CS 600 Example When Master Theorem Fails




Find T(n)   if tex2html_wrap_inline115 .

Solution:

This does not fall into any of the three cases of Master Theorem. We can use the iteration method to find T in this case.

tex2html_wrap_inline117

tex2html_wrap_inline119

tex2html_wrap_inline121

tex2html_wrap_inline123

tex2html_wrap_inline125

tex2html_wrap_inline127

tex2html_wrap_inline129

tex2html_wrap_inline131

tex2html_wrap_inline133

tex2html_wrap_inline135

Since tex2html_wrap_inline137 if tex2html_wrap_inline139 ,

tex2html_wrap_inline141

Since tex2html_wrap_inline143 , and tex2html_wrap_inline145 ,

tex2html_wrap_inline147 ,
where c is a constant.

Hence tex2html_wrap_inline151