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Confused on Homework Questions

Posted on 2004-10-02
Medium Priority
Last Modified: 2010-04-01
I am looking for conceptual step-by-step formulas and data that will allow me to do these homework questions below.

I have had bits of good information and realize that this is not a math forum but would appreciat some good ideas in the right direction in addition to,...and of course I am not asking for the problems to be solved.

Please advise.
Answer the following questions in a text file or turn in a hard copy.

1. Assume you have an input stream '1 2 3 4 5 6' reading from left to right. By using (1) a queue and (2) a deque, which of the following rearrangements can be obtained for output, reading from left-to-right?

a)  1 2 3 4 5 6           b) 2 4 3 6 5 1         c) 1 5 2 4 3 6
d)  4 2 1 3 5 6           e) 1 2 6 4 5 3         f) 5 2 6 3 4 1

2. Compute log2 1000 if all you know is log2 10. Show your work and justify why it is correct.

3. Show how logs "turn" multiplication into addition, division into subtraction, and exponentiation into multiplication.

4. A fully populated binary tree has all nodes (vertices) present. Assuming a tree with one node has height 1, what is the height of a fully populated tree with n nodes? A well-behaved binary tree may not have all levels fully populated, but all leaves in the tree will be on the same or on adjacent levels. What is the height of a well-behaved binary tree with n nodes? (hint: use the floor or ceil function from the math library.)


Question by:edelossantos
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LVL 36

Assisted Solution

Zyloch earned 1000 total points
ID: 12209602
Hi edelossantos,

Not too good at these things, but I can help with the log question.

A rule of logarithms is this:
logb(x^n) = n*logb(x).

For example,

log7 25 = 2*log7 5


Author Comment

ID: 12209607
Thank you, Zyloch.  Del
LVL 36

Assisted Solution

Zyloch earned 1000 total points
ID: 12209694
For #3, well, go to Google and search Logarithm Rules :)
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LVL 11

Accepted Solution

bcladd earned 1000 total points
ID: 12209802
On 4: How many nodes are there in a fully-populated tree of height 1? 2? 3? If you draw pictures, you can answer these questions. If you need to, draw the picture for 4 as well. Then, having written the simple funciton table:

   height | nodes
      1     |  ?
      2     |  ?
      3     |  ?

you should see a pattern. If you have the table and you don't see a pattern, post the table and maybe we can help you find the pattern.

Once you have that information, you will actually have bounds on the height of a well-behaved tree (a well-behaved tree is one that starts with a fully-populated tree and expands it with some number of new leaves from the leaves of the fully-populated tree...so your function of nodes to height (reverse of the table, actually) shows you how to figure out the height of a well-behaved tree.

On 1: Focus on queue: What order will items reach the front of the queue if you enqueue all of them before dequeuing any of them? Can the interleaving of enqueue and dequeue operations change that order? How?

LVL 20

Expert Comment

ID: 12211300
once more:
edelossantos, this side is not made to make your homework, it wouldn't help you understand the thinks you need
to understand, if anybody else but you makes it.
DON'T post here your homework-questions!!! how should your teacher see, what you are able to do,
and what you're not able to do. better ask your teacher once more and discuss the questions with her/him, so
he/she knows which steps need to be repeated in your lesson. i think that's what homework is for

LVL 20

Expert Comment

ID: 12211378
btw: lots of points(500) & money for homework, better use it for good books ;)
LVL 36

Expert Comment

ID: 12212479
Well, that's true. Of course, we would be inclined to help if you DO post your homework :-)

Author Comment

ID: 12213361
    Again,...I don't mind paying for knowledge...I come to you all to learn if you are willing to teach.  I have bought the books and do not buy the homework.  I will post my own work and if you don't mind...you can check it if for me.  I will comply with all of the experts per the member agreement...most of the time experts refrain from homework questions. I did not think that lots of points would be offensive nor a lack of respect...I think I will post lower points the next time. Thanks again.  Regards.  Del

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