rocedure function $($x: integer, a$1,$ a$2,...,$ an: increasing integers$)$

i :$=1\{$i is left endpoint of search interval$\}$

j :$=$ n $\{$j is right endpoint of search interval$\}$

while i $<$ j

m :$=|\_($i $+$ j$)/2\_|$

if x $>$ am then i :$=$ m $+1$

else j :$=$ m

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

else location :$=0$

return location$\{$location is the subscript i of the term ai equal to x$,$ or $0$ if x is not found$\}$

What is the worst$-$case scenario time complexity of this algorithm?

Group of answer choices

O$(1)$

O$($n$2)$

O$($n$)$

O$($logn$)$