Assignment soln, Exercises of Discrete Mathematics

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Q1 do it your self. Q2 (II)

Q2 (III)

Q1 do it your self. Q2 ‘T(2) = 1 and T(n) = 27(yn) +1 Tn) = 27(Vn) +4 Let m = Ign => 2 T(n) = T2") = 27 (27) +1 Upper Bound: Defining new series (a) = 12) = sm) = 27(F) +1 $24 4b 4 28" m1 Eq A.5, Appendix A, CLRS ‘<< 2m = 0(m) = O(ign) Lower Bound: Defining new series T(n) = T2") = S(m) = 25) 41 S1t2+ hte +2iem gm 2 a - y 2 = (2m-1)-(2¥m -1) .—Eq AS, Appendix A,CLRS me — 20m 22lm-ymym ; (m>2 >m24—n216 =m= Align)