Analysis of Algorithms Algorithm Challenge 2: Divide and Conquer

1.Design your algorithm for a given file of size 25 KIB first, and then do the same for a given file of size 2x KIB (for any given x). Note that x is a unsigned integer where x > 0. The best way to design your algorithm for this problem is to use diagrams or pics which detailed description of every component. Be as clear as possible, and define clearly each step taken during the process. Credit for this problem will be only given to those students that clearly define a step by step approach to solve this problem.

2. Write the recursive pseudocode that represents your algorithm in (1) when the size of the input file is 2x KIB. The pseudocode must be done in LaTeX

3. Create a complete analysis of your pseudocode-algorithm. First compute its complexity and time complexity using the Back Substitution method, and then check your time complexity results using the master theorem. Show ALL your work to get credit .

4. Modify the design of your algorithm from problem (1) to support files of any size (not only 2 x ). For instance in problem (1), we were assuming that the file size is in the form of 2x such as 2KIB, 4KIB, 16KIB….. However, your new modification should include files of any size such as 3KIB, 37KIB….. Note that you must show the modified pseudocode (in LaTeX) for this problem, and explain your modifications. In addition, do you think that the time complexity of this algorithm has been optimized as a result of the modifications applied? Why? .