DFS algorithm

z
2
Depth-First Search: The Code
Data: color[V], time, prev[V],d[V],
f[V]
DFS(G) // where prog starts
{
for each vertex u  V
{
color[u] = WHITE;
prev[u]=NIL;
f[u]=inf; d[u]=inf;
}
time = 0;
for each vertex u  V
if (color[u] == WHITE)
DFS_Visit(u);
}
DFS_Visit(u)
{
color[u] = GREY;
time = time+1;
d[u] = time;
for each v  Adj[u]
{
if(color[v] == WHITE){
prev[v]=u;
DFS_Visit(v);}
}
color[u] = BLACK;
time = time+1;
f[u] = time;
}
Initialize

z
DFS Example
3
source
vertex
S
A
B C
D
E
F
G

z
DFS Example
4
1 | | |
|||
| |
source
vertex
d fS
A
B C
D
E
F
G

z
DFS Example
5
1 | | |
|||
2 | |
source
vertex
d fS
A
B C
D
E
F
G

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DFS Example
6
1 | | |
||3 |
2 | |
source
vertex
d fS
A
B C
D
E
F
G

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DFS Example
7
1 | | |
||3 | 4
2 | |
source
vertex
d fS
A
B C
D
E
F
G

z
DFS Example
8
1 | | |
|5 |3 | 4
2 | |
source
vertex
d fS
A
B C
D
E
F
G

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DFS Example
9
1 | | |
|5 | 63 | 4
2 | |
source
vertex
d fS
A
B C
D
E
F
G

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DFS Example
10
1 | | |
|5 | 63 | 4
2 | 7 |
source
vertex
d fS
A
B C
D
E
F
G

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DFS Example
11
1 | 8 | |
|5 | 63 | 4
2 | 7 |
source
vertex
d fS
A
B C
D
E
F
G

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DFS Example
12
1 | 8 | |
|5 | 63 | 4
2 | 7 9 |
source
vertex
d f
What is the structure of the grey vertices?
What do they represent?
S
A
B C
D
E
F
G

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DFS Example
13
1 | 8 | |
|5 | 63 | 4
2 | 7 9 |10
source
vertex
d fS
A
B C
D
E
F
G

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DFS Example
14
1 | 8 |11 |
|5 | 63 | 4
2 | 7 9 |10
source
vertex
d fS
A
B C
D
E
F
G

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DFS Example
15
1 |12 8 |11 |
|5 | 63 | 4
2 | 7 9 |10
source
vertex
d fS
A
B C
D
E
F
G

z
DFS Example
16
1 |12 8 |11 13|
|5 | 63 | 4
2 | 7 9 |10
source
vertex
d fS
A
B C
D
E
F
G

z
DFS Example
17
1 |12 8 |11 13|
14|5 | 63 | 4
2 | 7 9 |10
source
vertex
d fS
A
B C
D
E
F
G

z
DFS Example
18
1 |12 8 |11 13|
14|155 | 63 | 4
2 | 7 9 |10
source
vertex
d fS
A
B C
D
E
F
G

z
DFS Example
19
1 |12 8 |11 13|16
14|155 | 63 | 4
2 | 7 9 |10
source
vertex
d fS
A
B C
D
E
F
G

z
20
DFS: Kinds of edges
 DFS introduces an important distinction among edges in the original graph:
 Tree edge: encounter new (white) vertex
 Back edge: from descendent to ancestor
 Forward edge: from ancestor to descendent
 Cross edge: between a tree or subtrees
 From a grey node to a black node

z
21
DFS Example
1 |12 8 |11 13|16
14|155 | 63 | 4
2 | 7 9 |10
source
vertex
d f
Tree edges Back edges Forward edges Cross edges

z
22
DFS Example
1 |12 8 |11 13|16
14|155 | 63 | 4
2 | 7 9 |10
source
vertex
d f
Tree edges Back edges Forward edges Cross edges

DFS algorithm

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DFS algorithm