Given the following Java function, answer the following questions.

public static int binarySearch$($int$[]$ array, int searchKey$)\{$

int lowerBound $=0,$ upperBound $=$ array.length $-1$;

while $($true$)\{$

int middle $=($lowerBound $+$ upperBound$)/2$;

if $($array$[$middle$]==$ searchKey$)$

return middle;

else if $($searchKey $>$ array$[$middle$])$

lowerBound $=$ middle $+1$;

else

upperBound $=$ middle $-1$;

$\}$

$\}$

$1)$ Suppose we are calling the above function below, write down the values of lowerBound and

upperBound during each while loop. At last, describe the returned result.

int$[]$ array $=\{1,3,5,8,10,11\}$;

System.out.println$($binarySearch$($array$,7))$;

$2)$ Suppose the parameter array contains random elements in increasing order and array does not

contain searchKey, we call the above method. After a certain amount of time, both lowerBound

and upperBound will point to the same index, suppose its value is x$.$ We have two scenarios here:

array$[$x$]>$ searchKey and array$[$x$]<$ searchKey. Find out the values of lowerBound

and upperBound during the next three loops for each scenario.