For the following Bubblesort algorithm, how many times would the inner for loop

iterate $($give the closed form$)?$ What is the worst$-$case running time of Bubblesort?

BUBBLESORT$($A$)$

$1$ for i $=1$ to A$.$length$-1$

$2$ for j $=$ A$.$length downto i$+1//$downto means decrease by $1$

$3$ if A$[$j$]<$ A$[$j$-1]$

$4$ exchange A$[$j$]$ with A$[$j$-1]$

$4.[2$ pts$]$ Suppose you have a sorted array $[1..].$ What are the number of comparisons to

search for the existence of an element $$ in the given array using binary search?