4.4 dijkstra s algorithm demobasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7demodijkstra.pdf•consider...
TRANSCRIPT
![Page 1: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/1.jpg)
Algorithms, 4th Edition · Robert Sedgewick and Kevin Wayne · Copyright © 2002–2012 · October 26, 2014 11:53:41 AM
AlgorithmsF O U R T H E D I T I O N
R O B E R T S E D G E W I C K K E V I N W A Y N E
4.4 DIJKSTRA'S ALGORITHM DEMO
![Page 2: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/2.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
2
0
4
7
1 3
5
2
6
s
69
8
4
5
7
1
54
15
312
20
13
11
9
an edge-weighted digraph
0→1 5.0
0→4 9.0
0→7 8.0
1→2 12.0
1→3 15.0
1→7 4.0
2→3 3.0
2→6 11.0
3→6 9.0
4→5 4.0
4→6 20.0
4→7 5.0
5→2 1.0
5→6 13.0
7→5 6.0
7→2 7.0
![Page 3: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/3.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
3
0
4
7
1 3
5
2
6
choose source vertex 0
v distTo[] edgeTo[]
0 0.0 -
1
2
3
4
5
6
7
![Page 4: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/4.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
4
4
7
1 3
5
2
6
relax all edges incident from 0
9
8
5
v distTo[] edgeTo[]
0 0.0 -
1
2
3
4
5
6
7
0
0
∞
∞
∞
![Page 5: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/5.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
∞
Dijkstra's algorithm
5
4
7
1 3
5
2
6
relax all edges incident from 0
9
8
5
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2
3
4 9.0 0→4
5
6
7 8.0 0→7
0
∞
5
0
∞
8
9
![Page 6: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/6.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
6
0
4
7
3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2
3
4 9.0 0→4
5
6
7 8.0 0→7
1
![Page 7: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/7.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
7
0
4
7
1 3
5
2
6
choose vertex 1
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2
3
4 9.0 0→4
5
6
7 8.0 0→7
![Page 8: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/8.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
8
0
4
7
1 3
5
2
6
relax all edges incident from 1
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2
3
4 9.0 0→4
5
6
7 8.0 0→7
4
15
12
5
∞
∞
8
![Page 9: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/9.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
9
0
4
7
1 3
5
2
6
relax all edges incident from 1
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 17.0 1→2
3 20.0 1→3
4 9.0 0→4
5
6
7 8.0 0→7
4
15
12
✔
∞
∞5
17
20
8
![Page 10: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/10.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
10
0
4
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 17.0 1→2
3 20.0 1→3
4 9.0 0→4
5
6
7 8.0 0→7
7
![Page 11: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/11.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
11
0
4
7
1 3
5
2
6
choose vertex 7
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 17.0 1→2
3 20.0 1→3
4 9.0 0→4
5
6
7 8.0 0→7
![Page 12: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/12.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
∞
Dijkstra's algorithm
12
0
4
7
1 3
5
2
6
relax all edges incident from 7
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 17.0 1→2
3 20.0 1→3
4 9.0 0→4
5
6
7 8.0 0→7
6
78
17
![Page 13: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/13.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
13
0
4
7
1 3
5
2
6
relax all edges incident from 7
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 15.0 7→2
3 20.0 1→3
4 9.0 0→4
5 14.0 7→5
6
7 8.0 0→7
6
78
17
∞ 14
15
![Page 14: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/14.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
14
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 15.0 7→2
3 20.0 1→3
4 9.0 0→4
5 14.0 7→5
6
7 8.0 0→7
![Page 15: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/15.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
15
0
4
7
1 3
5
2
6
select vertex 4
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 15.0 7→2
3 20.0 1→3
4 9.0 0→4
5 14.0 7→5
6
7 8.0 0→7
![Page 16: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/16.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
16
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 15.0 7→2
3 20.0 1→3
4 9.0 0→4
5 14.0 7→5
6
7 8.0 0→7
relax all edges incident from 4
4
5
20
8
14
9 ∞
![Page 17: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/17.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
17
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 15.0 7→2
3 20.0 1→3
4 9.0 0→4
5 13.0 4→5
6 29.0 4→6
7 8.0 0→7
relax all edges incident from 4
4
5
20
✔
∞ 29
8
14
9
13
![Page 18: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/18.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
