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