Suppose we are given a sorted array

$$

$[$

$1...$

$$

$]$

A$[1...$n$],$ and we wish to determine where in

$$

A the element

$$

x belongs$$that is$,$ the index

$$

i such that

$$

$[$

$$

$$

$1$

$]$

$<$

$$

$<=$

$$

$[$

$$

$]$

A$[$i$1]$