Dijkstra Shortest Path Algorithm

1
Dijkstra Shortest Path Algorithm

• ??????????????????????????
• ??????????????
• ????????????????

2
?????????????? Dijkstras Algorithm

• ?????????????? Dijkstras Algorithm
• ????????????? ??????????????? A ???
  ??????????????????????????????????

????????
4
6
A
C
B
D(v)
Pred(v)
A
0
infinity
A
0
7
3
5
5
0
B
infinity
0
3
C
infinity
F
D
0
D
infinity
0
4
E
infinity
7
5
0
F
infinity
0
G
infinity
E
G
4
3
?????? 1
??????
??????????????
Adjacency Node
Arc ??????????
Weight(i,j)
Weight(i,j)d(i)
d(v)
1
A
B
(A,B)
4
4
4
F
(A,F)
5
5
5
????? B
4
6
A
C
B
D(v)
Pred(v)
B
0
A
0
7
3
5
5
0
A
B
4
infinity
0
3
C
infinity
F
D
0
D
infinity
0
4
E
infinity
7
5
0
F
infinity
0
G
infinity
E
G
4
4
?????? 2
??????
??????????????
Adjacency Node
Arc ??????????
Weight(i,j)
Weight(i,j)d(i)
d(v)
2
A,B
C
(B,C)
6
10
10
F
(A,F)
5
5
5
(B,F)
3
7
5
4
6
A
C
B
D(v)
Pred(v)
B
A
0
0
7
????? F
3
5
5
A
B
4
0
3
C
infinity
F
F
D
0
D
infinity
0
4
E
infinity
7
5
0
A
F
infinity
5
0
G
infinity
E
G
4
5
?????? 3
??????
??????????????
Adjacency Node
Arc ??????????
Weight(i,j)
Weight(i,j)d(i)
d(v)
3
A,B,F
C
(B,C)
6
10
10
D
(F,D)
3
8
8
E
(F,E)
4
9
9
G
(F,G)
7
12
12
4
6
A
C
B
D(v)
Pred(v)
B
A
0
0
7
3
5
5
A
B
4
????? D
0
3
C
infinity
F
F
D
D
0
F
D
infinity
8
0
4
E
infinity
7
5
A
F
5
0
G
infinity
E
G
4
6
?????? 4
??????
??????????????
Adjacency Node
Arc ??????????
Weight(i,j)
Weight(i,j)d(i)
d(v)
4
A,B,D,F
C
(B,C)
6
10
10
(D,C)
5
13
10
E
(F,E)
4
9
9
(D,E)
5
13
9
G
(F,G)
7
12
12
4
6
A
C
B
D(v)
Pred(v)
B
A
0
0
7
3
5
5
A
B
4
0
3
C
infinity
F
F
D
D
F
D
8
0
F
4
E
infinity
9
7
5
A
F
5
????? E
0
G
infinity
E
G
E
4
7
?????? 5
??????
??????????????
Adjacency Node
Arc ??????????
Weight(i,j)
Weight(i,j)d(i)
d(v)
5
A,B,D,E,F
C
(B,C)
6
10
10
(D,C)
5
13
10
G
(E,G)
4
13
12
(F,G)
7
12
12
????? C
4
6
A
C
B
D(v)
Pred(v)
B
C
A
0
0
7
3
5
5
A
B
4
0
B
3
C
infinity
10
F
F
D
D
F
D
8
F
4
E
9
7
5
A
F
5
0
G
infinity
E
G
E
4
8
?????? 6
??????
??????????????
Adjacency Node
Arc ??????????
Weight(i,j)
Weight(i,j)d(i)
d(v)
6
A,B,C,D,E,F
G
(E,G)
4
13
12
(F,G)
7
12
12
4
6
A
C
B
D(v)
Pred(v)
B
C
A
0
0
7
3
5
5
A
B
4
B
3
C
10
F
F
D
D
F
D
8
F
7
4
E
9
5
A
????? G
F
5
0
infinity
G
E
G
E
G
4
9
?????? 6
??????
??????????????
Adjacency Node
Arc ??????????
Weight(i,j)
Weight(i,j)d(i)
d(v)
6
A,B,C,D,E,F
G
(E,G)
4
13
12
(F,G)
7
12
12
4
6
A
C
B
D(v)
Pred(v)
B
C
A
0
0
7
3
5
5
A
B
4
B
3
C
10
F
F
D
D
F
D
8
F
7
4
E
9
5
A
F
5
F
12
G
E
G
E
G
4
10
Dijkstras Algorithm ( ??? )

• ???????????????????????????????????? A
  ????????????? ???? ???????????????????????????? A
  ?????????? E ???????????????????? F
  ????????????????????????? ??????? 9

11
????

• Dijkstras Algorithm ?????????????????????????????
  ??????????????????? ??????????????????????????????
  ?????????????? ???????????????????????????????????
  ???????????? ??????????????? dijkstras algorithm
  ?????????????????????????? ???????????????????????
  ??????????????????????????????????????????????????
  ???? network ??????????

12
?????????????

• http//www.cs.kau.se/cs/education/courses/davb03/l
  ectures/graphs1.pdf
• http//www.cs.vassar.edu/walter/cs241index/lectur
  es/PDF/graphs.pdf
• http//www.cs.nott.ac.uk/mzt/G6DSWE2002/pdfs/grap
  hs4.pdf
• http//www.cs.montana.edu/defrance/classes/spring
  -2003/cs223/Lectures/graphs.html
• http//www.cs.kau.se/donald/ds_alg/lectures/grap
  hs1.ppt

13
????? ?
Question