Java Algorithms:

a$)$ Draw a recursion tree for the recurrence T$($n$)=2*$T$($n$/3)+\backslash$Theta $($n$).$

Draw at least the top three levels of the recursion tree. Write$/$label all of the following:

Nonrecursive work done by each invocation.

Problem size at each invocation.

Number of subproblems on each level you drew.

Total work done on each level.

Height of the recursion tree.

b$)$

Solve the recurrence given in part a$,$ by writing it in closed form.

Hint: Consult your recursion tree from part a$.$ Show your algebra and show your work.