Suppose you have an algorithm A$($G$,$k$)$

that solves the decision version of the independent set problem for input graph G$=($V$,$E$)$

and positive integer k

in time O$($f$($n$))$

$,$ where n

denotes the number of vertices in the input graph instance.

Give an algorithm $($using pseudocode$)$ that solves the optimization of the independent set problem in time O$($f$($n$)\backslash$times log$2$n$)$

$.$ Ensure you justify why your algorithm has the stated running time. Your algorithm only needs to return the size of a largest independent set $($that is$,$ it doesn't need to return an independent set of largest size$).$