$5.(25$ points$)$ Closest pair problem on a single dimension. We have n points sprinkled on the $\backslash ($ x $\backslash )-$axis of our cartesian space $($i$.$e$.,\backslash ($ y $\backslash )-$ccordinates of all of the points are zero$).$ We want to find the distance between the closest of these two points, i$.$e$.$ the minimum distance between all point pairs on the x$-$axis. Devise a divide$-$and$-$conquer algorithm that finds the distance between the two closest points among n disfinct points spread on the $\backslash ($ x $\backslash )-$axis. The input to your algorithm is an array of values, representing the $\backslash ($ x $\backslash )-$coordinate values of the given points $($no need for $\backslash ($ y $\backslash )-$coordinates, since all are zero$),$ and your algorithm should return the minimum distance between any point pairs. Do a complexity analysis of your algorithm and indicate its time complexity. Support your analysis by proper arguments about the characteristics of the problem.

Algorithm closestPairOneDimension $($Pjp$.$nn$)//$Computes the minimum distance between the $//$closest pair of $\backslash ($ n $\backslash )$ points placed on the x$-$axis, $//$with the divide$-$and$-$conquer technique.

Ifloput: An array representing n poirts on $\backslash ($ x $\backslash )-$atis IOUtput: The distance between the closeat point par.