$10$ points Let $R$ be a set of rectangles in the $2-$D plane represented as a pair of points,

$((x,y),(x^{\text{'}},y^{\text{'}}))$ where $(x,y)$ is the lower left point of the rectangle and $(x^{\text{'}},y^{\text{'}})$ is the upper

right point of the rectangle. Design and analyze an algorithm that given a set $R$ of $n$

rectangles finds the pair of rectangles whose intersection has the greatest area.

$1$

$.$

$$Complete pseudocode

$2$

$.$

$$Identify the input and input size, n

$3$

$.$

$$Identify the elementary operation

$4$

$.$

$$Compute how many times the elementary operation is executed with respect to input size

$5$

$.$

$$Provide a Big

$-$

O asymptotic characterization for the algorithm's complexity