Question

Considering a lane to be one$-$dimensional, you are provided with an array police station conarning of $n$ distinct integers representing the coordinates of police stations.

You, as a prosperous individual, aspire to acquire exactly capacity distinct properties across the entirety of this one$-$dimensional lane $($which may be located anywhere on the number line$),$ with the condition that they do not coincide with the coordinates of any police station and neither any older property acquired.

The cost associated with purchasing a property is determined by its minimum distance from any police station. The total cost incurred will be the sum of costs associated with purchasing each property. Here distance between $1$ and $2$ means the absolute difference of $1$ and