00:01
Hello, let's have a look on this question.
00:02
So we have equation pn is equal to a, t n by b plus f of n, where f of n belongs to theta n to the power d.
00:19
Now master theorem states that tn belongs to theta n d if a.
00:35
Is less than bd.
00:38
So from here, tn belongs to theta n to the power d, log of n if a equals to b to the power d.
00:50
So we can write t n belongs to theta n log b to the power a if a is greater than b to the power d.
01:01
So from above theorem, for the a part we have, tn is equal to 2t, n by 4 plus 1.
01:22
In this, recurrence, a equals to t, d equals to 4, d equals to 0, a of 2 is greater than b to the power d into 1.
01:37
Therefore t n belongs to theta n to the power log 4 2 which is equal to theta n to the power 1 by 2 now for the b part for the b part we have t n is equal to 2p n by 4 plus n 1 by 2 in this a is equal to 2 b is equal to 4 and b is is equal to 1 by 2.
02:13
So from here we can say that a2 is equal to d d to the power d 2.
02:22
Therefore, tn belongs to theta n 1 upon 2 log n...