Question: INTRODUCTION TO ALGORITHMS question T(n)=kT(kn)+ckn;T(1)=0. (a) Derive a closed-form formula for T(n) in terms of c,n, and k. In addition, determine the computational complexity of

INTRODUCTION TO ALGORITHMS question

INTRODUCTION TO ALGORITHMS question T(n)=kT(kn)+ckn;T(1)=0. (a) Derive a closed-form formula for T(n)

T(n)=kT(kn)+ckn;T(1)=0. (a) Derive a closed-form formula for T(n) in terms of c,n, and k. In addition, determine the computational complexity of this algorithm in a "Big-O" sense. (Hint: To have a well-defined recurrence, assume that n=km with the integer m=logkn and k ). (b) What value of k=2,3, or 4 results in the fastest processing? (Hint: Use the relation logkn=lnklnn where 'In' is the natural logarithm with the base e=2.71828..)

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