *
6:32
17:34

15. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
19:26
6:28
17:34
value
back *
15:30

16. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
6:28
15:30
17:30
value
back *

17. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
17:30
15:30
18:35
value
back *

18. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
15:30
18:35
value
back *

19. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
18:35
4:37
16:35
value
back *

20. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
16:35
4:37
value
back *

21. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
4:37
13:40
value
back *

22. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap
13:40
value
back *

23. 29 34 27 22 32 26 27 20 2 2 4 7 8 9 4 3 5 1 9 10 20 3 8 19 17 15 16 9 5 8 7 6 3 6 1 1 1 3 7 3 5 5 7 6 2 2 4 8 2 8 1 6 5 5 5 5 5 5 2 7 2 8 6 2 2 6 3 3 9 7 9 4 4 3 3 2 4 6 9 3 7 8 8 11 14 12 5 2 7 6 18 4 13 3 4 7 7 3 2 1 1 2 22 28 30 35 31 31
heap empty
value
back *
The heap is empty and we are done.