- Expand the relation so that summation dependent on n is obtained
- Bound the summation
Let there is k iteration. So, for the first iteration, k=1. K=2 represents second iteration and goes on.
Let’s find what is T(n/2)
For this, put it in original function T(n)
i.e Replace n with n/2.
Now the further step gives,
For second iteration, i.e k=2
Now, we need to find what is T(n/4)
Replace n with n/4 in T(n)
For third iteration, i.e when k=3
Again, we need to find T(n/8)
Replace n with n/8
It gives T(n/8)=2T(n/8)/2+1
For forth itera++tion, i.e when k=4
Which can be generalised as
T(n) = 2^k * T(n/ (2^k) )+ 2 *(2^k — 1)
T(n) = 2^k * T(n/ (2^k) )+ 2^(k+1) — 2
2^k*T(n/(2^k)+Summation from i=0 to k-1 [2i]
To be continued.. check note
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