Download - Depth-First Search Algorithm
![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
![Page 43: Depth-First Search Algorithm](https://reader030.vdocument.in/reader030/viewer/2022033103/568150bb550346895dbed916/html5/thumbnails/43.jpg)
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
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![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
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![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