bab-discussions Computer Science Assignment Help

3. Prove by induction that Fi =
φ
i−φˆi
√
5
where φ =
1+√
5
2
and φˆ =
1−
√
5
2
(Note: Fibonacci numbers
(F0 = 0, F1 = 1, F2 = 1, F3 = 2, . . .) satisfy the relation Fi = Fi−1 + Fi−2). (20 pt)

4. Solve the follwoing recurrences using the master method. (20pt)

(a) T(n) = 4T(n/3) + nlgn

(b) T(n) = 4T(n/2) + n
2√
n.

(c) T(n) = 2T(n/4) + √
n.

(d) T(n) = 7T(n/2) + n
2
.

5. Recall the following partition algorithm from quicksort:

Partition (A , p , r )
x = A [ r ]
i = p – 1
for j = p to r – 1 {
if ( A [ j ] <= x ) {
i = i + 1
swap A [ i ] and A [ j ]
}
}
swap A [ i +1] and A [ r ]
return i + 1

(a) Explain the running time of the algorithm if the initial call is Partition(A, 1, n) (In other words,
the input array is A[1, . . . , n] with size n). (10 pt)

(b) Assume that all elements of the input array A has the same value, e.g., A = [1, 1, . . . , 1] with size
n. What value does the partition algorithm return? (10 pt)

6. Describe an O(nlgn)-time algorithm to solve the following problem. (20pt)

Input: a set S of integers with |S| = n, and an integer k

• Decide: if there exists two elements in S whose sum is exactly k.

Type a school reform plan and create a 24 slide presentation using popplet or prezi. Must use data from an actual school

*Identify strengths

*collect data

*review district mandates

525-700 words, APA format

Address:

How would you expect your plan to affect the culture and climate of the school you selected

What types of professional development would you implement in your plan? Why did you identify these types of professional development? how do you anticipate these types of professional development will help transform the school you selected?

In your opinion, what will be the easiest changes to incorporate? Why? Explain and provide specific examples.

In your opinion, what will be the most challenging changes to incorporate? Why? Explain and provide specific examples.

Please based on the last part “Alternatives” of the following analysis, the best option chosen by us is Maintain the same strategy, provide recommendation and implantation plan.

RECOMMENDATION AND IMPLEMENTATION PLAN

A clear identification of the selected alternative, matched with supporting arguments and a specific implementation plan.

• a) Recommendation: Why is this alternative the most appropriate? Using strategic management concepts, defend the alternative, outline the expected results and support the argument with a summary of how it fairs against the decision criteria.
  • Highlight your recommendation’s key benefits, and sell it as to why it is the best solution
  • Chosen recommendation aligned with body of analysis and in particular with Problem statement
  • Understanding different levels of strategies
• b) Actions Plan: Brief implementation plan provided
  • Identify required resources (most probably financial), contingencies, etc.
    • Who: the marketing department will execute the solution
    • What: the plan is to invest on more marketing and promotion in order to reach retailor and increase local sales
    • When: first online study, then social media marketing strategy before implementation
    • Where: new marketing campaign should carry out mainly online; certain retailers’ locations (restaurants, bars) may be
    • How: focus on twitter, Instagram, Facebook, corporate e-mail (with retailers), face-to-face-meeting.
  • Identify timeline: Short term, intermediate, & Long term: based on the questions above

The task is simple and does not requires extensive writing.

There is no word/page limit. Just make sure that the answeres are fully provided and graphed

Do not attached downloaded graphs from the internet. You are free to use any sources but please either redo them (you can draw them by yourself) or modify them in any drawing software.

There are 4 economic problems which need to be solved. You can find them in the attached file. I know most of the answers are online, and you are free to use those answers as long as they are correct and they are paraphrased. Please include full answer and make sure nothing is missing.

For someone who has knowledge in the international economic field this should be a very easy to do task and should not take too much time at all.

Thanks for your support. You can complete the answers directly on the provided file. No specific format is required.