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Problem 1 Using iteration, obtain a tight asymptotic bound for T(n) given by the following recurrence. You may assume that n is a power of 3. T(n) = { ( ) Problem 2 a). Show how to compute ac, ad+bc and bd using three multiplications, given reals a, b, c and d. Note that since (ax+b)(cx+d) =abx2 +(ad+bc)x+bd, this result allows us to multiply two degreeone polynomials using three real multiplications). b). Develop a divide-and-conquer algorithm for multiplying two degree-n polynomials A(x)=anx n +….+a1x+a0 and B(x)=bnx n +…+b1x+b0 in O( ) time, and prove the bound of the running time by writing and analyzing a recurrence relation. You may assume that n is a power of 2. Your algorithm takes as input coefficients an,…,a0, bn,….,b0 and outputs the coefficients c2n,…c1,c0 of the polynomial C(x)=A(x)*B(x). Note that is trivial to do this in O(n2 ) time.

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