find shortest path from s to t
DESCRIPTION
Dijkstra's Shortest Path Algorithm (from “Algorithm Design” by J.Kleinberg and E.Tardos). Find shortest path from s to t. 2. 24. 3. 9. s. 18. 14. 6. 2. 6. 4. 19. 30. 11. 5. 15. 5. 6. 16. 20. t. 7. 44. Dijkstra's Shortest Path Algorithm. S = { } - PowerPoint PPT PresentationTRANSCRIPT
1
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
Dijkstra's Shortest Path Algorithm (from “Algorithm Design” by J.Kleinberg and E.Tardos)
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
44X
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
44X
delmin
X 33X
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
44X
35X
59 X
24
X 33X
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
44X
35X
59 X
delmin
X 33X
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
44X
35X
59 XX 51
X 34
X 33X
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
44X
35X
59 XX 51
X 34
delmin
X 33X
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
44X
35X
59 XX 51
X 34
24
X 50
X 45
X 33X
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
44X
35X
59 XX 51
X 34
24
X 50
X 45
delmin
X 33X
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
44X
35X
59 XX 51
X 34
24
X 50
X 45
X 33X
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
44X
35X
59 XX 51
X 34
X 50
X 45
delmin
X 33X
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
44X
35X
59 XX 51
X 34
X 50
X 45
X 33X
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
44X
35X
59 XX 51
X 34
X 50
X 45
X 33X
32