Write the Recursive algorithm for Merge Sort.Consruct the recurrence relation for recursive algorithm and solve using bachward Subtution.

Design of algorithms - divide-and-conquer: (a) Design a divide-and-conquer algorithm DC_PROD that receives as input an array A with n>0 integers and returns the product of the elements in A. You may assume n is a power of 2. In your algorithm identify the relevant parts of a divide-and-conquer strategy: (i) divide, (ii) conquer, and (iii) combine. (b) Establish the recurrence relation for the running time, T(n), of DC_PROD. (c) Apply the Master Theorem to give a tight bound for T(n).

What's the runtime of the following recurrence relation: T(N) = 4T(N/2) + O(N^2)? Use the Master theorem. You may show your work for partial credit.

I will Upvote correct and detailed answer. Neat and clean diagrams if necessary. Thank you!