Problem 8: Divide and Conquer Recurrences Consider the recurrence that naturally arises in some divide-and-conquer algorithms:   T(1) = 1,   T(n) = 4T(n/2) + n for n > 1    [a] Explain what the initial condition and the various parts of this recurrence mean in the context of the analysis of algorithms. [b] Use the Master Theorem to determine the order of magnitude of T(n). [c] Using the methods of our course, derive a closed-form formula for T(n). [d] For the case n = 2, test your formula for T(n) against the original recurrence.

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Q: f. T(n) = 2T (n/4) + √n.

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A: Below is the answer with explanation:

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Q: g. T(n) = T(n − 2) + n².

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Q: code

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A: A1.  T(n) = 2T (n/4) + 3T(n) = 2T (n/4) + 3T(n) = 2 (2T (n/16) + 3) + 3T(n) = 4T (n/16) + 6 + 3T(n)…

Q: Algorithm

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