Design an algorithm and derive runtime $(25$ points$)$

Design an algorithm that receives an array of $2$D points $A=[(x_0,y_0),(x_1,y_1),$cdots$(x_{n-1},y_{n-1})]$

as input. The algorithm should return a pair of indices $(i,j)$ such that the slope of the line

passing through $A[i]$ and $A[j]$ is greater than or equal to that of the line passing through any

other two points in the input array. A vertical line should be considered to have a slope of

$+.$

Write your algorithm in clear pseudocode. $($Do not submit Java$/$C code.$)$ Express the runtime

as a function of $n.$ Give the big$-$O worst$-$case runtime of the function. State the big$-$O best$-$

case runtime of the algorithm.