1.What is a recurrence relation in computer science, and how is it used to define the time complexity of recursive algorithms? 2.Provide an example of a recurrence relation and explain how it can be solved to determine the overall time complexity of an algorithm.

Provide an explanation of the recursive binary search's stopping condition and the justification for why stopping conditions are necessary for all recursive algorithms.

Provide an explanation of Hobb's algorithm and centering algorithms as they pertain to the occurrences being referred to.

To what extent can heuristic search help? Is there a comparison between the merits and flaws of this algorithm and similar algorithms?

If an algorithm A is in the complexity class P, is it necessarily in the complexity class NP? Explain why or why not

Given three sequences of length m, n, and p each, you are to design and analyze an algorithm to find the longest common subsequence (LCSS) for the three sequence. Is it possible to use dynamic programming to find the LCSS between the three sequences? If yes, provide recursive solution to the above problem.

Answer the following question: What are the three possible keys lengths for the AES algorithm?

Please answer with at least 2 paragraphs. Define the concepts of logarithm, linear, and quadratic when analyzing algorithms. What are some of the pros and cons associated with utilizing Big-Oh notation to analyze an algorithm? How can analyzing the efficiency of an algorithm lead to improvements in the initial design? In your answer, specifically, think of and give a real-life scenario where: Algorithm analysis is important Algorithm efficiency is paramount