Traversing graphs

- UnkleRhaukus

Traversing graphs

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- UnkleRhaukus

##### 1 Attachment

- UnkleRhaukus

I know how to traverse: a tree (an undirected, acyclic graph, with one root),
but how i am supposed to traverse: a cyclic graph with no root?

- UnkleRhaukus

... maybe it helps to redraw the graph?
|dw:1433579283033:dw|

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## More answers

- UnkleRhaukus

I can't see how breadth, depth, or level make sense here

- rational

|dw:1433580732682:dw|

- rational

dequeue and grab all the adjacent vertices
|dw:1433580852616:dw|

- rational

push all the unseen vertices into Queue :
|dw:1433580916917:dw|

- rational

dequeue and grab all the adjacent vertices
|dw:1433580986838:dw|

- rational

push all the unseen vertices into Queue :
|dw:1433581041015:dw|

- rational

dequeue and grab all the adjacent vertices :
|dw:1433581119983:dw|

- rational

push all the unseen vertices into queue :
|dw:1433581254223:dw|

- rational

dequeue and grab all the adjacent vertices :
|dw:1433581272392:dw|

- rational

push all the unseen vertices into queue :
|dw:1433581330168:dw|

- rational

dequeue and grab all the adjacent vertices :
|dw:1433581347294:dw|

- rational

push all the unseen vertices into queue :
|dw:1433581402680:dw|

- rational

dequeue and grab all the adjacent vertices :
the queue is empty, so we're done!

- rational

|dw:1433581460670:dw|

- UnkleRhaukus

adj(D) = {A,C}

- rational

right! my mistake, but that wont change anything because both A and C are seen already

- rational

since {E,D,C} are at same level, we will have 3! = 6 different paths using breadth first search

- UnkleRhaukus

hmm, ok, should i start by making the adjacent list?

- rational

you want to implement ?

- UnkleRhaukus

or adjacent matrix perhaps?

- rational

for representing graph is it ?

- rational

this is a small graph so anything will do i guess

- UnkleRhaukus

\[\begin{array}{cccccc}&A&B&C&D&E\\
A&\infty&1&\infty&\infty&\infty\\B&\infty&\infty&1&1&1\\C&1&\infty&\infty& 1&\infty\\D&1&\infty&1&\infty&\infty\\E&\infty&\infty&\infty&\infty&\infty
\end{array}\]

- UnkleRhaukus

hmm ok, i haven't yet been through the detail but that method seems like it works for breadth first traversal.
what is the method for depth first traversal?

- rational

for depth first, just replace queue with a stack

- UnkleRhaukus

ok thanks !

- UnkleRhaukus

i had no idea stack and queues could be used for anything like this, but it kinda makes perfect sense now

- UnkleRhaukus

10.
The Adjacency List
A: {B}
B: {C, D, E}
C: {A, D}
D: {A, C}
E: {}
Operation Queue Output
__________________________________
enqueue(A) |A|
dequeue | | A
enqueue( adj(A) ) |B| A
dequeue | | AB
enqueue( adj(B) ) |E,D,C| AB
dequeue 1 |E,D| ABC
dequeue 1.1 |E| ABCD
| | ABCDE.
dequeue 1.2 |D| ABCE
| | ABCED.
dequeue 2 |C,E| ABD
dequeue 2.1 |C| ABDE
dequeue | | ABDEC.
dequeue 2.2 |E| ABDC
dequeue | | ABDCE.
dequeue 3 |C,D| ABE
dequeue 3.1 |C| ABED
dequeue | | ABEDC.
dequeue 3.2 |D| ABEC
dequeue | | ABECD.

- UnkleRhaukus

so the six possible breadth first traversals are:
ABCDE (a)
ABCED (b)
ABDCE
ABDEC (c)
ABEDC
ABECD
so the answer to 10. is (d) all of the above [(a,b,c)]

- UnkleRhaukus

but, i suppose i would have been able to guess from 1.2

- rational

Nice!

- UnkleRhaukus

i got these questions from a past paper of a subject i've almost completed [just final exam to go], seems like the course has changed quite a bit since 2012,
ive learnt about graphs, digraphs, adjacency lists/matrices, trees, traversals, stacks, queues, etc.
Now i can put all the ideas together!

- UnkleRhaukus

##### 1 Attachment

- UnkleRhaukus

Now, lets see what happens if add . . .
|dw:1433594282292:dw|

- UnkleRhaukus

Node ￼ Adjacent Elements
A: B
B: C, D, E
C: A, D
D: A, C
E: F

- UnkleRhaukus

Is this right for breadth first?
Operation Queue Output
__________________________________
enqueue(A) |A|
dequeue | | A
enqueue( adj(A) ) |B| A
dequeue | | AB
enqueue( adj(B) ) |E,D,C| AB
dequeue |E,D| ABC [1]
dequeue |E| ABCD
dequeue | | ABCDE
enqueue( adj(E) ) |F| ABCDE
dequeue | | ABCDEF.
[other traversals are valid]

- UnkleRhaukus

Is this right for breadth first?
Operation Queue Output
__________________________________
enqueue(A) |A|
dequeue | | A
enqueue( adj(A) ) |B| A
dequeue | | AB
enqueue( adj(B) ) |E,D,C| AB [1 of 6]
dequeue |E,D| ABC
dequeue |E| ABCD
dequeue | | ABCDE
enqueue( adj(E) ) |F| ABCDE
dequeue | | ABCDEF.

- UnkleRhaukus

breadth first
ABCDEF, ABCEDF, ABDECF, ABDCEF, ABEDCF, ABECDF
depth first
ABCDEF, ABCEFD, ABDEFC, ABDCEF, ABEDCF, ABEFCD
is this right?

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