depth-first search algorithm
DESCRIPTION
b. d. a. c. d. d. a. b. b. e. a. ·. ·. ·. ·. ·. ·. ·. ·. ·. ·. ·. a. a. e. d. b. c. Depth-First Search Algorithm. dfs ( a ) a .marked 1 print a for each ( a , u) E if (u.mark != 1) dfs (u). dfs(“a”). a. ·. b. ·. c. ·. d. ·. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/1.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 1
Depth-First Search Algorithm
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
dfs(“a”) ....dfs(“a”) ....
a
dfs ( a ) a.marked 1 print a for each (a, u) E if (u.mark != 1) dfs (u)
![Page 2: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/2.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 2
Depth-First Search Algorithm
dfs ( a ) a.marked 1 print a for each (a, u) E if (b.mark != 1) dfs (b)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
dfs(“a”) ....dfs(“a”) ....
a
dfs(“b”) ....
dfs(“b”) ....u=b
![Page 3: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/3.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 3
Depth-First Search Algorithm
dfs ( b ) b.marked 1 print b for each (b, u) E if (u.mark != 1) dfs (u)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....
![Page 4: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/4.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 4
Depth-First Search Algorithm
dfs ( b ) b.marked 1 print b for each (b, u) E if (a.mark != 1) dfs (a)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....u=a
![Page 5: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/5.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 5
Depth-First Search Algorithm
dfs ( b ) b.marked 1 print b for each (b, u) E if (d.mark != 1) dfs (d)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....
dfs(“d”) ....
dfs(“d”) ....
u=d
![Page 6: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/6.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 6
Depth-First Search Algorithm
dfs ( d ) d.marked 1 print d for each (d, u) E if (u.mark != 1) dfs (u)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....
dfs(“d”) ....
dfs(“d”) ....
![Page 7: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/7.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 7
Depth-First Search Algorithm
dfs ( d ) d.marked 1 print d for each (d, u) E if (e.mark != 1) dfs (e)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....
dfs(“d”) ....
dfs(“d”) ....
dfs(“e”) ....
dfs(“e”) ....
u=e
![Page 8: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/8.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 8
Depth-First Search Algorithm
dfs ( e ) e.marked 1 print e for each (e, u) E if (u.mark != 1) dfs (u)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....
dfs(“d”) ....
dfs(“d”) ....
dfs(“e”) ....
dfs(“e”) ....
![Page 9: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/9.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 9
Depth-First Search Algorithm
dfs ( e ) e.marked 1 print e for each (e, u) E if (d.mark != 1) dfs (u)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....
dfs(“d”) ....
dfs(“d”) ....
dfs(“e”) ....
dfs(“e”) ....
u=d
![Page 10: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/10.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 10
Depth-First Search Algorithm
dfs ( e ) e.marked 1 print e for each (e, u) E if (u.mark != 1) dfs (u)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....
dfs(“d”) ....
dfs(“d”) ....
dfs(“e”) ....
dfs(“e”) ....
![Page 11: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/11.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 11
Depth-First Search Algorithm
dfs ( d ) d.marked 1 print d for each (d, u) E if (b.mark != 1) dfs (b)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....
dfs(“d”) ....
dfs(“d”) ....
u=b,a
![Page 12: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/12.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 12
Depth-First Search Algorithm
dfs ( d ) d.marked 1 print d for each (d, u) E if (u.mark != 1) dfs (u)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....
dfs(“d”) ....
dfs(“d”) ....
![Page 13: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/13.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 13
Depth-First Search Algorithm
dfs ( b ) b.marked 1 print b for each (b, u) E if (u.mark != 1) dfs (u)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e
dfs(“a”) ....dfs(“a”) ....
dfs(“b”) ....
dfs(“b”) ....
![Page 14: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/14.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 14
Depth-First Search Algorithm
dfs ( a ) a.marked 1 print a for each (a, u) E if (d.mark != 1) dfs (d)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e
dfs(“a”) ....dfs(“a”) ....
u=d
![Page 15: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/15.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 15
Depth-First Search Algorithm
dfs ( a ) a.marked 1 print a for each (a, u) E if (c.mark != 1) dfs (c)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e
dfs(“a”) ....dfs(“a”) ....
u=cdfs(“c”) ....
dfs(“c”) ....
![Page 16: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/16.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 16
Depth-First Search Algorithm
dfs ( c ) c.marked 1 print c for each (c, u) E if (u.mark != 1) dfs (u)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e c
dfs(“a”) ....dfs(“a”) ....
dfs(“c”) ....
dfs(“c”) ....
