Question

T(n)=2T(n/2)+n^2

can you please solve it using subsitution method?

which is

1-guess

2-induction goal

3-induction hypothesis

then proof it

Answer 1

TOn) : 2 I (0) ta using manters theorem 2 (D) 2 2T_m ( n) (2) + - २) AL Tf 2. 2- 2 (27 . + + २ n2-4222+4 २५ 2 । L for k time २९+ (क) if n m + २-7 m २ m = 2K - taking doga Lear: layer Sogn = kloge ( logmn=nlogmy ( 022 - KX)

Page togen IT T() = 0 Twt n? lon th 2 + 2 In 20² + n? 2 2 n +7 lughal 2 2 this is a decreasing ge so the value of a decreening of will be the first clenet. Titt = m2 - + 1 2 2 --- 놈 o 2 xZ 0 (n2 Tod=0CA) Файлды 0 (n2) ② Induction goal for value n=1 TQ) = 2 x I(22) + n2 =2TW 2? =4 T(nl=0Cn) 2. - n=2. it is true for induction step

Page : n=k thee for for h Date: 100 Induction hypotherie ter 3 ruppere it is true for TIK) = ock²) na K* L'HIS-T (2K2= 2 I (2K12.2+(2k)? 121(K) +2K) 200 (K2)fo (2 kg of(2 k)} OCK ) += R.His from the property of Bigo of the to be taken maa will Hease proved so this is also the for hypotheis gules then ou goed in three as o 090²) is true for every ges the value for substitution We