18
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 15.0 7→2
3 20.0 1→3
4 9.0 0→4
5 13.0 4→5
6 29.0 4→6
7 8.0 0→7
![Page 19: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/19.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
19
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 15.0 7→2
3 20.0 1→3
4 9.0 0→4
5 13.0 4→5
6 29.0 4→6
7 8.0 0→7
select vertex 5
![Page 20: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/20.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
20
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 15.0 7→2
3 20.0 1→3
4 9.0 0→4
5 13.0 4→5
6 29.0 4→6
7 8.0 0→7
relax all edges incident from 5
1
13
29
13
15
![Page 21: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/21.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
21
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 20.0 1→3
4 9.0 0→4
5 13.0 4→5
6 26.0 5→6
7 8.0 0→7
relax all edges incident from 5
1
13
29
13
15 14
26
![Page 22: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/22.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
22
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 20.0 1→3
4 9.0 0→4
5 13.0 4→5
6 26.0 5→6
7 8.0 0→7
![Page 23: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/23.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
23
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 20.0 1→3
4 9.0 0→4
5 13.0 4→5
6 26.0 5→6
7 8.0 0→7
select vertex 2
![Page 24: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/24.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
24
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 20.0 1→3
4 9.0 0→4
5 13.0 4→5
6 26.0 5→6
7 8.0 0→7
relax all edges incident from 2
3
11
26
14
20
![Page 25: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/25.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
25
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 17.0 2→3
4 9.0 0→4
5 13.0 4→5
6 25.0 2→6
7 8.0 0→7
relax all edges incident from 2
3
11
26
14
20 17
25
![Page 26: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/26.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
26
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 17.0 2→3
4 9.0 0→4
5 13.0 4→5
6 25.0 2→6
7 8.0 0→7
![Page 27: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/27.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
27
0
4
7
1 3
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 17.0 2→3
4 9.0 0→4
5 13.0 4→5
6 25.0 2→6
7 8.0 0→7
select vertex 3
![Page 28: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/28.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
28
0
4
7
1
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 17.0 2→3
4 9.0 0→4
5 13.0 4→5
6 25.0 2→6
7 8.0 0→7
relax all edges incident from 3
9
3
25
20
![Page 29: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/29.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
29
0
4
7
1
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 17.0 2→3
4 9.0 0→4
5 13.0 4→5
6 25.0 2→6
7 8.0 0→7
relax all edges incident from 3
9
✔
3
25
20
![Page 30: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/30.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
30
0
4
7
1
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 17.0 2→3
4 9.0 0→4
5 13.0 4→5
6 25.0 2→6
7 8.0 0→7
3
![Page 31: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/31.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
31
0
4
7
1
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 17.0 2→3
4 9.0 0→4
5 13.0 4→5
6 25.0 2→6
7 8.0 0→7
3
select vertex 6
![Page 32: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/32.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
32
0
4
7
1
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 17.0 2→3
4 9.0 0→4
5 13.0 4→5
6 25.0 2→6
7 8.0 0→7
3
relax all edges incident from 6
![Page 33: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/33.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
33
0
4
7
1
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 17.0 2→3
4 9.0 0→4
5 13.0 4→5
6 25.0 2→6
7 8.0 0→7
3
![Page 34: 4.4 DIJKSTRA S ALGORITHM DEMObasics.sjtu.edu.cn/~xiaojuan/algo16/slides/7DemoDijkstra.pdf•Consider vertices in increasing order of distance from s (non-tree vertex with the lowest](https://reader036.vdocument.in/reader036/viewer/2022071415/610feab908334812ca2db02a/html5/thumbnails/34.jpg)
• Consider vertices in increasing order of distance from s(non-tree vertex with the lowest distTo[] value).
• Add vertex to tree and relax all edges incident from that vertex.
Dijkstra's algorithm
34
0
4
7
1
5
2
6
v distTo[] edgeTo[]
0 0.0 -
1 5.0 0→1
2 14.0 5→2
3 17.0 2→3
4 9.0 0→4
5 13.0 4→5
6 25.0 2→6
7 8.0 0→7
3
shortest-paths tree from vertex s
s