Think about perfect $($completely full$)$ M$-$ary trees. Assume each leaf node is full as well.

$23.$ What is the total number of keys in the tree when the total number of levels is $5?$

a$)M=2$

b$)M=10$

$24.$ In order to look for a particular key in a perfect $M-$ary tree having $N$ elements$($keys$),$ which makes it faster? Having a smaller M$,$ or larger M$?$ Why?

$25.$ Think about the worst case scenario where your key is found at the bottom of the tree. Calculate the total number of comparisons in a perfect tri$-$ary tree $($Each leaf node is full as well$)$ using your own algorithm given in #$22$ above. Express your answer as $T(K)=???$ where $K$ is the total number of keys.

$26.$ What is the worst$-$case big$-$O for searching in a perfect tri$-$ary tree? Explain.

$27.$ What is the best case big$-$O for searching in a perfect tri$-$ary tree? Explain.

$28.$ What is the average big$-$O for searching in a perfect tri$-$ary tree? Explain.