Dijkstra's Shortest Path Algorithm

1
Dijkstra's Shortest Path Algorithm

• Find shortest path from s to t.

3
2
23
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
?
?
3
2
23
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()
?
?
3
2
23
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, 3, 4, 5, 6, 7, t
decrease key
?
?
9
X
3
2
23
0
9
s
18
14
?
14
X
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, 3, 4, 5, 6, 7, t
PQdelmin()
?
?
9
X
3
2
23
0
9
s
18
14
?
14
X
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 3, 4, 5, 6, 7, t
?
?
9
X
3
2
23
0
9
s
18
14
?
14
X
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 3, 4, 5, 6, 7, t
decrease key
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
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 3, 4, 5, 6, 7, t
?
32
X
?
9
X
3
2
23
0
9
PQdelmin()
s
18
14
?
14
X
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 3, 4, 5, 7, t
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
44
4
?
19
X
30
11
5
15
5
6
16
20
t
7
44
?
15
?
X
10
Dijkstra's Shortest Path Algorithm
S s, 2, 6 PQ 3, 4, 5, 7, t
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
44
4
?
19
X
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, 4, 5, t
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
35
44
X
4
?
19
X
30
11
5
15
5
6
16
20
t
7
44
?
59
15
?
X
X
12
Dijkstra's Shortest Path Algorithm
S s, 2, 6, 7 PQ 3, 4, 5, t
PQdelmin()
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
35
44
X
4
?
19
X
30
11
5
15
5
6
16
20
t
7
44
?
59
15
?
X
X
13
Dijkstra's Shortest Path Algorithm
S s, 2, 3, 6, 7 PQ 4, 5, t
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
35
34
44
X
X
4
?
19
X
30
11
5
15
5
6
16
20
t
7
44
?
51
59
15
?
X
X
X
14
Dijkstra's Shortest Path Algorithm
S s, 2, 3, 6, 7 PQ 4, 5, t
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
35
34
44
X
X
4
?
19
X
30
11
5
15
5
6
16
PQdelmin()
20
t
7
44
?
51
59
15
?
X
X
X
15
Dijkstra's Shortest Path Algorithm
S s, 2, 3, 5, 6, 7 PQ 4, t
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
45
35
34
44
X
X
X
4
?
19
X
30
11
5
15
5
6
16
20
t
7
44
?
51
50
59
15
?
X
X
X
X
16
Dijkstra's Shortest Path Algorithm
S s, 2, 3, 5, 6, 7 PQ 4, t
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
45
35
34
44
X
X
X
4
?
19
X
30
11
5
PQdelmin()
15
5
6
16
20
t
7
44
?
51
50
59
15
?
X
X
X
X
17
Dijkstra's Shortest Path Algorithm
S s, 2, 3, 4, 5, 6, 7 PQ t
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
45
35
34
44
X
X
X
4
?
19
X
30
11
5
15
5
6
16
20
t
7
44
?
51
50
59
15
?
X
X
X
X
18
Dijkstra's Shortest Path Algorithm
S s, 2, 3, 4, 5, 6, 7 PQ t
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
45
35
34
44
X
X
X
4
?
19
X
30
11
5
15
5
6
16
20
t
7
44
?
PQdelmin()
51
50
59
15
?
X
X
X
X
19
Dijkstra's Shortest Path Algorithm
S s, 2, 3, 4, 5, 6, 7, t PQ
?
32
X
?
9
X
3
2
23
0
9
s
18
14
?
14
X
6
2
6
?
45
35
34
44
X
X
X
4
?
19
X
30
11
5
15
5
6
16
20
t
7
44
?
PQdelmin()
51
50
59
15
?
X
X
X
X