Fall 2006 EE 5301 - VLSI Design Automat ion I 1 Depth-First Search Algorithm a c d e b b · c · d · e · a · b · d · c · a · d · a · e · b · b · a · d · dfs(“a”) .... a dfs ( a ) a.marked 1 print a for each (a, u) E if (u.mark != 1) dfs (u)
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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)
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
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”) ....
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
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
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”) ....
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
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”) ....
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
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”) ....
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
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”) ....
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”) ....
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
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”) ....
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”) ....
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
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”) ....
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”) ....
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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