Computing the minimum distance between each pain of points

Question

I am trying to read an algorithm for computing minimum distance between each pair of points from the book: Algorithm Design

Algorithm Design

It considers the points in a line. If the points are in a line why we need to sort them? We can start from the beginning and compute the distances from starting pint to all the points on the right.

Some body please guide me why we need sorting?

Answer 1

Suppose the points are $[4,1,10,11]$. The distance from the starting point (whether you interpret that as $4$ or $1$) to each other point does not give you the nearest pair of points.

In this problem, the input is an array containing numbers, not in sorted order.