Algorithms & Data Structures Question

I need help with my assignment for algorithm class, this assignment has two different book to follow. The first book is called Erikson is attached with hw2.pdf and Sanjoy to solve reset problems. Please follow all the instructions says in pdf is really important! I want it done using Word docx

Each question is worth 25 points.
• Submission should be in PDF. There are some scanner apps that improves the
readability if you handwrite the solutions.
• You can work in groups of 4. Make sure to list the names of people in your group.
Each student must still submit a copy on Canvas.
• When you are asked to design an algorithm, do the following: a) describe the
algorithm, b) prove/argue why it is correct, and c) provide the running time.
• [Erickson] denotes the book by Jeff Erickson (available for free online at
http://jeffe.cs.illinois.edu/teaching/algorithms/).
• [DPV] denotes the book by Dasgupta, Papadimitriou, and Vazirani (the required
textbook).
(1) Question 1: Problem 21a of [Erickson], page 55. For simplicity, assume n is power
of 2 and define the median to be the one with rank n (i.e., nth smallest) in A ∪ B.
Note that A ∪ B has 2n elements. The median must be larger than exactly n − 1
elements and smaller than n other elements. The problem also assumes that all
elements are distinct.
Let C = A[1 . . . n/2], D = A[n/2+ 1 . . . n], E = B[1 . . . n/2], F = B[n/2+ 1 . . . n].
You may break the solutions into smaller parts by answering the following subquestions.
(a) Show that if A[n/2] < B[n/2], then the median of A ∪ B must be in D ∪ E.
(b) Furthermore, show that the median of A∪B must also be the median of D∪E.
(c) By symmetry, what can you say about the case A[n/2] > B[n/2]?
(d) Design a divide-and-conquer algorithm based on the above observation

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