Question

For practice, please help me find the order of growth for the solution of these three recurrences. Answer fast, please. Upvote depends on how quickly this is answered and if it is correct.

T(n) = 3TC) +nº,T(1) = 0 T(n) = 4T + nº, T(1) = 0 T(n) = 5T + nº,T(1) = 0

Answer 1

we the bol Ans: (1) Given, T(n ) = 3902) + n2 17()-0 Here are solving by using Mastere method, so for this companing given problem with, TO=01(%) + f(60) ar Here a=3 fm) = n2 b=2 in Putting all these values $() ==2(bogen => n?= 2 (n S8+€ logga= log23 Putting € = 0.42 70 , we get. = 1.58 2 Cml.5€ +0:42) 3262) This holds true, Now Check the second condition: f(0) 3 (2/2)? & cn? => 3 n² scn² ¿t? 11 be true If we C = 3/4 will choose n? will also we .n? +2) = (%) ) с 3/4 1 & nyl n2 스 3/4 3/4 ina So it follows and care of master theoriem, T() ) - 8 @ c f(n)) + TW) = 0(m2) Ans (1)

(3) T(1) - о т (9) Чт(,) + n? So by comparing with тео) - ат (%) - Хо) with an b" 2 2 - - 2. a> Ч fo) -2 Б. 2 Loaь" Yo3,Ч (04. 2 \o1.? Putting all the values in, Хо) с 9 ( Logga - Ф (2) which is true Therefore, T(0)= o (n (ч. Соат) case-II ) = 0 (* lojn ) 9 (2) Т( ) - 5т (6) +? T( )=0 By comparina т (0 ) = ат (%) + #6 ) , 7 ) a=5 *(9) = 2 Б. - п? qoas (3) 2.

loggare) 2.32-€ ) logia = logas = logs log2 2.32. putting all the values è f(0) = och => n²=0cn we choone t = 0.32 we gets n2=0 (92.32-0:32 = o(m2) Since this equation holds, the of master theorem applies to the given recurfrance melation, Thus, T (nla och To If ist cas logna ر 2.32 1 (6) = oln 32) Ans (3).