Question: (a) Design a divide-and-conquer algorithm DC_POSITIVE_PROD that receives as input an array A with n > 0 integers and returns the product of ONLY the

(a) Design a divide-and-conquer algorithm DC_POSITIVE_PROD that receives as input an array A with n > 0 integers and returns the product of ONLY the POSITIVE 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_POSITIVE_PROD. (c) (5 points) Apply the Master Theorem to give a tight bound for T(n) (i.e., notation)

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