Problem. Design an $(nlogn)$ time algorithm $($assuming any of the usual arithmetic operations on real numbers can be done in constant time$)$ that takes an unordered set $L$ of $n$ lines expressed as a sequence of pairs $(\{$:$a_i,b_i)$ of real numbers which each represent a line $y=a_i*x+b_i$ and outputs the sequence $V$ defining the scene. You may assume you have access to a function intersect $(l_1,l_2)$ which takes as input $2$ lines $l_1$ and $l_2$ and returns the x$-$coordinate of their intersection, and a function $y(l,x)$ which computes the $y-$value of a given line $l$ at the point $x.($a$)$ Give pseudocode $($and$/$or English$)$ to describe a divide$-$and$-$conquer algorithm for this problem. $($b$)$ Prove that your algorithm runs in $(nlogn)$ time.