We are given an array A of n distinct positive numbers in sorted $($ascending$)$ order. $($Assume n is a power of $2.)$ The minimum distance in such an array is defined as the distance between a closest pair of numbers stored in the array.

Consider the following algorithm to find the minimum distance in such an array.

Split the array into two equal halves, find minimum distances in each, and then take the minimum of the two.

Will this work correctly? Fix it if not.