Binary trees

[n.noumia]

- with 10 nodes, give one example of an unbalanced binary tree and
one example of a balanced binary tree
- what is the advantage of having a balanced binary tree over an
unbalanced tree?
- number your nodes, then give the order in which nodes will be
visited by a depth-first-search
- explain the differences between traversing the tree pre-order, in-
order and post-order

 

[Dave Vandervies]

- with 10 nodes, give one example of an unbalanced binary tree and
one example of a balanced binary tree

Example of a balanced binary tree: [IMAGE]
Example of an unbalanced binary tree: [IMAGE]

- what is the advantage of having a balanced binary tree over an
unbalanced tree?

A balanced tree won't fall over when you stop holding it.

- number your nodes, then give the order in which nodes will be
visited by a depth-first-search

42, pi, 17, e, 105, 69, i, sqrt(2), 3, -1.

- explain the differences between traversing the tree pre-order, in-
order and post-order

The order you traverse it in is different.

DYODH.



dave

 

[Eric Sosman]

- with 10 nodes, give one example of an unbalanced binary tree and
one example of a balanced binary tree

Unbalanced tree: AB,C'K'EH:FJ:G: (notation adapted
from Knuth, TAOCP 2.3.3 equation 3)

To balance the tree, put another one on the other pan.

- what is the advantage of having a balanced binary tree over an
unbalanced tree?

Easier access to firewood. When the next high wind topples
the unbalanced tree, the balanced tree that's over it will fall
at the same time and save you the work of cutting it down.

- number your nodes, then give the order in which nodes will be
visited by a depth-first-search

Numbers: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Depth-first order: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

- explain the differences between traversing the tree pre-order, in-
order and post-order

With pre-order, the pizza is ready when you arrive at the
shop and you needn't wait. With in-order, you may need to pay
a restaurant tax to eat the pizza on the premises. With post-
order, the pizza reaches you three to five business days later
and is unpalatable.

 

[Chris Dollin]

- with 10 nodes, give one example of an unbalanced binary tree and
one example of a balanced binary tree
- what is the advantage of having a balanced binary tree over an
unbalanced tree?
- number your nodes, then give the order in which nodes will be
visited by a depth-first-search
- explain the differences between traversing the tree pre-order, in-
order and post-order

I think you should have posted to comp.lazy.domyhomework, since (a)
this is homework; having someone else do it for you misses the point;
(b) it's off-topic, since it isn't about C at all.

 

[Clever Monkey]

- with 10 nodes, give one example of an unbalanced binary tree and
one example of a balanced binary tree http://en.wikipedia.org/wiki/Binary_tree

- what is the advantage of having a balanced binary tree over an
unbalanced tree?

A balanced tree will not fall over in a storm, as long as the wind blows
evenly from all directions.

- number your nodes, then give the order in which nodes will be
visited by a depth-first-search http://en.wikipedia.org/wiki/Binary_tree#Depth-first_order

- explain the differences between traversing the tree pre-order, in-
order and post-order

http://en.wikipedia.org/wiki/Binary_tree#Pre-order.2C_in-order.2C_and_post-order_traversal.

 

[Dave Vandervies]

(e-mail address removed) wrote:
A balanced tree will not fall over in a storm, as long as the wind blows
evenly from all directions.

But the wind in most storms doesn't blow evenly from all directions.
If you're going for storm tolerance, you really want an unbalanced tree,
but the problem with that is that every time the wind changes you have
to go out and re-unbalance it for the new wind direction.


dave

 

[Dave Vandervies]

Unbalanced tree: AB,C'K'EH:FJ:G: (notation adapted
from Knuth, TAOCP 2.3.3 equation 3)

Unless you have a different edition than I do (3rd), I think you meant
equation 4.


dave

 

[Eric Sosman]

Dave Vandervies wrote On 05/04/07 16:08,:

Unless you have a different edition than I do (3rd), I think you meant
equation 4.

The renumbering was part of the adaptation.

 

[Clever Monkey]

But the wind in most storms doesn't blow evenly from all directions.
If you're going for storm tolerance, you really want an unbalanced tree,
but the problem with that is that every time the wind changes you have
to go out and re-unbalance it for the new wind direction.

So true. I think I'm barking up the wrong tree here. We better leaf
this alone for while, or we might end up branching off into the wrong
direction. If I twig onto anything else, I'll let you know, but I think
this conversation will not bear any new fruit. Either that, or I'm the
fall guy and can't see the tree for the forest.