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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

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

?

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

?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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