$[5\%]$ Which of the following statements is $($are$)$ correct?

$($A$)$ Searching a particular data item in a binary search tree with $n$ nodes requires at most $lo{g}_2(n+1)$

comparisons.

$($B$)$ A full binary tree of a given height $h$ has $2^h-1$ nodes. $($The root is at height of $1.)$

$($C$)$ Represent a binary tree in an one$-$dimensional array $($say$,$ a$[]).$ Assume the root is stored in a$[1].$ Then,

the index of node $i\text{'}$s parent is floor$($i$/2).$

$($D$)$AVL$,$ red$-$black tree and compressed trie are binary trees.