![Page 17: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/17.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 17
Depth-First Search Algorithm
dfs ( c ) c.marked 1 print c for each (c, u) E if (a.mark != 1) dfs (a)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e c
dfs(“a”) ....dfs(“a”) ....
dfs(“c”) ....
dfs(“c”) ....u=a
![Page 18: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/18.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 18
Depth-First Search Algorithm
dfs ( c ) c.marked 1 print c for each (c, u) E if (u.mark != 1) dfs (u)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e c
dfs(“a”) ....dfs(“a”) ....
dfs(“c”) ....
dfs(“c”) ....
![Page 19: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/19.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 19
Depth-First Search Algorithm
dfs ( a ) a.marked 1 print a for each (a, u) E if (u.mark != 1) dfs (u)
a
c
de b
b ·
c ·
d ·
e ·
a · b · d · c ·
a · d ·
a ·
e · b ·
b ·
a ·
d ·
a b d e c
dfs(“a”) ....dfs(“a”) ....
![Page 20: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/20.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 20
Dijkstra’s Algorithm - an example
0
v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
Edges examined
![Page 21: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/21.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 21
Dijkstra’s Algorithm - an example
0
13
16
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
updated, min picked
![Page 22: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/22.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 22
Dijkstra’s Algorithm - an example
0
13
16
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
S Augmented
![Page 23: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/23.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 23
Dijkstra’s Algorithm - an example
0
13
16
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
Edges examined
![Page 24: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/24.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 24
Dijkstra’s Algorithm - an example
0
18
13
25
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
updated, min picked
![Page 25: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/25.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 25
Dijkstra’s Algorithm - an example
0
18
13
25
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
S Augmented
![Page 26: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/26.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 26
Dijkstra’s Algorithm - an example
0
18
13
25
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
Edges examined
![Page 27: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/27.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 27
Dijkstra’s Algorithm - an example
0
18
13
25
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
updated, min picked
![Page 28: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/28.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 28
Dijkstra’s Algorithm - an example
0
18
13
25
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
S augmented
![Page 29: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/29.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 29
Dijkstra’s Algorithm - an example
0
18
13
25
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
Edges examined
![Page 30: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/30.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 30
Dijkstra’s Algorithm - an example
0
18
13
20
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
updated, min picked
![Page 31: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/31.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 31
Dijkstra’s Algorithm - an example
0
18
13
20
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
S augmented
![Page 32: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/32.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 32
Dijkstra’s Algorithm - an example
0
18
13
20
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
Edges examined
![Page 33: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/33.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 33
Dijkstra’s Algorithm - an example
0
18
13
20
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
updated, min picked
![Page 34: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/34.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 34
Dijkstra’s Algorithm - an example
0
18
13
20
15
8v1
v6
v2
v3
v4
v7
v5
u0 8
1613
10
6
11
14
17
5
7
9
S augmented
![Page 35: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/35.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 35
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1}
Node v1 v2 v3 v4 v5 - 2 4 3 - v1 v1 v1 -
2
4
31
1
2
3
25
![Page 36: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/36.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 36
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1}
Node v1 v2 v3 v4 v5 - 2 4 3 - v1 v1 v1 -
2
4
31
1
2
3
25
![Page 37: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/37.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 37
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1, v2}
Node v1 v2 v3 v4 v5 - 2 4 3 - v1 v1 v1 -
2
4
31
1
2
3
25
![Page 38: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/38.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 38
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1, v2}
Node v1 v2 v3 v4 v5 - 2 1 2 5
- v1 v2 v2 v2
2
4
31
1
2
3
25
![Page 39: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/39.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 39
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1, v2}
Node v1 v2 v3 v4 v5 - 2 1 2 5
- v1 v2 v2 v2
2
4
31
1
2
3
25
![Page 40: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/40.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 40
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1, v2, v3}
Node v1 v2 v3 v4 v5 - 2 1 2 5
- v1 v2 v2 v2
2
4
31
1
2
3
25
![Page 41: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/41.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 41
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1, v2, v3}
Node v1 v2 v3 v4 v5 - 2 1 1 2
- v1 v2 v3 v3
2
4
31
1
2
3
25
![Page 42: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/42.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 42
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1, v2, v3}
Node v1 v2 v3 v4 v5 - 2 1 1 2
- v1 v2 v3 v3
2
4
31
1
2
3
25
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Fall 2006 EE 5301 - VLSI Design Automation I 43
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1, v2, v3, v4}
Node v1 v2 v3 v4 v5 - 2 1 1 2
- v1 v2 v3 v3
2
4
31
1
2
3
25
![Page 44: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/44.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 44
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1, v2, v3, v4}
Node v1 v2 v3 v4 v5 - 2 1 1 2
- v1 v2 v3 v3
2
4
31
1
2
3
25
![Page 45: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/45.jpg)
Fall 2006 EE 5301 - VLSI Design Automation I 45
Prim’s Algorithm Example
v1
v2
v3
v4
v5
S = {v1, v2, v3, v4, v5}
Node v1 v2 v3 v4 v5 - 2 1 1 2
- v1 v2 v3 v3
2
4
31
1
2
3
25