Question. (15 points) Given the following recurrence relations of some algorithms. Solve them using recursion tree method then estimate their time complexity.

Note: There will be one point for every correct answer. The remaining 8 points will be allocated to your work.

\begin{tabular}{|l|l|} \hline Algorithm's Recurrence Relation & T(n)=O(?) \\ \hlineT(n)=2T(2n)+1 & \\ \hlineT(n)=2T(2n)+C,C>0 & \\ \hlineT(n)=2T(2n)+n & \\ \hlineT(n)=2T(2n)+n2 & \\ \hlineT(n)=2T(2n)+n3 & \\ \hlineT(n)=2T(2n)+nlgn & \\ \hlineT(n)=T(3n)+T(2n/3)+n & \\ \hline \end{tabular}