please derive the binary recurrence equation ie t(n) = t(n/2) + 1, t(1)=1 given that n...
please derive the binary recurrence equation ie
t(n) = t(n/2) + 1,
t(1)=1
given that n is not restricted to be power of two by considering
the case that n can either be an odd or even number.
Homework Answers
Here we have to solve the given recurrence relation ,
Using substitution method
1. Putting n = n /2 .
2. Finding Relation of T(n), for n = n/2.
3. Generalising T(n) for k steps.
4. After constantly dividing by 2 at last we will get 1.
So , equate 
5. As ,
, so T(
)
= T(1) , which is equal to 1.
6. At last substitute all values in generalised equation of T(n).
Final answer will be 
, i.e. big O of 
.
It is valid for all n greater than 1.
Please upvote.
Add Answer to:
please derive the binary recurrence equation ie
t(n) = t(n/2) + 1,
t(1)=1
given that n...
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