else $j$:$=m$

end

if $x=a_i$ then location :$=i$

else location :$=0$

Vbrace location is the subscript of term equal to $x,$ or $0$ if $x$ is not found $\backslash$rbrace

Suppose our list of increasing integers is shown in the table below

$1357891013$

Suppose we conduct the binary search algorithm on this list where we search for $10.$

$($a$)$ In the language of the algorithm above, enter the correct values for the following variables for this particular search:

$x=10n=,a_2=3a_4=7$

$($b$)$ After the first iteration of the while loop, what are the values of the following variables?

$i=,j=,m=4$

$($c$)$ Intuitively, after the first iteration of the while loop, we have cut down our search to a set S of roughly half of the original numbers on the list. Check the numbers that are in the set S after the first iteration of the while loop:

$S$ has the following elements:

A$.1$

B$.8$

$q,$ C$.7$

D$.13$

E$.10$

F$.5$

G$.3$

H$.9$

$($d$)$ After the second iteration of the while loop, some of the variables have altered values. Enter the values of the following variables after the second while loop iteration:

$i=,j=,m=$

$($e$)$ After the third iteration of the while loop, some of the variables have altered values. Enter the values of the following variables after the third while loop iteration:

$i=,j=,m=1$

$($f$)$ After the $3$rd iteration of the while loop, the while loop terminates and the variable 'location' is computed. Enter the value for this variable in this case: location $=$