Question

3. Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using expansion/substitution and upper and/or lower bounds, when necessary. You may not use the Master Theorem as justification of your answer. Simplify and express your answer as O(n*) or O(nk log2 n) whenever possible. If the algorithm is exponential just give exponential lower bounds c) T(n) T(n-4) cn, T(0) c' d) T(n) 3T(n/3) c, T() c' e) T(n) T(n-1)T(n-4)clog2n, T(0) c'

Answer 1

Given Thut :- The asympto tfo complexfty o furtion dutinecl by TecuTYere relation. ustify your solution substituution adl upper and lor louer boundi when necessas Tn-4 cn, Tto) c (C) TU) TInT C-4)+cn unuT t cn-u)-l TCn-)TCn-12)+C Cn-8 )-) Puttng vatu ot 1)andl (1) in) TCD-)+ C(nn4tcn-) TCD) (n-4)tn-t-+o hT TOtl numbes oy Terms 4 (d) Tn)3T TU) TinS)- ITtt3 TL13) nei ntot Tre TA) TA) (1t 3+9t GP Sum n 3-1

TCTn-1)+ T(0_4)+C log (e) Tree method TCO) T(n-u) T-) day(n4onu) Logm - 2 T2) T(n-T(»s) T€n-4) C (S7Tor Hel gh eTree zn Jag01 Logn day Cittute+-)neter (1 dog) 6

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