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Solve the following recurrence (you may use any of the methods we studied in class). Make your baunds as small as possible (in the big- 0 big- notation). Note T(n)=1 for n=1. T(n)=2(2n)+mogn Correct Answer: (n)=2(2)+nogn=22(22n)+rlog2n+rlogn=23(23n)+nlog22n+nlog2n+nlogn=24(24n)+nlog23n+nlog22n+nlog2n+nlogn=2(2in)+nlog2i1n++nlog22n+nlog2n+nlogn==2k(2kn)+nlog2k1n++nlog22n+nog2n+nlogn=k=lognn(1)+nlog2k1n++nlog22n+nlog2n+nlogn=n+nog2k1n++nlog22n+nog2n+nlogn=n+n(lognlog2k1)+n(lognlog2k2)++n(lognlog22)+n(lognlog21)+n(lognlog20)=n+n(logn(k1))+n(logn(k2))++n(logn2)+n(logn1)+n(logn0)=n+nklogni=0k1=n+nlog2n2k(0+k1)=n+nlog2n2log2n1=O(nlog2n) Question 2 20cot of 20 paicis Solve the following recurrence (you may use any of the methods we studied in class) Make your hounds as small as possible (in the big- O or big- notation) Nate T(n)1 for n1 (n)=3(3n)+sekctedanswer:[WoneGivendCarectinene7RuplyWuwartheerom1andset