n a "perfect" SkipList, elements at odd$-$numbered positions $($within the current level$)$ get promoted to the next level. For example, elements of L$0$ with indices $1,3,5,7,9,11,...$ will appear in L$1.$ Half of them, $-$ elements with indices $3,7,11,15,19,...$ will appear in L$2.$ Elements with indices $7,15,23,...,$ will appear in L$3$ and so on$.$

Which of the following facts, which are all true about the "perfect" SkipList, are still true about the original $($randomized$)$ SkipList?

This is a multi$-$select question. Points are evenly distributed across all answers. Learners earn partial points for each answer correctly selected and left blank. Learners lose points for answers incorrectly selected or left blank. Learners cannot receive less than $0$ points.$$

Question $13$ options:

Assuming that the number of elements, n$,$ is the power of $2,$ every level has exactly half the nodes of the level below.

The runtime of get$($i$),$ set$($i$,$x$),$ and find$($x$)$ is O$($length of search path to index i $($or element x$)).$

The amount of space required by the SkipList is: $($space required for the dummy node$)+|$L$0|+|$L$1|+...+|$Lh$|,$ where h is the height of the SkipList.

Every node will have height $$ O$($log n$),$ where the height of a node is the number of lists Lr that contain that node $($or$,$ equivalently, the length of its next array$)$

$|$Lr$|$ ~ $1/2|$Lr$-1|($in expectation$)$ for all r$.$